Magali Cariou

Edith Galy

Claudine Mélan
email: cmelan@univ-tlse2.fr

Differential 24-h variations of alertness and subjective tension in process controllers: investigation of a relationship with body temperature and heart rate

Keywords: shift-work, time on shift, alertness, subjective tension, heart rate, body temperature

published or not. The documents may come     Differential 24-h variations of alertness and subjective tension in process controllers: investigation of a relationship with body temperature and heart rate

INTRODUCTION

Several authors have suggested that there are two distinct forms of arousal, labelled tense and energetic. Energetic arousal (or alertness) is a continuum ranging from tired to energetic which describes the subject's alertness state. Tense arousal (or mood) is on a continuum ranging from calmness to anxiety, which describes a variety of emotions (i.e. anxiety) and stress reactions in response to external stressors [START_REF] Dickman | Dimensions of arousal: wakefulness and vigor[END_REF]Koscec & Radosevic-Vidacek, 2004;[START_REF] Matthews | Refining the measurement of mood: the UWIST Mood Adjective Checklist[END_REF][START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF]. While time-of-day effects have been intensively studied for alertness, there have been few investigations of mood, and in particular negative mood in a chronobiological context, despite obvious consequences on performance, and hence work safety and security.

Field studies of alertness indicate a similar trend for this dimension in shift-work conditions and in controlled laboratory conditions, with a maximum of alertness on the late afternoon [START_REF] Folkard | Shift work, safety and productivity[END_REF][START_REF] Kecklund | Morning work: effects of early rising on sleep and alertness[END_REF][START_REF] Knauth | Design of shiftwork systems[END_REF][START_REF] Rosa | Extended workshifts and excessive fatigue[END_REF][START_REF] Tucker | Shift length as a determinant of retrospective on-shift alertness[END_REF]. A close relationship has been reported between self-reported alertness and core body temperature, a measure that has been directly linked to metabolism [START_REF] Colquhoun | Experimental studies of shift-work I: A comparison of 'rotating' and 'stabilized' 4-hour shift systems[END_REF][START_REF] Edwards | The effects of circadian rhythmicity and time-awake on a simple motor task[END_REF]Koscec & Radosevic-Vidacek, 2004;[START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF][START_REF] Wright | Relationship between alertness, performance, and body temperature in humans[END_REF]. These findings are generally interpreted as indicating a strong dependency of alertness on endogenous mechanisms that underlie circadian rhythms, i.e. a circadian system inducing a nocturnal trough of most physiological and psychological variables and a homeostatic system reflecting the fatigue accumulated across waking hours (Borbély, 1982;McCarley & Massaquoi, 1986;[START_REF] Achermann | Simulation of daytime vigilance by additive interaction of homeostatic and a circadian process[END_REF]Folkard & Ackerstedt, 1992). In performing shift work many individuals experience chronic sleep deprivation and increased fatigue, that aggravate the nocturnal decline in alertness and performance [START_REF] Akerstedt | Sleepiness at work: effect of irregular work hours[END_REF][START_REF] Akerstedt | Altered sleep/wake patterns and mental performance[END_REF]Dinges et al., 1996;[START_REF] Glazner | Shiftwork: its effect on workers[END_REF][START_REF] Knauth | Design of shiftwork systems[END_REF][START_REF] Lammers Van Der Holst | Are individuals' nighttime sleep characteristics prior to shift-work exposure predictive for parameters of daytime sleep after commencing shift work?[END_REF][START_REF] Van Dongen | Shift work and inter-individual differences in sleep and sleepiness[END_REF] and increase accident risk [START_REF] Costa | Influence of flexibility and variability of working hours on health and well-being[END_REF][START_REF] Folkard | Shift work, safety and productivity[END_REF][START_REF] Folkard | Estimating the circadian rhythm in the risk of occupational injuries and accidents[END_REF][START_REF] Tucker | The Impact of Rest Breaks on Temporal Trends in Injury Risk[END_REF]. In addition, peak-time alertness depends to some extent on shift-scheduling features, such as the number of successive night-shifts [START_REF] Folkard | Shift work, safety and productivity[END_REF], shift-duration [START_REF] Knauth | Design of shiftwork systems[END_REF][START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF], and night-to-morning shift hand-over time [START_REF] Tucker | Shift length as a determinant of retrospective on-shift alertness[END_REF].

Despite chronic fatigue and differences between shift-scheduling systems, the general shape of the alertness curve remains day-oriented, at least in shift-workers working rapid rotating shift systems.

Around-the-clock variations of perceived tension or other negative mood measures were less extensively studied, and the situation appears to be less clear. Subjective tension was shown to vary with time of day in some laboratory studies [START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF]Koscec & Radosevic-Vidacek, 2004), but not in others [START_REF] Monk | Diurnal variation in mood and performance in a time isolated environment[END_REF][START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF]. Likewise, air traffic controllers' tension ratings have been found to be comparable on night-and day-work [START_REF] Luna | A study of USAF air traffic controller shiftwork: sleep, fatigue, activity, and mood analyses[END_REF], or displaying a typical circadian trend [START_REF] Galy | Alertness and tension in air traffic controllers: Investigation of time of day, time on duty and workload[END_REF][START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF]. Inconsistency amongst the findings has been attributed to a marked sensitivity of mood measures to a number of external influences, including sleep timing and duration, task demands, meal times (Folkard, 1990;[START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF], and shift-work conditions. More specifically, negative mood variations across the 24-h day have been found in shift-workers but not in non shift-workers [START_REF] Prizmic | Shiftwork tolerance and 24-h variations in moods[END_REF]. In addition, early compared to late morning-shift start was associated with higher apprehension stress [START_REF] Kecklund | Morning work: effects of early rising on sleep and alertness[END_REF]. We recently reported higher self-rated tension in air traffic controllers who were on duty for six hours or more rather than for four hours or less [START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF].

Taken together, the literature data raise the possibility that negative mood shows a lesser dependence on the endogenous mechanisms underlying circadian variations than other psychological measures, in particular alertness. [START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF][START_REF] Thayer | The biopsychology of mood and arousal[END_REF] proposed that in every-day life subjective tension would display a circadian trend, while in tension-inducing conditions external influences would mask the circadian trend. Such a masking effect has been explained by fragmented sleep and a de-stimulating environment in controlled laboratory conditions [START_REF] Eriksen | Sleepiness and sleep in a simulated "six hours on/six hours off" sea watch system[END_REF]Koscec & Radosevic-Vidacek, 2004) and by time on duty and task-related factors, in particular traffic intensity in real air traffic control conditions [START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF]. Real-job performance variations over the 24-h day have also been reported to be critically influenced by task-specific factors, as indicated by a masking affect on the nocturnal performance drop by workload, incentives, and motivation (Andorre-Gruet & Queinnec, 1998;[START_REF] Blake | Temperament and time of day[END_REF][START_REF] Horne | High incentive effects on vigilance performance during 72h of total sleep deprivation[END_REF]. Likewise, in real and simulated air traffic conditions, unexpected events and traffic intensity increases enhance controllers' subjective workload and heart rate, without affecting control operations [START_REF] Rose | Endocrine activity in air traffic controllers at work. II. Biological, psychological and work correlates[END_REF][START_REF] Brookings | Psychophysiological responses to changes in workload during simulated air traffic control[END_REF][START_REF] Averty | Mental workload in air traffic control: an index constructed from field tests[END_REF].

The aim of this study was to test the hypothesis of a differential sensitivity of alertness and tension to endogenous versus exogenous influences in satellite controllers, and to compare the 24-h variations of psychological measures with those of two particular physiological measures, body temperature and heart rate. Contrary to what is known about body temperature and alertness, little is known about heart rate and tension variations in shift-work conditions, though there is some evidence of a similar response profile for heart rate and tension. On the one hand, heart rate indicates circadian variations in controlled laboratory conditions (Wojtczak-Jaroszowa & Banaszkievicz, 1974;[START_REF] Furlan | Continuous 24-hour assessment of the neural regulation of systemic arterial pressure and RR variabilities in ambulant subjects[END_REF]; for a review, [START_REF] Guo | Circadian rhythm in the cardiovascular system: chronocardiology[END_REF], even in the absence of physical activity [START_REF] Yamasaki | Diurnal heart rate variability in healthy subjects: effects of aging and sex difference[END_REF], and in total sleep deprivation conditions [START_REF] Miro | Effects of total sleep deprivation on cardiovascular parameters: An absence of biologically significant findings?[END_REF]. On the other hand, a heart rate activation effect was reported for various exogenous factors, including general work conditions such as external temperature or shift-work [START_REF] Khaleque | Circadian rhythms in heart rate of shift and day workers[END_REF][START_REF] Van Eekelen | Circadian variation in cardiac autonomic activity: reactivity measurements to different types of stressors[END_REF], and task-specific factors like workload [START_REF] Averty | Mental workload in air traffic control: an index constructed from field tests[END_REF][START_REF] Brookings | Psychophysiological responses to changes in workload during simulated air traffic control[END_REF][START_REF] Rose | Endocrine activity in air traffic controllers at work. II. Biological, psychological and work correlates[END_REF] and cognitive load [START_REF] Backs | Metabolic and cardio-respiratory of mental effort: the effects of level of difficulty in a working memory task[END_REF][START_REF] Carroll | Heart rate and oxygen consumption during active psychological challenge: the effects of level of difficulty[END_REF][START_REF] Fairclough | A metabolic measure of mental effort[END_REF]. Subjective tension ratings have also been proposed to be sensitive to external factors, at least in tension-inducing conditions [START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF][START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF][START_REF] Thayer | The biopsychology of mood and arousal[END_REF]Koscec & Radosevic-Vidacek, 2004). Such conditions may be encountered during satellite control, given for instance the high workload involved in shift-commencement during continuous supervision of a dynamic process [START_REF] Hoc | Diagnosis: some theoretical questions raised by applied research[END_REF], and the ecologic and economic consequences of a maintenance error. In light of these considerations, heart rate was seen as an objective marker of perceived tension in the present study. Likewise, body temperature, the most common indicator of circadian variation in physiological activation, was considered as an objective measure of operators' alertness state.

On three occasions during each shift, i.e. one hour following shift-start, in the middle of the shift and one hour before shift-end, the operators completed [START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF] check-list and measured their oral temperature, while heart rate was recorded continuously throughout shifts.

The repeated-measures design enabled a two-factor analysis of the effects of shift and recordingtime on shift to be conducted. As operators worked a rapid forward rotating 3-shift system, we expected to find a typical circadian trend for body temperature and for alertness (Folkard, 1990;[START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF][START_REF] Folkard | Shift work, safety and productivity[END_REF][START_REF] Wright | Relationship between alertness, performance, and body temperature in humans[END_REF], evidenced by an interaction between the two factors under investigation. Furthermore, if heart rate and tension were indeed sensitive to the same, ill-defined, external factors in this job-situation, rather than to circadian influences, we should observe an effect of recording-time on shift for both measures. In addition, a positive relationship was expected between oral temperature and alertness scores on one the hand, and between heart rate and tension scores on the other.

SUBJECTS AND METHODS

Subjects

The study was carried out with 14 volunteer satellite controllers (11 males and 3 females), living in the south-west of France, aged 36.7 years (range 23 to 59 years) and with an average of 3.75 years seniority in the control centre (range 2 to 12 years). Their job entails the supervision of an automated continuous process which maintains a satellite in its orbit and to check whether information is correctly transmitted. The 10-day work cycle starts with 2 mornings, followed by 2 afternoons, 1 day off, 2 nights, and terminates following 3 days off. Work is scheduled according to a continuous 3-shift system, with shifts lasting 8+/-1h and starting at 07:00, 14:00 and 22:00 respectively.

Prior to the study they were also asked to complete Horne and Östberg's (1977) questionnaire. The results indicated that no participant displayed extreme morningness or eveningness. The study protocol and data analysis respected the identity and privacy of the workers [START_REF] Touitou | Ethics, standards and procedures in human and animal research in chronobiology[END_REF].

Material and Methods

Subjective and physiological measures (except for heart rate) were recorded on three occasions on each shift, respectively one hour after shift-start, in the middle of the shift, and one hour before shift-end at the following times: 08:00, 10:30, and 13:00 of the first morning-shift; on 15:00, 18:00 and 21:00 of the first afternoon-shift, and on 22:00, 02:30, and 6:00 of the first night-shift.

Subjective measures: On each of the 9 recording times participants completed the French paper-and-pencil version of Thayer's activation-deactivation adjective checklist [START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF], by quoting, for each of 20 listed adjectives, one of the following responses "not at all", "don't know", "little", "much". The responses have an assigned weight respectively of 1, 2, 3 and 4.

However, two adjectives have a negative weight assigned to them. The responses are compiled into four factors, general activation (GA), deactivation sleep (DS), high activation (HA), and general deactivation (GD). Subject's energetic alertness was assessed by the ratio GA/DS, reported to be a reliable index of alertness in shift-work conditions [START_REF] Galy | Alertness and tension in air traffic controllers: Investigation of time of day, time on duty and workload[END_REF][START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF] and their negative mood scores by HA, a factor "associated with subjective tension" (Thayer, 1978, p.5).

Physiological measures: On each of the 9 recording times oral temperature was measured sublingually, for 2 minutes, by means of an electronic thermometer (Viosiomed ThermoFluoKF-201). During measurement, subjects sat comfortably in an armchair. They were instructed not to consume food or beverages during the 15 minutes prior to each measurement to preserve normal mouth temperature. Heart rate (HR) was recorded continuously throughout each shift with an ambulatory heart rate monitor (Polar S610i), comprised of a transmitter worn around the chest and a receiver worn on the non-dominant wrist. The receiver stores the HR values before transferring them by infrared communication to a computer where they are subsequently analyzed using the Polar precision software.

Statistics

The subjective and physiological variables were analysed using 2-way ANOVAs testing for the effects of recording-time on shift (with repeated measures: 1 h following shift-start, middle of the shift, 1 h before shift-end), and shift (morning-shift, afternoon-shift, night-shift).

Post hoc analyses were conducted using Scheffe's test. To enable a similar 2-way ANOVA for heart rate, recorded continuously, we computed, for each subject, the median number of heart beats per minute recorded during 15 min prior to and following each of the three recording times on each shift (i.e. 1 h following shift-start, in the middle of the shift, 1 h prior shift-end).

Pearson's correlation was used to test whether any two measures were correlated with one another. Correlations were computed within participants (n=9 for each person separately), by using the 9 time-of-day values of two measures. The 14 r values were tested against the null hypothesis by using a 1-sample t test.

RESULTS

Figure 1 represents the mean data relating to on-shift alertness with a maximum at 15:00 and a minimum during early morning hours. A 2-way ANOVA with repeated measures revealed significant effects for shift (F(2,117) = 35.86, p < 10 -4 ), recording on shift (F(2,117) = 3.54, p < .04), and a significant interaction between these factors (F(4,117) = 4.33, p < .003). Post-hoc analysis revealed that operators rated alertness at a lower level on the last two recordings of the night-shift compared to all other recordings (in each case, p < .01), except for the first recording on the night-shift.

[Insert Figure 1 about here] Inspection of Figure 2, representing operators' mean subjective tension on the same 9 recordings across the 24-h day, shows higher values for the first recording compared to the remaining recordings on each shift. A 2-way ANOVA revealed a significant main effect of recording on shift (F(2,117) = 5.85, p< .01), but no significant effect of shift or interaction between the two factors. Post-hoc tests confirmed the impression gained from the figure, as tense arousal was significantly enhanced on the first recording compared to the second (p < .01), and the third recording (p < .05) on the shift. It is noteworthy that 7 out of the 14 subjects quoted the same responses throughout recordings for this measure.

[Insert Figure 2 about here] Mean sublingual temperature measures obtained on each of the nine recordings (Figure 1) resulted in a classic diurnal trend, with a maximum between 15:00 and 21:00, followed by a sharp decrease on early morning hours with a minimum at 06:00. Statistical analysis revealed, similar to alertness, a significant effect of shift (F(2, 117) = 13.139, p < .001), phase of shift (F(2,117) = 4.956, p < .01), and a significant interaction between the two factors (F(4,117) = 18.172, p < .001). Post-hoc tests indicated a lower oral temperature on the last recording of the night-shift compared to the recordings performed on the morning-and afternoon-shift (p <.001).

[Insert Figure 3 and Table 1 about here] Figure 3, representing subjects' median heart rate per 5-min period, indicates overall higher heart rate values on shift-start than on the remaining time of the shift. On the morning and afternoon shifts, the operators' median heart rate decreased earlier and more rapidly than on the night-shift. A 2-way ANOVA of the median data collected around each of the 9 recording times (see statistics in the METHOD section; Table 1), revealed a significant effect of recording time on shift (F(2,117) = 16.72, p < .001), and an interaction of this factor and shift (F(4,117) = 3.96, p < .001). The significant main effect resulted from a higher median heart rate on the first recording than on the second and third recordings for the shift (in each case, p < .001). The interaction resulted from lower heart rates when ending the night-shift (06:00), rather than starting either shift (08:00, p < .05; 15:00, p< .001; 23:00, p<.01), or ending the morning-shift (13:00, p < .05).

A similar decrease was observed in the middle of the night-shift (02:00) compared to starting the afternoon-(p < .01), and night-shift (p < .05).

Furthermore, intra-subject correlation scores differed significantly from the null hypothesis for alertness/temperature data (t(13) = 13.03, p < .0001), alertness/heart rate (t(12) = 4.47, p < .001) and temperature/heart rate (t(12) = 7.62, p < .0001). No similar relationship was found between tension and any other measure.

DISCUSSION

As expected, satellite controllers displayed a circadian trend for alertness and oral temperature. In contrast, the trend observed for heart rate, and more especially for tension differed from a typical circadian trend.

In agreement with the literature, reliable circadian trends were observed for alertness and oral temperature (Colquhoun, 1977;[START_REF] Galy | Alertness and tension in air traffic controllers: Investigation of time of day, time on duty and workload[END_REF]Koscec & Radosevic-Vidacek, 2004;[START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF], despite lack of control over a number of factors known to affect in particular psychological measures in controlled laboratory conditions, including light exposure, noise and motivation (Smith et al., 2002;[START_REF] Wright | Relationship between alertness, performance, and body temperature in humans[END_REF]. Data were recorded on three occasions on each 8-hour shift (1 h following beginning, in the middle and 1 h prior ending a shift), enabling a 2-factor analysis of shift and recording time on shift to be used. Alertness and oral temperature peaked at 15:00, and alertness decreased thereafter to reach its minimum on 02:30, while the oral temperature peak persisted until 21:00, before sharply decreasing until 06:00. Significant interactions indicated that the nocturnal drop was significant both at 02:00 and 06:00 for operators' alertness, and only at 06:00 for their temperature. Thus, alertness decreased earlier in the afternoon and reached its nocturnal trough earlier than oral temperature, thereby extending to a real-job situation the finding of a moderate phase advance of this subjective state variable compared to the objective temperature measure [START_REF] Edwards | The effects of circadian rhythmicity and time-awake on a simple motor task[END_REF]Koscec & Radosevic-Vidacek, 2004;[START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF]. Though data collected in real-job situations are the result of a complex interaction between the combined actions of the circadian and homeostatic sleep-wake regulation systems and situational factors, and most prominently shift-work itself [START_REF] Akerstedt | Sleepiness at work: effect of irregular work hours[END_REF][START_REF] Akerstedt | Altered sleep/wake patterns and mental performance[END_REF][START_REF] Costa | Influence of flexibility and variability of working hours on health and well-being[END_REF]Dinges et al., 1996;[START_REF] Folkard | Shift work, safety and productivity[END_REF][START_REF] Glazner | Shiftwork: its effect on workers[END_REF][START_REF] Knauth | Design of shiftwork systems[END_REF], the present findings fit with the concept of a homeostatic effect upon alertness [START_REF] Lammers Van Der Holst | Are individuals' nighttime sleep characteristics prior to shift-work exposure predictive for parameters of daytime sleep after commencing shift work?[END_REF][START_REF] Van Dongen | Shift work and inter-individual differences in sleep and sleepiness[END_REF]. Furthermore, controllers' alertness scores displayed a highly significant correlation with their oral temperature trend that has been closely linked to individuals' metabolism [START_REF] Colquhoun | Experimental studies of shift-work I: A comparison of 'rotating' and 'stabilized' 4-hour shift systems[END_REF]Koscec & Radosevic-Vidacek, 2004;[START_REF] Owens | Diurnal variations in the mood and performance of highly practiced young women living under strictly controlled conditions[END_REF][START_REF] Wright | Relationship between alertness, performance, and body temperature in humans[END_REF]. This result indicates that subjective rating tools may provide a reliable indication about participants' functional state in real-job conditions. Similar to variations of alertness and oral temperature, heart rate variations resulted from the combined effects of shift and recording-time on shift, with the lowest values observed at the middle and end of the night-shift. In addition, intra-subject comparisons revealed a positive relationship for operators' heart rate and both oral temperature and alertness, indicating that the circadian trend persisted for this measure. This result may be explained by the marked sensitivity of the heart rate rhythm to environmental cues (i.e., zeitgebers), in agreement with other shift-work studies [START_REF] Khaleque | Circadian rhythms in heart rate of shift and day workers[END_REF], and the finding of circadian oscillations of heart rate during sixty hours of sleep deprivation [START_REF] Miro | Effects of total sleep deprivation on cardiovascular parameters: An absence of biologically significant findings?[END_REF]. On the other hand, the nocturnal heart rate values differed only from those recorded at the start of either shift, whereas for alertness and oral temperature the nocturnal values differed from all six morning-and afternoon-recordings. Thus, operators' heart rate trend differed from a typical circadian trend in that it was increased one hour following each shift-start.

Operators' self-rated tension was also systematically enhanced on the first recording compared to the two remaining recordings of each shift, but contrary to the heart rate recordings, this effect was independent of the shift worked. Several studies have indicated that the circadian variations of negative mood measures may be masked by external factors, including shift-work, time on duty, work-load, sleep fragmentation (Koscec & Radosevic-Vidacek, 2004;[START_REF] Mélan | Mnemonic processing in air traffic controllers (ATCs): Effects of task parameters and work organization[END_REF][START_REF] Thayer | Toward a psychological theory of multidimensional activation (arousal)[END_REF][START_REF] Thayer | The biopsychology of mood and arousal[END_REF]. Accordingly, in the job-situation examined here, some external factor may have increased operators' subjective tension specifically at shift-start, and in a similar way on all three shifts. The most obvious factor meeting these criteria would be shift hand-over, known to be a critical moment in a shift. If, in the present study, shift hand-over had enhanced operators' perceived tension, this effect should have faded once shift hand-over was terminated, i.e. about 20 minutes after shift-start. This was not observed, however, as increased tension was recorded one hour after shift-start. Alternatively, reduced injury and accident risk within the first half-hour on duty, compared to the second and third half-hour, have been suggested to reflect an increased use of effortful controlled processing [START_REF] Folkard | Shift work, safety and productivity[END_REF][START_REF] Tucker | The Impact of Rest Breaks on Temporal Trends in Injury Risk[END_REF]. Likewise, taking over the responsibility of a sea watch system has been proposed to account for suppression of sleepiness on the initial duty period, even during the night-watch [START_REF] Eriksen | Sleepiness and sleep in a simulated "six hours on/six hours off" sea watch system[END_REF]. Similar "masking effects" may also have been involved following the start of satellite control in the present study.

In line with this hypothesis, supervision of a dynamic process would require an incoming operator to establish a mental model or situation awareness of the system to be controlled, and to plan the sequence of operations to be performed for the remaining time in a shift [START_REF] Hoc | Diagnosis: some theoretical questions raised by applied research[END_REF]. Enhanced cognitive work-load during supervisory control has been proposed to account for the significant performance increase observed throughout the first duty-hour of each shift in a chemical plant (Andorre & Queinnec, 1998). Likewise, high levels of activity required when taking over the responsibility of a sea watch system has been suggested to explain initial sleepiness suppression even following reduced sleep duration and on the night-shift [START_REF] Eriksen | Sleepiness and sleep in a simulated "six hours on/six hours off" sea watch system[END_REF]. According to the studies, following a critical initial phase, operators would carry out the procedures they had programmed at the beginning of the shift to ensure safety and productivity throughout the rest of the shift, a less demanding duty. A three-process model describing the interaction of task demands, in addition to the well-documented circadian and metabolic factors, successfully simulated the unusual performance profile observed between the start and the main body of the shift [START_REF] Andorre-Gruet | Three-process model of supervisory activity over 24 hours[END_REF]. Given that in the present study operators were also involved in continuous supervisory control activities, aimed at running a dynamic process, it is tempting to propose that high cognitive load induced by difficult shiftchange may have accounted for satellite controllers' enhanced tension one hour following the shift-start. Furthermore, though a similar overall increase was observed for operators' subjective tension and heart rate at shift-start, intra-subject comparison of the two variables across the nine recordings provided no evidence of a significant relationship between participants' heart rate and their self-rated tension. This would then indicate that some external, presumably task-related, factor affected both variables at an individual level, but in a different way. Manipulation of work load, task difficulty, and time pressure have been shown to be associated with an activation of cardio-vascular events, including heart rate, both in controlled laboratory conditions [START_REF] Backs | Metabolic and cardio-respiratory of mental effort: the effects of level of difficulty in a working memory task[END_REF][START_REF] Carroll | Heart rate and oxygen consumption during active psychological challenge: the effects of level of difficulty[END_REF][START_REF] Fairclough | A metabolic measure of mental effort[END_REF][START_REF] Van Eekelen | Circadian variation in cardiac autonomic activity: reactivity measurements to different types of stressors[END_REF], and in realjob simulation conditions [START_REF] Averty | Mental workload in air traffic control: an index constructed from field tests[END_REF][START_REF] Brookings | Psychophysiological responses to changes in workload during simulated air traffic control[END_REF][START_REF] Rose | Endocrine activity in air traffic controllers at work. II. Biological, psychological and work correlates[END_REF]. In the latter studies, operators' self-rated workload scores paralleled the heart rate activation, indicating that under high workload operators have to invest more mental effort in order to maintain an adequate level of performance, something associated with heart rate activation. In order to test whether enhanced cognitive load associated with shift-change may have accounted for heart rate activation and increased tension during satellite control, further investigation should include an analysis of task demands in addition to physiological and psychological measures.

Taken together, the present data indicate that despite the fact that shift-workers' capabilities are generally lowest between 03:00 and 04:00 [START_REF] Folkard | Shift work, safety and productivity[END_REF], variations in psychological and physiological variables are the product of many different factors including shift-work features, task demands, motivational factors, work/family conflicts, inter-individual differences, and so on [START_REF] Katie | Predicting the time and duration of sleep in an operational setting using social factors 1[END_REF][START_REF] Kerkhof | Vital working hour schemes: The dynamic balance between various interests[END_REF]. Most importantly, these factors may exert a more or less marked influence depending on the measure used. The present findings then support the development of models describing alertness or job-performance by including work-scheduling features, and in particular task demands and duration [START_REF] Akerstedt | Predictions from the three-process model of alertness[END_REF][START_REF] Andorre-Gruet | Three-process model of supervisory activity over 24 hours[END_REF].

FIGURE CAPTIONS Figure 1 .

 CAPTIONS1 FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. Mean tension (+/-S.E.) provided by self-ratings on 3 occasions within each shift.

Figure 3 .

 3 Figure 3. Median heart rate (median beats . min -1 over 5-min periods per subject, averaged across

  Figure 1.

Table 1

 1 Median Heart beats (+/-interquartile range) averaged over the 15 Minutes Prior and the 15Minutes Following each of the nine Recordings across the 24-h day.

		Morning-shift		Afternoon-shift		Night-shift
	08:00 10:30 13:00 15:00 18:00 21:00 22:00 02:30 06:00
	81.75	76.35	82.48	84.80	78.33	80.57	83.99	73.64	71.98
	5.87	7.17	9.97	10.11	8.38	6.59	11.83	10.59	9.31


Ilan Shlesinger

Pascale Senellart
email: pascale.senellart-mardon@c2n.upsaclay.fr

Loïc Lanco

Jean-Jacques Greffet
email: jean-jacques.greffet@institutoptique.fr

Time-frequency encoded single-photon sources and broadband quantum memories based on a tunable one-dimensional atom

A one-dimensional atom-an atomic system coupled to a single optical mode-is central for many applications in optical quantum technologies. Here we introduce an effective one-dimensional atom consisting of two interacting quantum emitters coupled to a cavity mode. The dipole-dipole interaction and cavity coupling gives rise to optical resonances of tunable bandwidth with a constant mode coupling. Such versatility, combined with a dynamical control of the system, opens the way to many applications. It can be used to generate single photon light pulses with continuous variable encoding in the time-frequency domain and light states that show sub-Planck features. It can also be exploited to develop a versatile quantum memory of tunable bandwidth, another key ingredient for quantum networks. Our scheme ensures that all above functionalities can be obtained at record high efficiencies. We discuss practical implementation in the most advanced platform for quantum light generation, namely the semiconductor quantum dot system where all the technological tools are in place to bring these new concepts to reality.

I. INTRODUCTION

A single atom coupled to a single mode of the electromagnetic field, also called a "one-dimensional atom" [START_REF] Turchette | Measurement of conditional phase shifts for quantum logic[END_REF], is a long sought system to generate and manipulate quantum light [START_REF] Lodahl | Interfacing single photons and single quantum dots with photonic nanostructures[END_REF]. Single atoms are known to interact with a single photon [START_REF] Kimble | Photon antibunching in resonance fluorescence[END_REF][START_REF] Grangier | Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences[END_REF], a property that can be exploited to develop efficient single photon sources or to fabricate devices showing non-linearities at the single photon level. This requires however that the atom interacts mostly with a single mode of the electromagnetic field, so as to collect every emitted photon or to ensure the deterministic interaction of a single photon with the atom.

Highly efficient atom-photon interfaces have been demonstrated with natural and artificial atoms using geometrical approaches [START_REF] Lee | A planar dielectric antenna for directional single-photon emission and near-unity collection efficiency[END_REF], or controlling the emitter spontaneous emission [START_REF] Purcell | Spontaneous Emission Probabilities at Radio Frequencies[END_REF] through inhibition-as demonstrated for emitters in very thin nanowires [START_REF] Babinec | A diamond nanowire single-photon source[END_REF][START_REF] Claudon | A highly efficient single-photon source based on a quantum dot in a photonic nanowire[END_REF]or through acceleration of spontaneous emission-as shown using various types of optical microcavities [START_REF] Madsen | Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity[END_REF][START_REF] Gazzano | Bright solid-state sources of indistinguishable single photons[END_REF]. Such systems have led to the demonstration of ultraefficient sources of indistinguishable single photons [START_REF] Somaschi | Near-optimal singlephoton sources in the solid state[END_REF][START_REF] Ding | On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar[END_REF][START_REF] Snijders | Fiber-coupled cavity-qed source of identical single photons[END_REF][START_REF] Senellart | Highperformance semiconductor quantum-dot single-photon sources[END_REF] that allows scaling-up intermediate quantum computing tasks [START_REF] Loredo | Boson sampling with single-photon fock states from a bright solid-state source[END_REF][START_REF] Wang | High-efficiency multiphoton boson sampling[END_REF] and have shown non-linearities at the single photon level [START_REF] Santis | A solid-state single-photon filter[END_REF][START_REF] Snijders | Observation of the unconventional photon blockade[END_REF], a critical step for efficient photon gates and quantum relays.

These one-dimensional atom structures however present a fixed spectral bandwidth, which defines once and for all the temporal profile of the emitted photons and the temporal window for the non-linear gates. This spectral bandwidth is determined by the modified spontaneous emission rate that is engineered through the Purcell effect (for cavity based structures) or dielectric screening (for nanowire based structures). In the case of cavity structures, one can continuously tune the atom bandwidth by controlling its detuning with the cavity mode, yet at the expense of reduced mode coupling.

In the present work, we propose an effective onedimensional atom that offers bandwidth tunability with a mostly constant mode coupling to the cavity. We consider the system made of two atoms mutually coupled through dipolar interaction [START_REF] Ficek | Cooperative Effects in the Spontaneous Emission from Two Non-identical Atoms[END_REF][START_REF] Sitek | Interplay of coupling and superradiant emission in the optical response of a double quantum dot[END_REF][START_REF] De Léséleuc | Optical Control of the Resonant Dipole-Dipole Interaction between Rydberg Atoms[END_REF] and coupled to the same cavity mode. In the bad cavity limit, the eigenstates are superpositions of sub-radiant and superradiant states with controllable weight [START_REF] Shlesinger | Tunable bandwidth and nonlinearities in an atom-photon interface with subradiant states[END_REF]. Remarkably, while the eigenstates present bandwidth tunability, their coupling to the cavity remains mostly constant.

These unique features open many possibilities for optical quantum technologies where one can dynamically tune the system parameters during the emission or absorption of light while remaining in the one-dimensional atom regime. We first demonstrate the generation of single photon wavepackets with continuous variable encoding in the time frequency domain, light states that have recently attracted strong interest for quantum computing and quantum sensing [START_REF] Brecht | Photon temporal modes: A complete framework for quantum information science[END_REF][START_REF] Toscano | Sub-planck phase-space structures and heisenberg-limited measurements[END_REF]. Single photon wavepackets in the form of cat and compass states are generated, both presenting sub-Planck features. We then propose a bandwidth tunable quantum memory, that stores short photon pulses and releases them with tunable bandwidth. Such device shows great potential for quantum networks, be it for interfacing various quantum systems [START_REF] Akopian | Hybrid semiconductor-atomic interface: Slowing down single photons from a quantum dot[END_REF][START_REF] Kurizki | Quantum technologies with hybrid systems[END_REF][START_REF] Meyer | Direct Photonic Coupling of a Semiconductor Quantum Dot and a Trapped Ion[END_REF] or for synchronization [START_REF] Yang | Experimental synchronization of independent entangled photon sources[END_REF][START_REF] Yuan | Synchronized independent narrow-band single photons and efficient generation of photonic entanglement[END_REF][START_REF] Sun | Entanglement swapping over 100 km optical fiber with independent entangled photon-pair sources[END_REF]. The new concepts introduced here are applicable to all kinds of coupled natural or artificial atoms. They are ready to be implemented in the semiconductor platform for quantum light generation based on quantum dots, where all basic ingredients have individually been demonstrated [START_REF] Somaschi | Near-optimal singlephoton sources in the solid state[END_REF][START_REF] Ding | On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar[END_REF][START_REF] Snijders | Fiber-coupled cavity-qed source of identical single photons[END_REF][START_REF] Senellart | Highperformance semiconductor quantum-dot single-photon sources[END_REF][START_REF] Widhalm | Ultrafast electric phase control of a single exciton qubit[END_REF].

II. A TUNABLE ONE DIMENSIONAL ATOM

The probability for an atom to emit into a desired optical mode, also referred to as "mode coupling", scales as

β = Γ0
Γ0+γ where Γ 0 (γ) is the spontaneous decay rate into the cavity mode (other modes). The most common way to obtain a one-dimensional atom (β ≈ 1) is thus to control its spontaneous emission. High β can be obtained either by reducing γ, i.e. inhibiting the spontaneous emission in the other modes, or by increasing Γ 0 , i.e. accelerating the emission in the chosen mode. In both cases, changing the atom bandwidth Γ 0 +γ automatically modifies its mode coupling [START_REF] Laucht | Electrical control of spontaneous emission and strong coupling for a single quantum dot[END_REF][START_REF] Faraon | Fast electrical control of a quantum dot strongly coupled to a photonic-crystal cavity[END_REF][START_REF] Petruzzella | Fully tuneable, Purcell-enhanced solid-state quantum emitters[END_REF][START_REF] Kuklewicz | Electro-elastic tuning of single particles in individual self-assembled quantum dots[END_REF]. We hereafter introduce an effective one dimensional atom where the system bandwidth and mode coupling are largely independent. We consider the system consisting of two atoms represented by two level systems (TLS) strongly coupled through a dipole-dipole interaction and coupled to the same cavity mode [START_REF] Shlesinger | Tunable bandwidth and nonlinearities in an atom-photon interface with subradiant states[END_REF]. The TLS have ground states |g i and excited states |e i (i = 1, 2), with transition energies E |ei -E |gi = ω i and a dipole-dipole coupling strength Ω 12 [START_REF] Ficek | Cooperative Effects in the Spontaneous Emission from Two Non-identical Atoms[END_REF]. When both TLS are degenerate, ∆ 12 = ω1-ω2 2 = 0, the atomic eigenstates are the wellknown collective states, i.e. the subradiant antisymmetric state |-= |e,g -|g,e √ 2

and the superradiant symmet-

ric state |+ = |e,g +|g,e √ 2
. Both states are energy split by 2Ω 12 2γ 3 4(kd) [START_REF] Kimble | Photon antibunching in resonance fluorescence[END_REF] where k = 2πn λ and n is the index of the material for two parallel dipoles separated by a distance d much smaller than the emission wavelength λ [START_REF] Andrews | Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach[END_REF][START_REF] Lehmberg | Radiation from an N-atom system. I. General formalism[END_REF][START_REF] Ficek | Entangled states and collective nonclassical effects in two-atom systems[END_REF].

Introducing the symmetric σ s and antisymmetric σ a lowering operators, such that |± = σ † s,a |gg , with |gg = |g 1 ⊗|g 2 , the coherent evolution of the system is given by the following Hamiltonian, written in the frame rotating at the mean frequency ω 0 of the two TLS:

H(t) = Ω 12 σ † s σ s -σ † a σ a + (ω c -ω 0 )a † a + ∆ 12 σ † s σ a + σ s σ † a + i √ 2g a † σ s -aσ † s , (1) with ω 0 = ω1+ω2 2
, ω c the frequency of the cavity mode, a the cavity field annihilation operator, and g the coupling between one TLS and the cavity mode, taken equal for both TLSs. A standard master equation for the density matrix of the system allows accounting for the coupling to the environment: [START_REF] Lodahl | Interfacing single photons and single quantum dots with photonic nanostructures[END_REF] where γ ± = γ ± γ 12 and for a given operator ô, L(ô) = ôρô † -1 2 ô † ôρ -1 2 ρô † ô. κ corresponds to the energy decay rate of the cavity and γ is the spontaneous emission rate of each TLS into all the other modes. The collective states emission rates are either increased or reduced by γ 12 where γ 12 γ 1 -1 5 (kd) 2 is very close to γ for d < λ/2πn [START_REF] Lehmberg | Radiation from an N-atom system. I. General formalism[END_REF].

ρ = i[ρ, H] + κL(a) + γ + L (σ s ) + γ -L (σ a ) ,
As shown by eq. 1, ∆ 12 acts as an effective coupling between the states |+ and |-. The system eigenstates |eff and |+ eff are then a superposition of both symmetric and antisymmetric states for which simple analytical expressions can be obtained when γ Ω 12 , g [START_REF] Shlesinger | Tunable bandwidth and nonlinearities in an atom-photon interface with subradiant states[END_REF]:

|-eff µ |+ + ν |-, |+ eff ν |+ -µ |-, (3)
with

µ = δ δ 2 + 1 + √ 1 + δ 2 2 , ν = 1 + √ 1 + δ 2 δ 2 + 1 + √ 1 + δ 2 2 , ( 4
)
and δ = ∆12 Ω12 . The corresponding energy diagram is sketched in the Fig. 1(b) for ω 0 = ω c and the modulus for µ and ν are shown in Fig. 1(c).

The effective antisymmetric eigenstate |eff couples to the cavity mode only through its symmetric component µ |+ at a rate given by g |-eff = µ √ 2g. This corresponds to its symmetric component, µ, times the coupling rate of |+ with the cavity mode, √ 2g. This coupling can be tuned with δ from no coupling at all (µ ≈ 0), i.e. a completely dark state, for ∆ 12 = 0, to the same coupling as a single QD when ∆ 12 Ω 12 (µ ≈ 1 √ 2 from Eq. 4). Its emission rate into the cavity mode is then given by:

Γ |-eff = 4g 2 |-eff κ 1 1 + 2∆c κ 2 = 8µ 2 g 2 κ 1 1 + 2∆c κ 2 (5)
where the Fermi's golden rule gives rise to a dependence both on the coupling rate g |-eff and on the final optical density of states, that depends on the detuning with the cavity mode [START_REF] Andreani | Strongcoupling regime for quantum boxes in pillar microcavities: Theory[END_REF][START_REF] Auffèves | Controlling the dynamics of a coupled atom-cavity system by pure dephasing[END_REF].

∆ c = ω |-eff -ω c = ∆ 2 12 + Ω 2 12 -Ω 12
The emission of the effective antisymmetric eigenstate into all modes other than the cavity mode takes place both through its symmetric and through its antisymmetric component as shown by Eq. 2. Considering that when d λ, we have γ - 0 and γ + 2γ, this emission is mainly due to its symmetric component and is given as:

γ |-eff µ 2 γ + 2µ 2 γ . ( 6
)
Remarkably, the dipole-dipole interaction results in a modification of the emission rate in the cavity mode and in all the other modes both proportional to the symmetric part of the state µ 2 . As a result, the coupling to the mode of the effective antisymmetric state reads as:

β = Γ |-eff Γ |-eff + γ |-eff = F p F p + 1 + 2∆c κ 2 . ( 7
)
where we have introduced the Purcell factor F p = 4g 2 κγ . As a result, as long as 2∆c κ 2 F p + 1, the |eff state remains a one dimensional atom, while having a highly tunable bandwidth.

To illustrate this effect, we now consider parameters corresponding to a technological platform that currently defines the state of the art in terms of emitterbased single photon sources [START_REF] Senellart | Highperformance semiconductor quantum-dot single-photon sources[END_REF], i.e. self-assembled In-GaAs quantum dots (QDs) in micropillar cavities [START_REF] Somaschi | Near-optimal singlephoton sources in the solid state[END_REF]. Yet the present concepts are also valid for other systems such as color centers in diamond [START_REF] Sipahigil | Indistinguishable photons from separated silicon-vacancy centers in diamond[END_REF] or QDs in photonic crystal cavities [START_REF] Laucht | Mutual coupling of two semiconductor quantum dots via an optical nanocavity[END_REF] The values used here are {g, κ, γ} = {20, 400, 0.6} µeV, corresponding to a system of high Purcell factor F p = 6.6 in the weak coupling or bad-cavity regime. We consider that the distance between the two QDs is d = 10 nm, a small distance that allows to neglect tunneling effects [START_REF] Bayer | Coupling and entangling of quantum states in quantum dot molecules[END_REF] whilst providing The spontaneous emission rate of the subradiant state Γ |-eff , normalized to the rate of a single QD in a cavity

Γ 0 = 4g 2
κ , is plotted in the inset of Fig. 2. It is plotted as a function of the detuning between the two QDs, ∆ 12 , normalized by the cavity linewidth κ = 400 µeV. The cavity is set to the frequency of the subradiant state at zero detuning: ω c = ω |-= ω 0 -Ω 12 . Γ |-eff goes from 0 for δ = 0 and increases with the detuning to reach 0.65Γ 0 for ∆ 12 /κ = 0.25 evidencing a widely adjustable linewidth. In the same range of parameters, the main part of Fig. 2 shows a mostly constant mode coupling, β, showing the persistence of the one-dimensional atom character over the whole range of detunings.

A straightforward application of such tunable onedimensional atoms concerns an important challenge for quantum networks, namely, the bandwidth mismatch. Indeed, quantum networks will most probably rely on interfacing various atomic systems, some of them providing the best quantum memories, such as atoms or ions, while others providing the most efficient single photon generation, such as QDs. A first experimental demonstration of QD-ion interfacing [START_REF] Meyer | Direct Photonic Coupling of a Semiconductor Quantum Dot and a Trapped Ion[END_REF] mitigated the large bandwidth mismatch between the QD and ion resonance by using a very low coherent excitation of the QD. Such excitation, where the light only undergoes elastic scattering, provides single photons with the laser bandwidth but is limited to very low efficiency. The effective onedimensional atom presented here allows a control of the single photon temporal profile at constant efficiency. In the case of QDs in micropillar cavities, the bandwidth ranges from around 10 GHz to 10 MHz for a mode coupling exceeding 85%. As shown in the next sections, this system opens many more possibilities, such as the full engineering of the temporal profile of single photon wave packets or the possibility to develop a versatile quantum memory.

III. TIME-FREQUENCY ENCODED SINGLE PHOTON SOURCES

The system introduced here allows not only to control the spectral bandwidth of the atomic emission, but also its phase and amplitude, and can eventually be used to obtain a full shaping of the single photon wavepackets [START_REF] Keller | Continuous generation of single photons with controlled waveform in an ion-trap cavity system[END_REF][START_REF] Thyrrestrup | Non-exponential spontaneous emission dynamics for emitters in a time-dependent optical cavity[END_REF][START_REF] Tufarelli | Coherently Opening a High-Q Cavity[END_REF] at constant high mode coupling. In the following, we discuss how to obtain bright single photon sources with the information encoded in the time-frequency domain [START_REF] Brendel | Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication[END_REF].

A. Tunable emission dynamics

In the following, we consider that one can dynamically control the detuning ∆ 12 (t) between the two emitters.

We model the spontaneous emission of our system restricted to the case of a single excitation. In the collective basis, we consider the states: {|g, g, 0 ; |-, 0 ; |+, 0 ; |g, g, 1 } where the first and second part of the ket correspond respectively to the two atomic states and number of photons in the cavity. In this basis the evolution of the mean values of single operators are described by a set of closed equations [START_REF] Auffèves | Spontaneous emission spectrum of a two-level atom in a very-high-Q cavity[END_REF]:

i ∂ ∂t   σ a σ s a   =   -Ω 12 -i γ- 2 ∆ 12 (t) 0 ∆ 12 (t) Ω 12 -i γ+ 2 -i √ 2g 0 i √ 2g ωc -ω 0     σ a σ s a   . ( 8
)
where ωc = ω c -i κ 2 . ∆ 12 is now a time dependent function.

Fig. 3 (a,b) illustrates the potential of ∆ 12 (t) dynamical tuning to control the emission time and emission dynamics. We consider that the system is in the subradiant state |-at t = 0 and that ∆ 12 = 0. The population of this subradiant state is uncoupled from the cavity and decays only slowly into the leaky modes at a rate γ -γ 12 . Considering the previous parameters for the QD systems, it corresponds to a decay time of 1/γ -= 93 ns, much slower than the natural decay time of around 1 ns for a QD in bulk. This slow decay is not visible on the time scale of Fig. 3. To turn on the spontaneous emission, ∆ 12 (t) is set to a finite value to induce an effective coupling of the subradiant state with the symmetric, superradiant, state while keeping the phase relations between the two emitters. This corresponds to plugging in the interaction with the cavity and hence Purcell enhancing the decay of the atomic state into the cavity mode. The process is performed adiabatically, i.e. ∆12 Ω 2 12 , so that the subradiant state |-is converted only into the effective antisymmetric state |eff . Otherwise, if the applied detuning is too fast, the excitation will also be transferred to the symmetric state |+ eff , and will be emitted rapidly without the possibility to control the emission. Most importantly, such adiabatic coherent process ensures the indistinguishability of the emitted light wavepackets.

The emission rate through the cavity mode depends on the symmetric portion of the |eff state and hence on the final value of the detuning to which the TLSs are brought. The more detuned the TLSs are at the end, the more radiant |eff becomes and the faster is the decay. In Fig. 3, a non-zero detuning is applied around t = 0.7 ns with a rise time equal to 280 ps. Two examples are shown: the solid blue case with final detuning ∆ 12 = 10 µeV decays slower than the dotted yellow case with final detuning ∆ 12 = 50 µeV.

The present approach requires a control of Ω 12 and a dynamical tuning of ∆ 12 . The dipole-dipole interaction strength depends on the distance between the TLSs, which can be thoroughly controlled during the growth process for QD structures. The detuning between the QD spectral resonances can be modified thanks to the confined differential stark effect by applying an external electric field [START_REF] Unold | Optical stark effect in a quantum dot: Ultrafast control of single exciton polarizations[END_REF][START_REF] Kim | Independent tuning of quantum dots in a photonic crystal cavity[END_REF][START_REF] Sonnenberg | Vertically stacked quantum dot pairs fabricated by nanohole filling[END_REF]. This can be done with electrical pulses as fast as 100 ps and rising edges below 50 ps as experimentally shown [START_REF] Widhalm | Ultrafast electric phase control of a single exciton qubit[END_REF].

B. Generation of cat-like state and compass state single photon wavepackets

We extend the control of the emission process to achieve complex pulse shaping of the single photon's amplitude. One can indeed obtain complex time structures for the emitted single photon wavepackets by turning on or off the coupling with the cavity mode through ∆ 12 (t) during the emission process.

We first apply two ∆ 12 (t) pulses separated in time as shown in Fig. 4(a). The mean value of the emitted power then shows two distinct peaks as shown in Fig. 4(c), corresponding to a time bin encoding of the information. The time interval between the peaks ∆t can be chosen at will and the duration of each peak τ is controlled by the maximum value of ∆ 12 which is applied. Two different examples are depicted with a waiting time ∆t = 5 ns (in dashed red) and ∆t = 11 ns (in solid blue), again considering experimental parameters for the QD system. Note that to obtain the same emitted power for the two peaks, the maximum applied detuning is higher for the second peak. We also assume that one can not only control the emitters detuning ∆ 12 (t) but also the mean frequency of the two emitters ω 0 (t) as shown in Fig. 4(b).

The corresponding energy spectral density is plotted in Fig. 4(e). As expected by Fourier transform, the two peaks in time-domain result in a frequency comb. The overall width is proportional to the inverse of the duration of one peak 1/τ , which is equal for the two different cases here. The interval between the fast frequency oscillations is proportional to the inverse of the waiting time 1/∆t. For the case where ∆t = 11 ns one obtains fast oscillations and narrow peaks.

A more detailed insight into the generated single photon wavepacket can be obtained by calculating the associated Wigner-Ville function [START_REF] Ville | Théorie et Applications de la Notion de Signal Analytique[END_REF], also called the chronocylic Wigner function [START_REF] Paye | The chronocyclic representation of ultrashort light pulses[END_REF]. Its expression is given for a detection between [0, T ] by:

W (t, ω) = 1 2π T /2-|t-T /2| -T /2+|t-T /2| dτ a † (t + τ 2 )a(t - τ 2 ) e -iωτ . ( 9
)
It corresponds to the Fourier transform of the electric field correlations as a function of time and is displayed in Fig. 4(f) for the two different waiting times ∆t. One recognizes a photonic cat-like state. The oscillations visible at the mean time between the two emission peaks result from the interference between the probability to emit a photon at a time t -τ /2 with the probability to emit a photon at t + τ /2. They present time-frequency sub-Planck features, subtle features of quantum states that have recently been proposed for advanced quantum sensing applications [START_REF] Toscano | Sub-planck phase-space structures and heisenberg-limited measurements[END_REF]. This first example illustrates the versatility of the tunable one-dimensional atom for the generation of light in two time bins. It can naturally be extended to more complex states of light since the effective atomic system presents a tunable lifetime and the phase of the state is controlled at the atomic level. This is illustrated in Fig. 5 where a set of four ∆ 12 (t) Gaussian pulses, separated in time are applied as plotted in Fig. 5(a). The pulses are 170 ps wide and are applied at t = {300, 1100, 1500, 2300} ps. The amplitude of each pulse is increased each time so as to compensate the smaller remaining emitter population. In parallel, the mean frequency of the emitters, ω 0 (t) = ω1+ω2 2 is shifted to four different values as shown in Fig. 5(b). As seen in Fig 5(c), a compass state, corresponding to a fourlegs time-frequency superposition, is generated. It shows an even richer structure in the time-frequency domain, similar to the higher class of state that was recently introduced for sensing application in optomechanics [START_REF] Howard | Hypercube states for sub-planck sensing[END_REF].

Such structure is also ideal for continuous variable time encoding of the quantum information, a new field of quantum computing that exploits the continuous degrees of freedom of time encoding to enlarge the Hilbert space of computation [START_REF] Brecht | Photon temporal modes: A complete framework for quantum information science[END_REF]. Until now, the generation of con-tinuous variable at the single photon level was limited to ultra-low source efficiency, whether it is based on parametric down-conversion [START_REF] Montaut | Compressive characterization of telecom photon pairs in the spatial and spectral degrees of freedom[END_REF][START_REF] Ansari | Tomography and purification of the temporalmode structure of quantum light[END_REF][START_REF] Boucher | Toolbox for continuous-variable entanglement production and measurement using spontaneous parametric down-conversion[END_REF][START_REF] Ansari | Heralded generation of high-purity ultrashort single photons in programmable temporal shapes[END_REF] or on the weak coherent excitation of an atomic system [START_REF] Pursley | Picosecond pulse shaping of single photons using quantum dots[END_REF][START_REF] Matthiesen | Phase-locked indistinguishable photons with synthesized waveforms from a solid-state source[END_REF]. The approach introduced here, based on the dynamical control of a tunable one-dimensional atom, allows generating arbitrary time-encoded photons with near unity efficiency.

IV. A BROADBAND AND VERSATILE QUANTUM MEMORY

Another application of the present architecture is single photon storage and bandwidth conversion. Many systems are explored to develop efficient quantum memories for quantum networks, most of them based on atomic vapors or ion-doped crystals [START_REF] Bussières | Prospective applications of optical quantum memories[END_REF]. They present very narrow bandwidths that prevent the efficient storage of short photon pulses, the latter being naturally desirable for high rate quantum networks. To date, the development of broadband single photon memories has been scarcely addressed. Such memory has recently been demonstrated using Raman assisted transition in warm atomic vapors: the proposed protocol offers interesting possibilities for releasing photons of improved quantum purity [START_REF] Gao | Optimal coherent filtering for single noisy photons[END_REF]. However, so far the storage times remains in the few nanosecond timescale [START_REF] Kaczmarek | High-speed noise-free optical quantum memory[END_REF]. Here we show that, by dynamically tuning the emission lifetime of the subradiant state, one can achieve the storage of 100 ps single photon pulses for over 100 ns using an implementation of these concepts in the QD system. Naturally, building on the results of the previous section, the quantum information could also be released with a highly tunable temporal profile, independently of the incoming single-photon profile.

The storage mechanism relies on sending a single photon wavepacket on the tunable one-dimensional atom. The process takes place in three steps as shown in Fig. 6(a). First the system parameters are tuned to a non-zero value for the detuning ∆ 12 so that they are effectively coupled to the cavity mode, allowing to absorb the incoming excitation, and excite the effective subradiant state |eff . More specifically, ∆ 12 is chosen to match Γ |-eff with the bandwidth of the light pulse that one wants to store. The photon is then stored by tuning back the two QDs into resonance to adiabatically go from the effective subradiant state |eff to the dark state |-. The photon absorption process is then the time-reversed of the emission process starting with the system in the ground state |g, g, 0 at t = 0 and dynamically tuning the detuning ∆ 12 (t) so as to progressively bring the system into the fully antisymmetric, dark state |-where it presents the minimal coupling to light. Finally, release of the single photon is obtained by applying a detuning ∆ 12 between the two QDs.

While the incoming pulse is a single photon Fock state, it is easier to calculate this storage process using a coherent state |α = k α k k! |k with a very low mean photon number n = |α| 2 = 0.01 1. Only the one photon component excites the atom so that the system response reflects the response to single photon Fock state when normalizing the atomic population by the probability of having one photon [START_REF] Kim | A quantum logic gate between a solid-state quantum bit and a photon[END_REF][START_REF] Giannelli | Weak coherent pulses for single-photon quantum memories[END_REF]. The system excitation is done via the cavity mode through the Hamiltonian of Eq. 1:

H p (t) = -iE p (t)(a † -a)
, where E p is the field amplitude coupled to the cavity mode. Fig. 6 shows the evolution of the atomic population corresponding to a single photon Fock state sent on a QD system with the same parameters as in the previous sections. The single photon wavepacket to store presents a Gaussian temporal profile with a FWHM of τ pulse = 550 ps. The system parameters are set so that the incoming photon is resonant with the |eff state:

ω |-eff = ω 0 -∆ 2 12 + Ω 2 12 . ( 10
)
The cavity frequency is tuned to ω c = ω 0 -Ω 12 and ∆ 12 (t = 0) is set to 40 µeV, in order to achieve the highest absorption probability. This condition is obtained when the |eff state linewidth is equal to 2 3 of the incident single-photon pulse width [START_REF] Wang | Efficient excitation of a two-level atom by a single photon in a propagating mode[END_REF][START_REF] Stobińska | Perfect excitation of a matter qubit by a single photon in free space[END_REF] (here it corresponds to FWHM = 367 ps). The QDs are then adiabatically brought into resonance: ∆ 12 (t) → 0 during the storage process in order to bring the |eff state into the darkest state |-. The photon will thus be stored for a time as long as 1/γ -= 93 ns and recovered by setting ∆ 12 (t) to a non-zero value.

Considering the present experimental parameters, we obtain a 68% storage efficiency, given by the maximum flip inversion of the atomic system with a single photon pulse excitation. To stay within 5% of such maximum efficiency, we find that the error in the start time of the detuning gate ∆ 12 (t) has to be smaller than 100 ps which corresponds to a fifth of the single photon pulse. If the QDs are brought to resonance too early, the excitation stops before maximum population is achieved, and if the QDs are brought to resonance too late, spontaneous emission takes place before reaching the dark state. This value already represents a very high storage probability considering all current memory architectures where typical values are in the tenths of percent range [START_REF] Heshami | Quantum memories: emerging applications and recent advances[END_REF]. The coupled quantum dot interface introduced here can thus be used to store short single photon pulses of 100 ps for around 100 ns, as shown in figure 6(a), surpassing by almost two orders of magnitude the current state of the art [START_REF] Kaczmarek | High-speed noise-free optical quantum memory[END_REF][START_REF] Poem | Broadband noise-free optical quantum memory with neutral nitrogen-vacancy centers in diamond[END_REF].

We note that tunable single photon memories have recently attracted attention for their ability to re-emit the photon with a different frequency and bandwidth than the initial ones [START_REF] Heshami | Quantum memories: emerging applications and recent advances[END_REF]. Indeed, frequency and bandwidth conversion is a valuable tool for building quantum networks. A bandwidth modulation of between 0.5 and 1.9 of the incoming bandwidth was recently demonstrated using a diamond memory via a Raman transition, and with a conversion efficiency of only 1% [START_REF] Fisher | Frequency and bandwidth conversion of single photons in a roomtemperature diamond quantum memory[END_REF]. The system proposed here can finally allow the storage of photons as short as 100 ps and convert them to much longer single photon pulses up to τ = 1/γ -100 ns.

V. CONCLUSION

We have proposed a new generation of devices for single photon production and manipulation by coupling two quantum emitters in a cavity. This is achieved by a dynamical control of the subradiant state which, when the emitters are detuned, acts as an effective dipole that can be externally modified.

These concepts are ready to be implemented thanks to the last decades of experimental effort in the quantumdot cavity systems, that have allowed to obtain nearoptimal single photon sources in the solid state with impressive values regarding efficiency, brightness and indistinguishably [START_REF] Somaschi | Near-optimal singlephoton sources in the solid state[END_REF][START_REF] Senellart | Highperformance semiconductor quantum-dot single-photon sources[END_REF][START_REF] Ding | On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar[END_REF]. These technological efforts can now lead to the on demand, efficient, single photon generation, with a tunable bandwidth on the range of [10MHz, 10GHz]. They can be used to expand the range of application of quantum light both in quantum computing and quantum sensing, with efficient single photon sources with continuous variable encoding in the time-frequency domain. The same architecture can also store broadband single photons, with pulse durations as low as 100 ps, stored during 100 ns, with an efficiency up to 68%. Both storage and bandwidth control would finally allow efficient bandwidth conversion of single photons.

Overall, the proposed device acts as a junction useful in any kind of hybrid quantum network, with the possibility to emit, store, and modify single photons of a wide variety of quantum systems. They also open new possibilities for both quantum sensing [START_REF] Howard | Hypercube states for sub-planck sensing[END_REF] and quantum computing [START_REF] Brecht | Photon temporal modes: A complete framework for quantum information science[END_REF], with inherently high efficiencies, as re-quired for scalability.

FIG. 1 . 2 .

 12 FIG. 1. (a) Two two-level systems (TLS) are weakly coupled to the same cavity mode. They are coupled to each other through dipole-dipole interaction with a rate Ω12 and their frequency mismatch ∆12(t) = ω1 -ω2. (b) Energy diagram of the eigenstates with at most one excitation. The first and second part of the kets correspond respectively to the atomic state and number of photons in the cavity. Double arrows represent coupling rates between the coupled-QD eigenstates and the cavity mode, single dotted arrows the decay rates into all other modes. Energy splittings are indicated in the energy scale. The cavity frequency is set here to the mean QD frequency ω0 = ω 1 +ω 2 2 . (c) Modulus of the coefficients µ and ν corresponding to the subradiant and superradiant parts of the eigenstates as a function of δ = ∆ 12 Ω 12 . See text for details.

FIG. 2 .

 2 FIG. 2. Coupling of the effective atom to the cavity mode β as a function of the detuning between the two over the cavity linewidth. Inset: ratio of the spontaneous emission rate Γ|eff of the subradiant state |eff normalized to the spontaneous emission rate Γ0 of a single TLS in the cavity. See the text for the parameters. Parameters corresponds to the case of two quantum dots in a micropillar cavity -see text for details.

FIG. 3 .

 3 FIG. 3. Controllable spontaneous emission. (a) Applied detuning ∆12(t) as a function of time. (b) Total population of the two TLS. (c) Emitted power through the cavity (scaled). Solid blue corresponds to a maximal detuning of ∆12 = 10 µeV and dotted yellow to a maximal detuning of ∆12 = 50 µeV. The vertical line across the three panels indicates the passage from the totally dark state |-to the partially radiant effective antisymmetric state |eff due to the applied detuning. The cavity is taken resonant to the final |eff state in both cases: ωc = ω0 -∆ 2 12 + Ω 2 12 .

FIG. 4 .

 4 FIG. 4. Time bin encoding of a single photon. (a) Applied detuning sequence ∆12(t) (b) and overall frequency shift ω0(t). (c) Corresponding emitted power by the cavity. Two pulse sequences are considered with a waiting time between each pulse of 5 ns (dashed red) and 11 ns (dashed red). (d) Population of the collective state |eff . (e) Density power spectrum of the power emitted by the cavity. (f) Corresponding Wigner-Ville function of the emitted electric field: left waiting time of 5 ns and right waiting time of 11 ns.

FIG. 5 .

 5 FIG. 5.Generation of a compass state. The emission of such a state is obtained by applying a four-pulse detuning ∆12(t) (a), and at the same time an overall frequency shift of the mean atomic frequency ω0(t) (b). The cavity frequency is fixed at ωc = ω0(0) -Ω12. (c) Wigner-Ville function of the emitted electric field for a one-photon state.

FIG. 6 .

 6 FIG. 6. Broadband memory operation. (a) Atomic population normalized by the average number of photons in the pulse n (solid blue) and applied detuning (∆12 = 0 in dashed green). The storage process takes place in three steps: first the two QDs are detuned so as to absorb the incoming photon , the excitation is then stored in the subradiant state by bringing the two QDs into resonance, and finally the photon is released by detuning again the two QDs at t=35 ns. The pump is resonant with the |eff state.During storage, the excitation leakage takes place at a rate γ-= γ -γ12 (as shown in dotted brown). (b) Close-up of figure (a) at short time delays. The Gaussian profile of the incoming wavepacket is shown by the black dotted line.

ACKNOWLEDGMENTS

The authors thank Andrew White, Perola Milman, Carlos Anton, Philippe Grangier and Riccardo Messina for fruitful discussions. This work was supported by SAFRAN-IOGS chair on Ultimate Photonics and a public grant overseen by the French National Research Agency (ANR) as part of the Investissements d'Avenir programme (Labex NanoSaclay, reference: ANR-10-LABX-0035). J.-J.G. acknowledges the support of Institut Universitaire de France.