Adrien Bolzer

Michel Hoen

Bettina Montaut-Verient

Charles Hoffmann

Marine Ardoi

Ariane Laplante-Lévesque

Nicholas Guevara

Thierry Mom

Chadlia Karoui

Christophe Vincent

Cécile Parietti-Winkler

Christian E Stilp

The Development of the "Telislife" Questionnaire for the Evaluation of Telephone Use in Cochlear Implant Users

Keywords: Glasgow Benefit Inventory, Short Form Health Survey, Health Utilities Index, or World Health

Purpose: For cochlear implant users, the ability to use the telephone is often seen as an important landmark during rehabilitation and an indicator of cochlear implant benefit. The goal of this study was to develop a short questionnaire exploring the ability to use the telephone in cochlear implant users, named Telislife, and test it in a group of experienced users. Method: This prospective multicenter study was based on the completion of self-administrated questionnaires. The Telislife includes 20 items using a 5-point Likert scale for answers. Speech recognition scores were obtained with monosyllabic word lists at 70 dB HL. Quality of life was evaluated with the Nijmegen Cochlear Implant Questionnaire.

This study included 55 adult patients wearing a cochlear implant for over 1 year. Results: The Telislife questionnaire showed excellent reliability (Cronbach's α = .91). A significant correlation was found between Telislife scores and Nijmegen Cochlear Implant Questionnaire scores (r = .69, p < .001) and speech recognition scores (r = .35, p = .007). Conclusion: Given significant correlations between Telislife scores and both speech recognition and quality of life and given its short form, the Telislife questionnaire appears to be a reliable tool to evaluate cochlear implant outcomes in clinical practice.

Organization Quality of Life) can be used in patients regardless of health condition to assess the impact of the health condition and the effectiveness of its treatment on general QoL. When considering the evaluation of the impact of CIs, these questionnaires typically lack sensitivity as they assess communication abilities or social aspects of life but rather focus on domains that are unrelated to CIs and their impact. Therefore, these generic questionnaires usually show only moderate improvements after CI and correlations with speech recognition scores only after subset analysis [START_REF] Mcrackan | Metaanalysis of quality-of-life improvement after cochlear implantation and associations with speech recognition abilities[END_REF]. To address the lack of sensitivity of generic questionnaires, disease-specific questionnaires were developed for populations with specific health conditions. For the purpose of CI, these questionnaires can again be divided in two groups, depending on their scope: hearing-specific questionnaires (e.g., Hearing Handicap Inventory, Abbreviated Profile of Hearing Aid Benefit [APHAB]) or CI-specific questionnaires (e.g., Nijmegen Cochlear Implant Questionnaire [NCIQ]). [START_REF] Mcrackan | Metaanalysis of quality-of-life improvement after cochlear implantation and associations with speech recognition abilities[END_REF] recently conducted a meta-analysis of hearing-and CI-specific questionnaires identifying 13 studies eligible for their synthesis, which included papers reporting adult data obtained either with the NCIQ as CI-specific questionnaire or with various hearing-specific questionnaires such as APHAB, Hearing Handicap Inventory, or the Speech, Spatial and Qualities of Hearing Scale [START_REF] Gatehouse | The Speech, Spatial and Qualities of Hearing Scale (SSQ)[END_REF], five different questionnaires in total). This analysis demonstrates that CIs have a large significant positive impact on QoL when comparing pre-to postimplantation scores on both types of questionnaires. However, the same metaanalysis reports a weak pooled correlation between CI-specific QoL measures and speech recognition scores (r = .22-.24, depending on the speech recognition test considered). This result highlights that speech perception, as currently evaluated by speech audiometry in clinical settings, only captures one dimension of the impact of CIs on communicative and social abilities as well as QoL. This also suggests that these two measures are complementary and that a complete evaluation of CI benefits must include both the evaluation of auditory abilities and QoL. One potential limitation in this context is that QoL questionnaires are not adapted to everyday clinical practice because of the high number of items they contain. For example, the World Health Organization Quality of Life contains 100 items, and the NCIQ contains 60 items. It is therefore important to develop new QoL assessment tools that are concise enough to be relevant in a clinical environment and that correlate with both comprehensive QoL questionnaires and with speech perception scores.

Measuring Ability to Use the Telephone

One of the benefits of cochlear implantation is, at least for most patients, the development or recovery of speech perception abilities, culminating with notable improvements in difficult communication situations such as in noisy environments or over the telephone, with compressed speech signals and without visual feedback. Around 70% of adult CI recipients with postlingual deafness use the telephone [START_REF] Anderson | Telephone use: What benefit do cochlear implant users receive[END_REF][START_REF] Cray | An investigation of telephone use among cochlear implant recipients[END_REF]. Telephone use is documented to increase after cochlear implantation, suggesting that ability to use the telephone could be considered as one dimension of CI benefits [START_REF] Anderson | Telephone use: What benefit do cochlear implant users receive[END_REF][START_REF] Cray | An investigation of telephone use among cochlear implant recipients[END_REF]. Other studies of telephone use in CI users show how communication abilities could be improved, either with videoconferencing [START_REF] Mantokoudis | Influence of telecommunication modality, Internet transmission quality, and accessories on speech perception in cochlear implant users[END_REF] or with connection accessories [START_REF] Rey | Technical aids for speech understanding in cochlear implanted adults using cell-phones[END_REF][START_REF] Wolfe | Evaluation of a wireless audio streaming accessory to improve mobile telephone performance of cochlear implant users[END_REF]. It has been shown that speech perception using mobile phones is better than when using landline telephones [START_REF] Tan | Mobile and landline telephone performance outcomes among telephone-using cochlear implant recipients[END_REF]. These results suggest that telephone use in CI users can be considered as an important factor pertaining to their general communication abilities and representing a symptomatic dimension of CI rehabilitation, potentially broadly related to postsurgical improvements. [START_REF] Cray | An investigation of telephone use among cochlear implant recipients[END_REF] noted that one of the correlates of telephone use was a good level of speech perception without speech reading. This direct link between speech perception outcomes and the ability to use a telephone could make it possible to use a measure of telephone use abilities to indirectly quantify speech perception outcomes in CI users.

We found no questionnaire dedicated to telephone ability in patients with CI, yet it seems that the telephone is a relevant area of CI outcome, with, for example, the Hearing Implant Sound Quality Index containing two items targeting telephone ability [START_REF] Amann | Development and validation of a questionnaire for hearing implant users to self-assess their auditory abilities in everyday communication situations: The Hearing Implant Sound Quality Index (HISQUI19)[END_REF] and the NCIQ containing one item targeting telephone ability [START_REF] Hinderink | Development and application of a health-related quality-of-life instrument for adults with cochlear implants: The Nijmegen Cochlear Implant Questionnaire[END_REF].

In a preliminary investigation with 26 CI users, we described ability to use the telephone with four mutually exclusive categories: (a) unable to use the telephone, (b) able to use the telephone with a familiar speaker on a familiar topic, (c) able to use the telephone with a familiar speaker on an unfamiliar topic, and (d) able to use the telephone with an unfamiliar speaker on an unfamiliar topic [START_REF] Rumeau | Quality of life and audiologic performance through the ability to phone of cochlear implant users[END_REF]. We reported a strong relationship between these categories and speech recognition measures. We concluded that the evaluation of the ability to use the telephone could be an effective, fast, and reliable tool to evaluate both speech recognition capacities and QoL in CI users. The goal of this study was to develop a short questionnaire, named Telislife, exploring CI users' ability to use a telephone and to test this questionnaire in a group of experienced CI users.

Materials and Method

Study Design

This prospective multicenter study is based on the completion of self-administrated questionnaires. The data collection occurred in collaboration with four university hospitals in France: Nancy, Lille, Clermont-Ferrand, and Nice. Four types of data were collected: (a) general and demographics, (b) ability to use the telephone (Telislife questionnaire), (c) QoL (NCIQ), and (d) speech audiometric data.

Consecutive patients were recruited during routine audiological, medical, psychological, or speech therapy appointments at one of the four participating University Hospitals. To be included, patients had to be adults (≥ 18 years old), implanted since at least 1 year with a unilateral or bilateral CI, be fluent in French, and follow the standard postimplantation follow-up and rehabilitation program. Speech tests were performed as part of the routine clinical follow-up of the patients, and at the end of one visit, a physician provided information about the questionnaire and obtained written informed consent from each patient. The questionnaires were completed in a pen-and-paper format in the waiting room of the hospital and sent anonymously to the local delegation for research and innovation (Délégation à la recherche clinique et à l'innovation) of the hospital. This observational, noninterventional study was conducted in agreement with the declaration of Helsinki, and the protocol was approved from the hospital's local ethics committee "Comité de Réflexion Ethique Nancéien Hospitalo-Universitaire," who approved the protocol on February 23, 2016.

General and Demographics

The following demographic data were collected: age group (18-45, 46-65, 66-85, or > 85 years), gender, hearing status (aided or unaided; type of aid, CI or hearing aid), onset of deafness (pre-or postlingual), duration of deafness (in years), etiology of deafness (11 options and an "other" free field), and CI experience (< 1, 1-2, 2-3, 3-4, or > 4 years). Then, the patients were asked about their CI system's brand and model, time of daily use, and accessories. Finally, patients were asked about their telephone habits: telephone brand(s) and model(s), amount of daily use (< 1, 1-3, 3-6, 6-9, 9-12, or > 12 hr), and modality of usage (giving/receiving calls, sending/receiving text messages or instant messages, using applications, surfing the Internet, and "other" free fields).

Ability to Use the Telephone: Development of the Telislife Questionnaire

To evaluate ability to use the telephone in CI users, we built a questionnaire of 20 items using a 5-point Likert scale for answers (see Supplemental Material S1). Items were inspired by our previous experience with measuring telephone ability [START_REF] Rumeau | Quality of life and audiologic performance through the ability to phone of cochlear implant users[END_REF], by the literature, and more specifically by two validated questionnaires, one of CI sound quality (Hearing Implant Sound Quality Index; Amann & Anderson, 2014) and one of hearing aid benefit (APHAB; [START_REF] Cox | The Abbreviated Profile of Hearing Aid Benefit[END_REF]. Items were generated to cover all dimensions of the construct "ability to use the telephone." Therefore, the questionnaire included several items related to speech perception, but also to voice recognition, voicemailusage, speech production, and perception of pitch cues, known to encode emotions.

The 20 items of the questionnaire cover four subdomains: (a) speech recognition in favorable situations (Items 5,8,11,13,and 19; e.g., "On the phone, how difficult is it to have a conversation in a quiet environment?"), (b) speech recognition in complex situations (Items 6, 7, 9, 10, and 14; e.g., "On the phone, how difficult is it to have a conversation in a noisy environment?"), (c) voice perception (Items 1, 2, 3, 4, and 15; e.g., "On the phone, how difficult is it to recognize the voice of a family member?"), and (d) speech production (Items 16, 17, and 18; e.g., "When calling a relative/someone from your family, how difficult is it for him/her to understand you?"). Finally, Items 12 and 20 are general satisfaction items and are not included in any subdomain.

The five first authors, who all have extensive experience interacting with adult CI users in their clinical and research roles, collaboratively generated, reviewed, and revised the 20 items of the questionnaire for good face validity. Response options were placed on scales of ease ("very easy" to "not easy at all"), difficulty ("very difficult" to "not difficult at all"), and satisfaction ("very satisfied" to "not satisfied at all"), as verbal answer options are associated with less confusions than numerical response options [START_REF] Krosnick | Designing rating scales for effective measurement in surveys[END_REF]. For each item, patients could also choose "not applicable" (NA) as answer. Five items (Items 2,12,15,18,and 20) were reverse-coded to ensure that patients remained attentive during questionnaire completion.

QoL: NCIQ

To evaluate CI-specific QoL, we used the French version of the NCIQ [START_REF] Hinderink | Development and application of a health-related quality-of-life instrument for adults with cochlear implants: The Nijmegen Cochlear Implant Questionnaire[END_REF]. The NCIQ explores QoL in CI users and is made of 60 items that are grouped in three main domains and six subdomains: (a) "physical" domain with three subdomains, "basic sound perception," "advanced sound perception," and "vocal production"; (b) "psychological" domain with the subdomain "self-esteem"; and (c) "Social" domain with two subdomains, "limitation of activities" and "social interaction." Each subdomain contains 10 items. The possible answers for every item appear in the form of a 5-point Likert-type scale varying from "never" to "always" (occurrence questions, 55 statements) or from "no" to "quite well" (ability questions, five statements), and the patient is required to answer which statement best fit their experiences.

Speech Audiometry

Speech recognition performance was evaluated once with and once without speechreading. Patients were tested with their own CI sound processor programmed with their everyday mapping parameters, processing strategy, and electrode configuration, and without hearing aid for bimodal users. Speech identification was measured with one randomly picked Lafon list, including 17 French monosyllabic words containing three phonemes. Speech identification was scored as the percentage of phonemes correctly repeated. Trained audiologists read the Lafon lists in a soundproof booth, with or without visual feedback.

Statistical Analyses

Results from the Telislife questionnaire were expressed as a score from 1 to 5 on the Likert scale; maximal score was thus 100. NA responses were treated as missing values, and all Telislife scores and subscores were calculated as percentages of answers (based on the total of non-NA answers). For the NCIQ, scores were also expressed as a percentage of expressed opinions, and a correlational analysis was run.

Descriptive statistics established the construct validity of the Telislife questionnaire. The normality of the distribution of Telislife scores was verified with a Shapiro-Wilk test. Reliability of Telislife scores was assessed with Cronbach's alpha coefficient and split-half reliability. Construct validity was assessed by comparing Telislife and NCIQ scores. We used a Pearson test for parametric data correlation between Telislife and NCIQ scores and between questionnaire and individual speech recognition scores. A p value of < .05 was considered statistically significant. When performing multiple tests on the same nonindependent factors, a Bonferroni correction for multiple corrections was applied by dividing the alpha value by the number of tests performed. For analyses of variance (ANOVAs), the Tukey's honestly significant difference (HSD) test was chosen for post hoc assessment of specific effects, as it includes a correction for multiple comparisons.

Results

Participants and Sample Demographics

Sixty-eight patients were initially included into the study. From these 68 participants, 13 (19.1%) were not included for further analyses: 11 (16.2%) because they had more than five out of 20 of NA answers, one (1.5%) because of a severe multihandicap (could not complete the questionnaire), and one (1.5%) because answers were obviously incoherent (oppositions between positively and negatively rated items). Further analyses are based on 55 respondents. Table 1 describes the 55 respondents.

Phone Usage Habits in CI Users

Most participants (59.6%) used smartphones, and 38.5% of participants used feature mobile phones. The majority of respondents (72.2%) used their phone for audio conversations and other use (e.g., texting, applications, access to the Internet), while 16.7% reported using their phone exclusively for audio conversations. Conversely, 27.8% of the respondents reported using a mobile phone without using the audio output (e.g., texting, applications, access to the Internet). Most respondents (74.5%) reported using their mobile phone mainly without a dedicated accessory. The primary usage reported was sending/ receiving text messages (58.6%), while audio conversations were the primary use in 36.2% of users. When giving or receiving audio calls, 75.5% of patients with CI used direct audio access, either through the traditional sound output of their phone (40.8%) or using the loudspeaker option of their phone (34.7%). The majority of patients (53.5%) used their phone for less than 1 hr a day, and 27.6% used their phone for 1-3 hr a day.

Telislife Questionnaire Analysis

Item analysis: The proportion of NA responses ranged from a minimum of 0% (0/55) for four items (Items 3,5,8,and 19) to a maximum of 16.4% (9/55) for Item 1: "On the phone, is it difficult to differentiate a female voice from a child's voice?" The overall proportion of NA responses over the 1,100 responses was 4.9%. All response options were used, the different ratios for the Likert scores being 214 (20.5%) for 1, 190 (18.2%) for 2, 208 (19.9%) for 3, 224 (21.4%) for 4, and 210 (20.1%) for 5. These scores were not significantly different from the theoretical distribution of 20% for each possible response as evaluated by a chi-square test: χ 2 (4, N = 55) = 0.28, p = .99. Moreover, the full range of answers (min = 1, max = 5) was used for 18 out of 20 items, and only two items (Items 6 and 7) were never attributed the maximal score. These two items (i.e., "On the phone, how difficult is it to have a conversation when in a noisy environment?" or "On the phone, how difficult is it to have a conversation when other people are speaking around you?") are challenging listening situations for CI users. This is also mirrored in the lowest average scores and lowest standard deviation on these two items (1.7 ± 0.9 and 1.8 ± 0.9, respectively), suggesting that most users experience these situations as difficult, and this explains the narrow range in response compared to other items.

Internal Consistency

The internal consistency (reliability) of the Telislife questionnaire was evaluated using Cronbach's alpha coefficient. For the questionnaire, globally, it was α = .91, corresponding to excellent reliability [START_REF] Saris | Design, evaluation, and analysis of questionnaires for survey research[END_REF]. Running a split-half reliability measure comparing odd and even items, the correlation between the two halves was r = .87, and the Guttman split-half reliability was .93. Looking into the four subcategories, the two subcategories evaluating speech perception showed very good reliability levels, with .90 for the subdomain speech perception "favorable situations" and .91 for the subdomain Note. CI = cochlear implant.

speech perception "complex situations," when the two other subcategories showed lower reliability levels of α = .68 and .71 for voice perception and speech production, respectively.

Distribution of Total Scores and Subdomain Scores

Telislife total scores (see Figure 1A) were, on average, 60.3 ± 17.8 points out of a maximum of 100 points, ranging from 25.3 to 94.0. Total scores followed a normal distribution (Kolmogorov-Smirnov d = 0.08, p > .20 and Shapiro-Wilk W = 0.97, p = .25). The median value of 62.1% was very close to the average value of 60.3% and the skewness at -0.17 suggests a rather symmetric distribution with a slight left skew (see Figures 1A and1B). The kurtosis value of -0.87 suggests a relatively light-tailed distribution with slightly more scores around the mean value than expected from a normal distribution.

The scores observed for the four subdomains were respectively 67.6 ± 22.0 points for the subdomain speech "favorable situations," 43.1 ± 19.4 for the speech "complex situations subdomain," 62.1 ± 17.8 for voice perception, and 75.8 ± 20.8 for speech production. A one-way repeatedmeasures ANOVA performed on the total score and four subdomains reveals a significant principal effect, F(4, 216) = 70.01, p < .05, and post hoc paired evaluations corrected for multiple comparisons (Tukey's HSD) revealed that all scores were significantly different from another (all ps < .05), except for the subdomain voice perception, which was not significantly different from the total score (p = .91) and the subdomain score speech "favorable situations" (p = .06).

Internal consistency was further evaluated by correlating all subdomains of the Telislife questionnaire with the total score. All observed correlations were significant with corrected alpha values (see Table 2).

Construct Validity

To test the construct validity of the Telislife, total scores and subdomain scores were compared with NCIQ scores and speech audiometry scores using correlation analyses. We expected that Telislife scores would converge with NCIQ scores and speech audiometry scores.

Associations Between Telislife Scores and NCIQ Scores

A significant correlation between the total score of the Telislife questionnaire and all scores, global and subdomains, from the NCIQ was observed (see Table 3). The correlation between the two total scores was significant: r(53) = .69, p < .001 (see Figure 2). Furthermore, the Telislife "speech production" subdomain appears more selective, and the strongest relation was found with the speech production dimension of the NCIQ, r(53) = .59, p < .001, and with two other subdomains from the NCIQ, advanced speech perception, r(53) = .47, p < .001, and the physical composite score, r = .53, p < .001.

Associations Between Telislife Scores and Speech Audiometry Scores

To test the potential association between measures of QoL by the Telislife questionnaire or the NCIQ and audiometric outcomes, we computed correlation coefficients between the Telislife and NCIQ scores and scores obtained during the speech audiometry tests. Telislife score is positively correlated with speech recognition score without speechreading (r = .33, p = .015). Figure 3 presents these results. No significant correlation was found between Telislife and speech recognition scores with speechreading (r = .21, p = .13) as well as between the NCIQ score and speech recognition score with or without speechreading (r = .12, p = .39, and r = .26, p = .059, respectively).

Exploratory Analyses of Telislife Scores in Relationship to Demographics

To further investigate Telislife scores regarding our CI population demographics, we performed a one-way ANOVA for all Telislife scores subcategories on the patients gender (F = 0.65, p = .65), CI experience (F = 1.09, p = .38), CI brand (F = 0.85, p = .6), and phone usage time (F = 1.39, p = .14), all nonsignificant. However, the analysis was significant for both age (F = 4.31, p = .02) and deafness onset (F = 5.42, p = .002) variables. Post hoc analyses (Tukey's HSD) for these latter two variables were found to be with significant effects for the Telislife "speech production" subdomain with age category of 45-65 years being significantly higher in comparison to age category of 65-85 years (mean scores = 84.27 and 68.89, respectively, p = .03) and pre-or paralingual deafness onset being significantly lower compared to postlingual deafness (F = 4.71, p = .035). Similarly, the Telislife "speech recognition in favorable situations" subdomain significantly varied depending on the deafness onset subcategory with subjects with pre-or paralingual deafness presenting lower scores than the ones with postlingual deafness (F = 8.78, p = .004). Finally, no significant correlation was to be found between the continuous variable "deafness duration" with any of the Telislife subdomains scores (Telislife total score, r = -.0894, p = .541), Telislife "voice perception" subdomain (r = .1183, p = .418), Telislife "speech recognition in favorable situations" subdomain (r = -.15, p = .31), Telislife "speech recognition in complex situations" subdomain (r = -.03, p = .81), and Telislife "speech production" subdomain (r = -.26, p = .08).

Discussion

The purpose of the study was to develop and test a new clinical tool that assesses both audiometric performance and QoL in CI users. We developed the Telislife, a 20-item questionnaire evaluating the ability of CI users to use the telephone. We found a significant correlation between Telislife scores and both speech recognition scores without speechreading and scores on the 60-item NCIQ.

Telephone Use in CI Users

CI recipients from our sample use a telephone, mostly to have audio conversations (72.2%), much in line with what was reported in former studies [START_REF] Anderson | Telephone use: What benefit do cochlear implant users receive[END_REF][START_REF] Cray | An investigation of telephone use among cochlear implant recipients[END_REF][START_REF] Sousa | Telephone usage and cochlear implant: Auditory training benefits[END_REF]. Most (74.5%) use audio communication over the telephone without a dedicated accessory, directly through the audio output or loudspeaker of their telephone (75.5%). It therefore makes sense to evaluate telephone use in patients with CI as they do use their telephone and use it for speech communication in most cases, even if 27.8% of the respondents in our study used their phone almost exclusively for visual applications such as surfing the Internet, texting/messaging, or using apps. These results could be influenced by sampling bias in our study: The sample of respondents was relatively aged, with 38% of the participants being over 65 years and only 16% being below 45 years. This bias was also reflected in the types of phones used, with 59.6% of respondents using smartphones and 38.5% of respondents using feature phones. The Telislife questionnaire therefore captures a relevant dimension of CI outcomes, namely, telephone usage, and can be used over a broad range of users. Undoubtedly, a whole dimension of economic cost would have to be taken account, as nowadays, the prices of mobile phones are extremely increasing, especially mobile Internet telephony considered with better intelligibility and quality [START_REF] Guignard | Mobile Internet telephony improves speech intelligibility and quality for cochlear implant recipients[END_REF] in comparison to GSM mobiles-along with all associated CI communication accessories such as audio cables.

The Telislife Questionnaire

The Telislife questionnaire was first evaluated by analyzing response patterns across all participants. Responses were in general valid, with 80.9% of valid questionnaires and a global proportion of NA responses below 5%. This suggests that most respondents could understand and rate the different items and that chosen items actually matched with realistic situations that respondents understand and experience. The fact that all possible Likert ratings over the selected 5-point scales were used for almost all items (only the max score of 5 was not used for two items) also suggests that the rating scales are appropriate and do capture the variety of experiences and opinions about the depicted telephone use situations. Along the same lines, the total scores Note. To correct for multiple comparisons, the alpha value was corrected to p = .0125. Significant correlations at corrected p threshold are indicated in bold.

followed a normal distribution, with an average and median values quite close to each other and not too far from the center of the distribution at 50%, showing a good variability of the total score allowing to differentiate between CI users who have both low and high ability with telephone usage. Reliability was rather high with a Cronbach's α of .91, and split-half reliability at r = .87, suggesting that the questionnaire showed a high internal consistency overall [START_REF] Slattery | A practical guide to surveys and questionnaires[END_REF]. The subdomains also showed some relevance with a high reliability for the subdomains speech "favorable situations" and speech "complex situations," with the three other subdomains showing, however, lower reliability levels. All subdomains participated to the global score, with significant correlations to the global score without being equivalent to it (except for the subdomain speech "favorable situations," which was nonsignificantly different from the global score).

Construct Validity

Associations Between Telephone Ability and QoL

Global Telislife and NCIQ scores were highly positively correlated. The Telislife global score was significantly correlated to all subdomains of the NCIQ, with r values ranging from .48 to .70, respectively, for subdomains Self-Esteem on the one hand and Advanced Speech Perception and Speech Production of the NCIQ on the other hand. Even if it showed a weaker correlation, it is interesting to note that telephone use is associated with self-esteem. This is suggesting again that telephone use is an important ability for CI users, contributing to their QoL beyond speech recognition. This observation is important as some authors have shown that psychological aspects associated with CI rehabilitation and, in particular, positive self-esteem were an important factor for patients' satisfaction toward CIs [START_REF] Kobosko | Satisfaction with cochlear implants in postlingually deaf adults and its nonaudiological predictors: Psychological distress, coping strategies, and self-esteem[END_REF]. It is thus important that this dimension can also be, at least partially, tackled with our short questionnaire. From these observations, we can consider that the Telislife shows good construct validity and constitutes a reliable tool to assess CI outcomes.

Association Between Telephone Ability and Speech Perception

Telislife scores show a significant positive correlation with speech recognition score without speechreading but not with speech recognition with speechreading. In a previous study, we found a relationship between the ability of CI users to use the telephone and speech perception [START_REF] Rumeau | Quality of life and audiologic performance through the ability to phone of cochlear implant users[END_REF]-in particular, between CI users' ability to have a telephone discussion with an unknown person and QoL as evaluated with the NCIQ as well as speech perception without speechreading. This discrepancy between the two speech perception tests, with or without speechreading, can be explained by at least two aspects. First, speech interactions over the telephone are still mostly done in an auditory-only mode, that is, without seeing the interlocutor's face, and therefore, it seems logical that speech perception scores without speechreading better describe the telephone communication experience of CI users. Second, speech scores with speechreading tend to show ceiling effects, with some patients scoring close to 100% leading to less interindividual variability in the scores, compared with the scores without speechreading. This suggests that the Telislife has a relatively good construct validity and would capture speech recognition information better than the NCIQ in telephone-listening situations.

Clinical Implications

Our results indicate that measuring telephone ability in CI users with the Telislife is clinically relevant, as it is correlated with QoL and speech identification yet captures broader aspects of functioning. The Telislife contains 20 items and is therefore an efficient patient-reported outcomes measure of the impact of CIs. From a practical point, with the raise of awareness of training session using telephones [START_REF] Borel | Rehabilitation of telephone communication in cochlear-implanted adults[END_REF], Telislife scores could be used as tool to assess subjects' progress on a long-term period. Hence, with the current direction toward telerehabilitation, the questionnaire could be a practical tool to indicate which subjects could be able to participate in telephone therapy or trainings. Finally, having clinical feedback on the ability of CI users to use the phone is crucial to improve the current CI features and their usability in CI users' daily life. Further analyses of Telislife scores regarding demographics would allow to establish more distinct profiles of patient.

Limitations and Future Research

This article presents the Telislife questionnaire and the first steps of its validation. It would have been interesting to pilot test the items with the target population, for example, using the think-aloud method (cognitive validation). We would have liked to validate the four intended subdomains and conduct a confirmatory factor analysis: This was, however, not possible given the limited sample size. This will be performed in a larger sample of respondents. Similarly, the test-retest reliability of the Telislife, documenting whether scores are stable over time, must be documented. Moreover, it would be intersting to test the subjects in phone-listening situations instead of Lafon measures in the booth because of lack of compression and limited bandwidth in the latter situation, despite sharing the common component of lacking visual cues. Besides, another set of stimuli, including context-related sentences, would have been advantegeous to include in our design as these would give more insights in comparable phone-listening situations of daily life. Finally, as age difference and deafness onset were found to be significant on Telislife subdomain scores, it could be interesting to assess the possibility to refine the understanding of how these scores vary in different subpopulations of CI users (with age, with experience, with type of solution; i.e., unilateral/bilateral/bimodal) for further research projects on wider CI user populations.

Conclusions

The current study confirmed the central role of the ability to telephone for patients with CI in their daily communication ability despite the need of further investigations. We found a significant correlation between Telislife scores and both speech recognition and QoL scores. This questionnaire is a reliable tool to evaluate CI outcomes in clinical practice.

Figure 1 .

 1 Figure 1. (A) Histogram distribution of total Telislife scores and comparison to the theoretical normal distribution (dotted line). (B) Scatter plots of the individual scores showing the distribution of the individual total scores and scores for each Telislife subdomain. The cross represents the mean and standard error of mean.

Figure 3 .

 3 Figure 3. Correlation between Telislife scores and speech perception scores (Lafon monosyllabic words) obtained in the auditory-only condition, without speechreading. Dotted lines show linear regression and 95% confidence interval.

Figure 2 .

 2 Figure 2. Correlation between Telislife and Nijmegen Cochlear Implant Questionnaire (NCIQ) scores. Black lines show linear regression and 95% confidence interval.

Table 1 .

 1 Demographic characteristics of the 55 respondents.

	Characteristic		n	Proportion (%)
	Gender	Female	29	52.7
		Male	26	47.3
	Age groups	18-45 years	9	16.4
		45-65 years	25	45.4
		65-85 years	21	38.2
	Implantation type	Unilateral	42	76.4
		Bilateral	13	23.6
	CI brands	Oticon Medical	35	63.6
		Med-El	11	20.0
		Cochlear	7	12.7
		Unknown	2	3.6
	CI experience	1-2 years	14	25.5
		2-4 years	10	18.2
		> 4 years	30	54.5
		Unknown	1	1.8
	Deafness onset	Pre-or paralingual	10	18.2
		Postlingual	41	74.5
		Unknown	4	7.3

Table 2 .

 2 Summary of correlations between the total score and the four subdomains of the Telislife.

	Telislife scores and subdomains	Voice	Speech favorable	Speech complex	Speech production
	Total score	.89	.95	.90	.63
	r(53) =	p < .0125	p < .0125	p < .0125	p < .0125

Bolzer et al.: The Development of the "Telislife" Questionnaire 187

Journal of Speech, Language, and Hearing Research • Vol. 64 • 186-195 • January 2021

Acknowledgments

The authors express their gratitude to the 68 patients who contributed to this study by completing the questionnaires.

Table 3. Correlations between the total scores and main subdomains evaluated by the Telislife questionnaire and the Nijmegen Cochlear Implant Questionnaire (NCIQ). Note. To correct for multiple comparisons, the alpha value was corrected to p = .001. Significant correlations at corrected p threshold are indicated in bold.

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee (committee "Comité de Réflexion Ethique Nancéien Hospitalo-Universitaire"), who approved the protocol on February 23, 2016, and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed Consent

Informed consent was obtained from all individual participants included in the study.

Copyright of Journal of Speech, Language & Hearing Research is the property of American Speech-Language-Hearing Association and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.


Xiaojiang Li

Peisong Peng

Grgory Geneste

Alireza Akbarzadeh

Sergey Prosandeev

L Bellaiche

Diyar Talbayev

Hichem Dammak

THz pulse-induced second harmonic generation and Kerr effect in quantum paraelectric KTaO 3

I. INTRODUCTION

The ultrafast optical control of ferroic orders in crystals presents both challenging fundamental questions and exciting technological opportunities 1-3 . Among the multitude of optical control schemes for various ferroic order parameters, we focus here on the control of the ferroelectric dipole moment using terahertz electric field transients. While other schemes for manipulating the ferroelectric order may be feasible [4][5][6][7][8][9][10][11][12][13] , this method of control is appealing due to its conceptual simplicity -electric field E couples directly to the electric dipole d via the -d • E energy term. The ferroelectric instability is often driven by the soft phonon mode that is resonant with the THz electric field, which means that this frequency approaches the fastest possible ferroelectric switching rates 14 . Despite a significant amount of theoretical and experimental effort in pursuit of terahertz switching of the static ferroelectric polarization in recent years, this particular goal remains elusive.

While the switching of the static polarization with a THz pulse has not been demonstrated yet, significant theoretical and experimental achievements took place in modeling the ferroelectric response, driving the soft mode phonons in nonlinear anharmonic regimes, and discovery of novel metastable ferroelectric states. An early theoretical proposal for THz control of ferroelectric polarization belongs to Qi et al., who deployed a train of THz pulses to effect a polarization reversal in PbTiO 3 in their molecular dynamics simulations 15 .

Prosandeev et al. also used a THz pulse train to computationally discover hidden metastable phases and neuromorphic computing functionality in the prototype relaxor ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 and in the antiferroelectric NaNbO 3 16,17 . Zhuang and Hu discovered the significance of polarization-photon coupling in increasing the soft phonon damping in a strained single-domain ferroelectic film 18 . Experimental exploration and understanding of nonlinear anharmonic phonon motion was advanced in quantum paraelectric SrTiO 3 19,20 and in ferroelectrics BaTiO 3 and LiNbO 3 [21][22][23] . Large THz-induced polarization modulation and associated changes in the electronic state of the magnetic ion were reported in the ferroelectric antiferromagnet BiFeO 3 24,25 . Modulation of the electronic states and THzinduced polar charge order was documented in organic molecular materials 26,27 . Excitation of high-frequency phonons and hidden metastable ferroelectricity driven by THz pulses were observed in quantum paraelectric SrTiO 3 28,29 .

The quantum paraelectric KTaO 3 (KTO) belongs to the perovskite family and has been intensively studied since the middle of last century [30][31][32][33][34][35] . KTO has a simple cubic structure with space group P m 3m (No.221) at room temperature and holds the cubic structure down to at least 10 K 33,36 . The quantum paralectric state results from the competitions among antiferrodistortive structural phase transition, ferroelectric ordering and quantum fluctuation below certain threshold temperatures 37 . KTO single crystal exhibits many interesting physical properties such as two-dimensional electron gas 38 , superconductivity under electrostatic carrier doping 39 and metal-insulator transitions 40 . Temperature-dependent dielectric constant of KTO increases continuously as the temperature drops down to 8 K and levels off toward 0 K without undergoing ferroelectric phase transition 41 . More interestingly, even though the long-range ferroelectric order is banned at low temperature, the local polar phase can still exist with R 0 /a ≈ 4 in both doped and nominally pure KTO 34,42 , where a is the lattice constant and R 0 is the size of ferroelectric nanoregion. So in the low temperature regime, the phase diagram of KTO crystal is almost temperature independent, but very sensitive to the external stimuli, such as electromagnetic irradiation or strain. These properties make KTO an ideal material for studying nonlinear phonon dynamics and ultrafast optical control. The TO 1 soft mode in KTO can be described very well by the mean-field Barrett formula 31,43,44 . By fitting the experimental data with such formula, Chen et al. found that the classical Curie temperature of KTO should be 1.6 K, the temperature at which the instability begins is 32 K, and the dielectric constant depends significantly on the external dc electric field 43 .

In this article, we study both experimentally and computationally the excitation of KTO with strong THz electric field pulses. The material's response is measured using two femtosecond optical probes: one is the THz-field-induced second-harmonic generation (TFISH) 45,46 and the other is the THz-induced polarization rotation (THz Kerr effect, or TKE) 47,48 . We interpret the TFISH probe as the indicator of the dipolar response, which is proportional to the degree of the inversion symmetry breaking. We find that the dipolar polarization response is rather short lived and well described in the picture of effective Hamiltonians applicable to this material. Our effective Hamiltonian simulations reproduce the experimentally observed temperature dependence of the TFISH response strength and the hardening of the driven soft mode oscillations with increasing THz peak field. We also find a novel long-lived metastable state detected via THz Kerr effect. The discovery of this hidden metastable state opens the door for its potential applications, for example, as in 3

Phys. Rev. B, 107 (2023) 064306.

novel neuromorphic computing architectures 16,17 .

II. EXPERIMENTAL AND COMPUTATIONAL RESULTS

We report optical time-resolved studies of KTO where we use intense single-cycle THz pulses are as the excitation. We employ optical rectification in a LiNbO 3 prism and tiltedwavefront phase matching to generate the THz pulses from femtosecond pulses with 800 nm center wavelength 49,50 . A small portion of the femtosecond pulse energy is split off before THz generation and is used as an optical probe pulse. Both the TFISH and TKE are measured with the probe beam transmitted through the sample. For the TFISH experiment, the polarization directions of the THz pump and the optical probe pulses are both set along the [100] direction in the KTO crystal. In the TKE experiment, the THz electric field is polarized along the [100] direction and the optical beam is polarized linearly at 45 • from the THz beam. The TFISH intensity is measured using a GaP photodiode and a blue filter after the KTO sample, which eliminates the fundamental 800 nm wavelength from the detected light. The KTO sample used here is a commercial product from MSE Supplies cut in the (100) direction with double-side polished surfaces.

A. TFISH

KTO crystal possesses inversion symmetry, so that no second-harmonic generation can occur in the equilibrium state. The presence of the strong THz electric field causes a bulk polarization of the crystal, which breaks the inversion symmetry and leads to the detection of the TFISH intensity. Therefore, TFISH intensity serves as an optical probe of polarization.

The TFISH intensity rises with the arrival of the THz electric field and decays within a few picoseconds after the THz pulse, Figure 1(a). Only positive values of the TFISH intensity are recorded because it is measured as a difference in the intensity of the TFISH light with and without the THz field, and the latter intensity is zero. This is in contrast to the measurements in noncentrosymmetric media where both positive and negative TFISH intensity can be observed 45,51 . shows the corresponding frequency domain spectra of the TFISH measurement, where the Fourier transform was performed on the derivative of the time-domain signals in Fig. 1(a).

The dependence of the frequency-domain spectra on the strength of the incident THz field at 15 K is shown in Fig. 1(c). The THz-field-induced second-order polarization p 2ω is described as a third-order nonlinear term

p 2ω ∝ χ (3) (ω T Hz , ω, ω)E T Hz (E ω ) 2 , ( 1
)
where E T Hz denotes the THz electric field and E ω denotes the electric field of the optical probe pulse. Our experiment measures TFISH intensity I 2ω that must scale as the square of the THz electric field: The TFISH oscillation occurs at double the frequency of the TO1 phonon motion because we measure the intensity of the second harmonic light, which is positive for both positive and negative phonon coordinates. The discrepancy between the cited values of the TO1 frequency in literature 31,32,41 and the TFISH frequency-domain peaks near 2 THz in Fig. 1(b) is rather high. We explain it by a combination of two factors. First, the strongest time-domain TFISH peaks represent the driven soft phonon motion and not its free oscillation. Second, when the soft mode is driven by a strong THz field to high amplitudes, a considerable hardening of the mode frequency can be expected due to the anharmonicity of the lattice potential.

I 2ω ∝ (p 2ω ) 2 ∝ E T Hz 2 .
Indeed, our effective Hamiltonian simulations described in a later section show significant increase in the soft mode frequency above 40 kV/cm peak THz electric field, Fig. 6(c).

B. TKE

The complementary TKE measurement is conducted right after the TFISH experiment.

TKE is a third order nonlinear optical effect that results from an additional polarization oscillating at the fundamental frequency of the probe beam 47,48 :

p ω ∝ χ (3) (ω T Hz , ω T Hz , ω)(E T Hz ) 2 E ω , ( 2
)
where χ (3) (ω T Hz , ω T Hz , ω) is the third order nonlinear susceptibility. The refractive index of the specimen changes proportionally to (E T Hz ) 2 according to Eq. ( 2), which leads to the polarization rotation of the probe beam E ω . Figure 2

α = α 0 + k ( ∂α ∂Q k )Q k + 1 2 k,k ( ∂ 2 α ∂Q k ∂Q k )Q k Q k + ... ( 3
)
The linear term of Q k in Eq. ( 3) is responsible for the first-order Raman scattering, while the quadratic term accounts for the second-order effect. Since the KTO crystal has cubic structure with inversion symmetry, all long-wavelength phonons at Γ point in k space have odd parity. As a result, the first-order Raman scattering in Eq. ( 3) is forbidden by selection rules.

The second-order Raman scattering is allowed and corresponds to the two-phonon response and results in the observed frequency-doubling behavior in our TKE measurement 35,[START_REF] Allodi | [END_REF] . As with TFISH, the frequency doubling is not exact due to the hardening of the soft mode frequency when it is driven to high amplitudes by strong THz fields.

Figure 3 shows the TKE measurements extended to long probe delay times. The oscillatory component at early time delays is not visible because of a long time step used in the collection of data in the figure. We observe that the TKE signal at low temperatures persists for over 100 ps. The small jumps at 31 ps are due to a copy of the main pump pulse from the reflection on the surfaces of a silicon wafer placed in the THz beam path as a filter. We used the biexponential function

f = A exp -(t -t 0 ) τ 1 + B exp -(t -t 0 ) τ 2 (4

C. Simulation

We performed simulations to better understand the effect of the temperature and the peak electric field of the THz pump pulse on the measured TFISH response. We used the effective Hamiltonian developed by Akbarzadeh et al. 55 and applied the RPMD (Ring Polymer Molecular-Dynamics) method 56 to take into account the nuclear quantum effects.

This Hamiltonian had been used to reproduce the quantum paraelectric behavior of KTO by the PIMC (Path-Integral Monte Carlo) method using a product P × T = 600, where P is the so-called Trotter number and T is the temperature 55 . In the present simulation, the soft-mode mass is slightly modified so that the frequency of the TO 1 mode is the closest to the experimentally measured one in the 10-150 K temperature range (Fig. 4). It is chosen equal to m = 80 g•mol -1 instead of 95.6 g•mol -1 . Indeed, the experimental value of this frequency at 20 K is equal to 0.66 THz, and calculations give values equal to 0.45 and 0.67 THz for an effective mass equal to 95.6 and 80 g/mol, respectively. Note that Phys. Rev. B, 107 (2023) 064306.

the frequency ratio (1.49) differs from the inverse of the square root of the mass ratio (1.09). This is due to the anharmonicity of the potential and nuclear quantum effects.

The inhomogeneous-deformation mode mass equals the KTaO 3 'molecule' mass, and the product P × T is equal to 1280. KTO is simulated in the isothermal-isobaric ensemble by using the extended Langevin thermostat 57,[START_REF] Quigley | Europhysics Conference on Computational Physics 2004[END_REF] that was previously implemented to study barium titanate [START_REF] Geneste | [END_REF] Experimental results are those from Ref. [49].

To calculate the frequency of the TO mode, we first determined the effective-potential energy vs. reduced polarization curve at T = 20 K using the method based on the integration of the average force under constrained polarization 60 . Figure 5(a) shows the curves obtained for a polarization along the [100] direction that can be fitted using the following expression:

V (u) = a 2 0 1 2 k u 2 + 1 4 b u 4 + 1 6 c u 6 (5)
where a 0 = 0.398 nm is the cell-parameter, u is the reduced soft-mode coordinate, k = k/m is equal to 0.67 THz which is close to the reported experimental values 31,32,41,52 .

Moreover, the RPMD method allows the calculation of temporal correlation functions in a satisfactory way for a short duration of a few oscillations 61 . We used it to predict the frequency of the TO 1 mode from the position of the peak of the imaginary susceptibility according to the following expression [START_REF] Kubo | Statistical physics II: nonequilibrium statistical mechanics[END_REF] :

χ (ω) = β ω 1 -e -β ω 1 V 3ε 0 k B T Re ω +∞ -∞
e iωt P(0) • P(t) dt (6) where P = Z * ea 0 N i=1 u i is the total electric dipole moment of the system, V = Na 3 0 is its volume, Z * e is the effective charge of the soft-mode, a 0 is the cell-parameter, and u i is the reduced polarisation of the i th cell. In practice, it is useful to calculate χ using the following approximation for a time length of τ :

χ (ω) β ω 1 -e -β ω 1 V 3ε 0 k B T ω τ τ 0 e iωt P(t) dt 2 (7)
At T=20 K under no field, the peak is at 0.64 ± 0.02 THz, which is a value very close to the one deduced from the effective potential. This comparison shows us that we can follow the system's dynamics over several ps to study the response of KTO to the pulse. Figure 4 shows that the present effective Hamiltonian and the RPMD method capture with very good accuracy the experimental-temperature dependence of the soft mode's frequency in KTO 31,32,41,52 .

Phys. Rev. B, 107 (2023) 064306.

To choose the amplitude values of the pulse's electric field, we have determined the induced polarization as a function of the external field, E, which corresponds to the position of the curve-minimum of the V (u) -E u function, Fig. 5(b). Figure 5(c) shows that at 20 K, the simulated response remains linear for a field below about 40 kV/cm. We simulated the ferroelectric response of KTO using a realistic time-domain THz pulse.

For a given temperature and a given peak field of the THz pulse (E T Hz max ), the curves of Fig. 6 are obtained by averaging through six independent trajectories. Since the intensity measured during the TFISH experiments appears proportional to (E T Hz max ) 2 , we focus on the square of the polarization induced by the pulse, u 2 , assuming that the response is quasilinear, Fig. 6(a). In addition, the Fourier transform amplitude of u 2 is reduced by using the following expression:

1 V 3ε 0 k B T ω τ τ 0 e iωt p 2 (t) dt (8)
where p = Z * e a 0 u is the average polarization per unit-cell, and τ = 12 ps.

Figure 6(b) shows that the peak Fourier transform frequency increases with increasing temperature. According to Fig. 4, this behavior is expected since this frequency is assumed to be the second harmonic of the TO 1 soft mode. However, the value of this frequency, at 20 K for example, is equal to 1.94 ± 0.02 THz for E T Hz max = 60 kV/cm, and it is higher than twice the frequency of the TO 1 mode, i.e., 1.34 THz for zero field, Fig. 4. This difference occurs because the strong THz electric field drives the soft mode coordinate into anharmonic regime, where the restoring force near the extremal points of the phonon motion exceeds the harmonic restoring force, Fig. 5(a). The resulting anharmonic hardening of the soft mode frequencies is observed in the simulation results of Fig. 6 fields cited in Figs. 5,6 are internal electric fields in the material. The highest TFISH oscillation frequency of 1.9 THz is observed at the peak incident field of 210 kV/cm (7.5 kV/cm internal peak field) in the experiment, Fig. 1(c). In computation, a comparable effect on the soft mode frequency is induced by 80 kV/cm peak internal field, Fig. 6(c).

Therefore, the computation overestimates the experimental electric field by about an order of magnitude. This situation is common in effective Hamiltonian simulations of ferroelectric and related materials and is known as the Landauer paradox [START_REF] Prosandeev | [END_REF] , which arises due to the contribution of the depolarizing field to the domain activation energy, making this activation significantly higher than observed in experiments.

We offer another interpretation of the effect of the strong THz electric field on the observed soft mode frequencies. Indeed, given the large ratio of the optical frequency used to probe 13 Phys. Rev. B, 107 (2023) 064306.

the induced polarization and that of the pulse (375 THz/1 THz), we can view KTO as being subjected to a static electric field at the time scale of the intensity measurement (0.1 ps).

The harmonic approximation of the modified effective potential V (u) -Eu, Fig. 5(b), then allows to estimate the frequency of the TO 1 mode as a function of E. According to Fig. 5(d), the second harmonic of the TO 1 mode at 60 kV/cm would correspond to 1.916 THz, which is in remarkable agreement with the value found in Fig. 6 (b). Similarly, the dependence of the peak frequency with increasing pulse amplitude in Fig. 6(c) follows the dependence of the soft mode frequency on the applied static electric field shown in Fig. 5(d).

III. DISCUSSION

By far, the most striking observation from the two complementary measurements, TFISH and TKE, is the order-of-magnitude difference between the non-oscillatory relaxation time τ 1 of TKE and τ of TFISH. The relaxation times for TKE is more than 20 times larger than TFISH from close to room temperature down to 8 K, Fig. 3. This difference is even more puzzling when the TFISH and TKE relaxation times are compared with the free induction decay time of the soft phonon mode, which was measured by THz and hyper-Raman spectroscopy 41,64 . The soft mode damping constant γ/2π = 0.06 THz in the 10-50 K range, and corresponding free induction decay time 2τ = 2/γ = 5.3 ps. The decay time of the square of the soft phonon mode coordinate u 2 (t) is τ = 2.7 ps. The latter number is of the comparable order of magnitude, but still much higher than the measured TFISH relaxation time 0.6-1.6 ps in the 10 -50 K range, Fig. 3. The phonon free induction decay time is also more than an order of magnitude lower than our measured relaxation time of TKE. Thus rises the question of the origin of the observed TFISH and TKE relaxation times.

The shorter relaxation time of TFISH compared to the phonon free induction decay can be explained by postulating the presence of an inhomogeneity in the material. Experimental and theoretical evidence suggests the existence of polar micro-or nano-regions in an overall paraelectric KTaO 3 crystal 34,55 . Let us label the spontaneous polarization of such polar micro/nano-regions as P i . There is no macroscopic polarization, so we set i P i = 0, where the index i runs over all polar regions (PRs). The THz pulse induces linear polarization p i in each PR. (For simplicity, P i and p i denote the scalar components of the three-dimensional 14 Phys. Rev. B, 107 (2023) 064306. polarization vectors along the direction of the THz electric field.) The presence of both P i and p i allows optical second order polarization and SHG when a fundamental optical wave E ω with intensity I ω traverses the KTO crystal. From this perspective, the earlier Eq. ( 1) can be re-written as :

p 2ω i ∝ [α(P i + p i )](E ω ) 2 ∝ (P i + p i )I ω , ( 9
)
where α is the hyper-Raman tensor 65 . The total intensity I 2ω of the emitted second harmonic light is due to the macroscopic second order polarization that can be obtained after summing over all PRs:

I 2ω ∝ i (P i + p i ) 2 (I ω ) 2 . ( 10
)
In our TFISH experiments, we measure the difference between the second harmonic intensity with and without the THz pulse:

I T F ISH ∝ ⎡ ⎣ i (P i + p i ) 2 - i (P i ) 2 ⎤ ⎦ (I ω ) 2 = ⎡ ⎣ 2 i P i i p i + i p i 2 ⎤ ⎦ (I ω ) 2 . ( 11
)
Because i P i = 0, we find

I T F ISH ∝ i p 2 i + 2 i =j p i p j (I ω ) 2 . ( 12
)
The quantity in the square brackets is dominated by the second summation of the products p i p j , because the first sum in brackets contains vanishingly fewer terms compared to the second sum (in a p i p j matrix, the first sum is the sum of the diagonal elements and the second sum is the sum of all other elements in the matrix) and because the THz-induced polarizations p i in each PR start their time evolution in-phase with each other after the excitation by the THz pulse. Hence, the second sum in brackets in Eq. ( 12) will determine the time evolution of the TFISH signal. If there exists an inhomogeneity that results in a fast dephasing of the induced polarizations between different PRs, then TFISH intensity in Eq. ( 12) can decay in time faster than the decay of the squares of individual polarizations p 2 i . Thus, the faster relaxation of the TFISH intensity compared with the phonon free induction decay can be the result of an intrinsic inhomogeneity in the material, although our measurement does not establish the nature of the inhomogeneity.

Phys. Rev. B, 107 (2023) 064306.

On the other hand, TKE results from the third-order nonlinear polarization that scales as (E T Hz ) 2 , Eq. ( 2). In a homogeneous medium of length L 47 , the intensity of the TKE signal is related to the change in refractive index Δn caused by the application of THz electric field: I T KE = (ΔnωL/c)I ω . In an inhomogeneous medium with PRs carrying spontaneous polarizations P i , as above, the refractive index change Δn i in each PR contributes to the TKE intensity

I T KE ∝ i Δn i I ω . ( 13
)
The dependence of refractive index on the electric polarization can be written as

n i = n 0 + n 2 (P i + p i ) 2
, where the polarization p i is induced by the THz electric field. Then

I T KE ∝ n 2 i (P i + p i ) 2 -P 2 i I ω = n 2 i 2P i p i + p 2 i I ω , ( 14
)
where the sum in the square brackets is dominated by the second term because i P i = 0.

Thus,

I T KE ∝ n 2 i p 2 i I ω . ( 15
)
Comparing Eqs. ( 12) and ( 15), we observe that the inhomogeneous dephasing term containing the products p i p j with i = j is absent from the TKE intensity, unlike the TFISH intensity. The absence of the inhomogeneous dephasing term in Eq. (15) means that TKE relaxation time can be much longer than the TFISH relaxation time, as found in the experiment. (We note that the initial in-phase motions of polarizations p i result in the coherent oscillation of the TKE intensity observed in experiment during the first 1-2 ps, Fig. 2, which is superimposed on the long-lived exponential background resulting from the incoherent contributions of PRs to the sum in Eq. ( 15).) The TKE relaxation time can be even longer than the phonon decay times measured by THz spectroscopy 41 , because the latter measurement includes the inhomogeneous broadening. Nevertheless, the nearly order-of-magnitude difference at low temperature between the measured phonon decay times 41,64 (2τ = 2/γ = 5.3 ps) and the TKE relaxation time, Fig. 3, remains remarkable. Our measurement does not identify the mechanism for such slow THz-induced dynamics. If allowed to speculate, we can borrow the notion of molecular orientational relaxation in liquids 47 and associate it with the orientational motion of PRs. This nematic orientation occurs along or opposite the direction of the applied THz field, as suggested by its coupling to the square of the field, Phys. Rev. B, 107 (2023) 064306.

(E T Hz ) 2 , and is characterized by the very long measured relaxation times, Fig. 3. This long-lived metastable state can be classified as a hidden THz-induced phase in KTO, as it is not accessible by other, thermodynamic routes.

IV. SUMMARY

We studied the response of quantum paraelectric KTaO 3 to intense THz pulses experimentally using the complimentary TFISH and TKE measurements and computationally using effective Hamiltonian methods. We observed the coherent excitation of the soft phonon mode in the material with both experiment and computation. In computation, we observed the increase in the frequency of the soft mode with the THz peak field strength. The computation largely reproduces the experimental observations with TFISH. Most strikingly, we found dramatically different relaxation times for the TFISH and TKE responses in the experiment. We show that the short relaxation of the TFISH can result from intrinsic inhomogeneity in KTO, such as from the previously suggested polar nanoregions 34,55 . The TKE measurement is insensitive to this inhomogeneity, which partially explains the disparity in the TFISH and TKE relaxation times. We also propose that other, slower dynamics may be contributing to the long-lived THz-induced polarization rotation. Very speculatively, such dynamics can be associated with the orientational motion of the polar nanoregions, which exist due to the material's proximity to the ferroelectric phase transition 55 . The persistent state observed via TKE can be categorized as a hidden metastable phase 29 with prospective novel applications in THz frequency electronics 16,17 .

Figure 1

 1 Figure 1(a) shows the temperature dependence of the time-resolved TFISH signal. The peak strength of TFISH gradually diminishes with increasing temperature. Figure 1(b)

FIG. 1 :

 1 FIG. 1: (Color online) THz field induced second-harmonic generation spectra. (a) Time domain spectra under various temperatures with incident THz peak field E = 210 kV/cm. Dashed line shows the excitation THz pulse. (b) Frequency domain spectra corresponding to the measurements in (a). First derivatives of the interpolated time domain spectroscopy were calculated before the Fourier transform to reduce the relative amplitude of the non-oscillatory signal. Inset: Fourier transform of the excitation THz pulse from (a). (c) Frequency domain spectra under various incident peak THz electric fields at 15 K. Inset: Peak values of TFISH time domain spectra vs. peak THz electric field. The red dots show the experimental data and the blue solid line is the quadratic function.

  The inset of Fig. 1(c) shows the normalized peak TFISH intensity in time domain as a function of the normalized peak THz electric field. The measurements fall almost perfectly on the parabolic function, which confirms the Phys. Rev. B, 107 (2023) 064306. quadratic scaling of the TFISH intensity with the THz electric field.The observed time-dependence of the TFISH signal consists of a sharp rise in intensity followed by a fast decay on which an oscillatory component is superimposed, Fig.1(a). We interpret the oscillation as the signature of the coherent motion of the TO1 soft phonon mode driven by the THz electric field. The TFISH intensity I 2ω is strongest when the phonon coordinate is at its extremal positive and negative values, because this corresponds to the maximal degree of inversion symmetry breaking in the paraelectric phase of KTO. The first three peaks in TFISH intensity in Fig.1(a) are mainly driven directly by the THz pulse packet and correspond to the extrema (positive and negative) of the THz electric field, as is evident from the comparison of the THz pump pulse shown as a dashed line in Fig.1(a)with the TFISH response. The weaker TFISH oscillation that follows the first three peaks represents the free induction decay of the TO1 soft phonon mode. The frequency-domain TFISH spectra in Fig.1(b) peak near 2 THz, close to double the frequency of the soft mode in KTO, which is placed in the 0.53 -0.65 THz range at 10 K by various measurements31,32,41,52 .

  (a) shows the temperature dependence of the time-domain TKE spectra that consist of a sharp rise and a slow decay on which an oscillatory component is superimposed. This behavior is a qualitatively similar to the TFISH response in Fig.1. In a major difference, the non-oscillatory TKE component relaxes much slower than that in TFISH measurement, specifically τ T KE > 100 ps at 8 K while τ T F ISH ∼ 1 ps at 11 K. Figure 2(b) shows the amplitude of the Fourier transform of the derivative of the data in Fig. 2(a), while Fig. 2(c) displays the dependence of the frequency-domain TKE spectra on the peak strength of the incident THz field at T = 15 K. The frequencydomain spectra in Figs. 2(b,c) peak approximately near twice the frequency of the TO1 soft phonon mode, similar to the frequency-domain TFISH spectra. The frequency of the TKE peak increases as we increase the external field, Fig. 2(c), with a similar increase of observed in the TFISH spectra, Fig. 1(c). The inset of Fig. 2(c) displays the dependence of normalized peak TKE response on the normalized peak THz electric field, which closely follows a quadratic function. This quadratic behavior follows from the description of TKE as the third order nonlinearity that scales as the square of incident THz field, (E T Hz ) 2 , according to Eq. (2).

Figure 2 (

 2 Figure 2(b) shows that the oscillation in TKE is governed by the doubling of the soft mode frequency, similar to the TFISH measurements. However, the underlying mechanism of the frequency doubling is quite different. The TKE measures the change of refractive index of the crystal, or in other words, the change in polarizability α. We can expand the polarizability as a series in normal phonon coordinates Q of the crystal 53 :

7 Phys.

 7 Rev. B, 107 (2023) 064306.

FIG. 2 :

 2 FIG. 2: (Color online) THz field induced Kerr effect spectra. (a) Time domain TKE spectra under various temperatures with incident THz peak field E = 210 kV/cm. (b) The frequency domain spectra corresponding to the measurements in (a). (c) Frequency domain spectra under various incident THz electric field at 15 K. Inset: the peak values of TKE time domain spectra vs. peak THz electric field, red dots are the experimental data and the blue solid line is the quadratic function.

Fig. 3 .

 3 Fig. 3. The relaxation time from TFISH increases relatively faster than τ 1 of TKE, from

FIG. 3 :τ 2 .

 32 FIG. 3: (Color online) Long time range THz field-induced Kerr effect spectra with incident THz peak field E = 210 kV/cm. The main figure shows long time domain TKE spectra vs. temperature. The dashed blue lines are the fitting curves with the biexponential function: f = Ae -(t-t 0 ) τ 1 +

FIG. 4 :

 4 FIG. 4: Frequency of the polar mode as a function of temperature obtained by RPMD simulations.

2. 30 ±

 30 0.01, b = (7.7 ± 0.3) × 10 3 , and c = (5.5 ± 0.1) × 10 7 N/m. The derived frequency 1 2π

10 Phys.

 10 Rev. B, 107 (2023) 064306.

FIG. 5 :

 5 FIG. 5: (Color online) RPMD simulations at 20K. (a) Effective energy-potential V (u) as a function of the reduced polarization along the [100] direction (blue line) and its harmonic approximation curve (red dashed line). The thermal energy k B T level is shown by the black dotted line. (b) Example of curves V (u) -E u under a static electric field, E. (c) Induced polarization as a function of E. (d) frequency of the polar mode (TO) as derived in the harmonic approximation close to the minimum of the V (u) -E u curve.

  (b), as well as the TFISH and TKE experiments of Figs. 1 and 2.

Figure 6 (

 6 c) shows the simulated dependence of the THz-driven soft mode oscillations and their frequency on the peak field strength, which qualitatively reproduces the measured dependence in TFISH and TKE, Figs. 1(c) and 2(c). To better understand the discrepancy between the measured and computed soft mode frequencies, we first point out that the field values cited in Figs. 1-3 are peak incident THz fields. When the incident THz field enters the KTO bulk through the surface, the electric field is reduced by the factor equal to the Fresnel transmission coefficient equal to 2/(n + 1) for normal incidence. For T = 20 K, the refractive index 41 n = 55, reducing the maximum incident 210 kV/cm electric field to 7.5 kV/cm inside KTO. In computation, the electric Phys. Rev. B, 107 (2023) 064306.

FIG. 6 :

 6 FIG. 6: (Color online) Computed dielectric response of KTO to a realistic time-domain THz pulse with an electric field parallel to [100]: panel (a) shows the square of the induced polarization u 2 (reduced unit) as a function of time in the case of E max = 60 kV/cm. The realistic THz field pulse used for the calculation is shown by the dashed blue line. Panels (b) and (c) show the reduced Fourier transform (FT) amplitude of u 2 in the 0 -12 ps range, according to the expression (8). Panel (b) is for E max = 60 kV/cm while panel (c) is for different E max for 20 K. Inset in panel (b) shows the FT amplitude of the pulse. Inset in panel (c) shows the integrated intensity in the 0.5 -5 THz range and its quadratic fit.

Phys. Rev. B, 107 (2023) 064306.

Acknowledgments

The work at Tulane was supported by the National Science Foundation under grant No. DMR-1554866. A.A. and L.B. thank the MonArk NSF Quantum Foundry supported by the National Science Foundation Q-AMASE-i program under NSF award No. DMR-1906383. S.P. and L.B. also acknowledge an Impact grant from the Arkansas Research Alliance, and ONR Grant No. N00014-21-1-2086.