Young-Sik Ra
email: youngsikra@gmail.com

Adrien Dufour

Mattia Walschaers

Clément Jacquard

Thibault Michel

Claude Fabre

Nicolas Treps

Non-Gaussian quantum states of a multimode light field

Advanced quantum technologies require scalable and controllable quantum resources [START_REF] Andersen | Hybrid discreteand continuous-variable quantum information[END_REF][START_REF] Biamonte | Quantum machine learning[END_REF]. Gaussian states of multimode light such as squeezed states and cluster states are scalable quantum systems [START_REF] Yokoyama | Ultra-large-scale continuous-variable cluster states multiplexed in the time domain[END_REF][START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF][START_REF] Chen | Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb[END_REF], which can be generated on demand. However, non-Gaussian features are indispensable in many quantum protocols, especially to reach a quantum computational advantage [START_REF] Mari | Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient[END_REF]. Embodying non-Gaussianity in a multimode quantum state remains a challenge as non-Gaussian operations generally cannot maintain coherence among multiple modes. Here, we generate non-Gaussian quantum states of a multimode light field by removing a single photon in a mode-selective manner from a Gaussian state [START_REF] Averchenko | Multimode theory of singlephoton subtraction[END_REF]. The selectivity and the controllability of the mode(s) for this photon subtraction process make it possible to extend the non-Gaussianity of a quantum state to the multimode regime, which has been a main obstacle for scalable quantum information processing. To highlight the potential for continuous-variable quantum technologies, we first demonstrate the capability to generate negativity of the Wigner function in a controlled mode. Subsequently, we explore the interplay between non-Gaussianity and quantum entanglement, and verify a theoretical prediction [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF] about the propagation of non-Gaussianity along the nodes of photon-subtracted cluster states. Our results demonstrate large-scale non-Gaussianity with an unprecedented flexibility, while ensuring the compatibility with quantum information protocols. This range of features makes our approach ideal to explore the physics of non-Gaussian entanglement [START_REF] Valido | Hierarchies of multipartite entanglement for continuous-variable states[END_REF][START_REF] Park | Conditional superpositions of Gaussian operations on different modes of light[END_REF], and to develop quantum protocols, ranging from quantum computing [START_REF] Lloyd | Quantum computation over continuous variables[END_REF][START_REF] Menicucci | Universal quantum computation with continuous-variable cluster states[END_REF], over entanglement distillation [START_REF] Eisert | Distilling Gaussian States with Gaussian Operations is Impossible[END_REF], to quantum simulations [START_REF] Banchi | Molecular Docking with Gaussian Boson Sampling[END_REF].

Our starting point is a multimode squeezed vacuum state of light, a basic quantum resource for continuous-variable quantum technologies such as quantum-enhanced sensing [START_REF] Aasi | Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light[END_REF] and deterministic quantum state teleportation [START_REF] Takeda | Deterministic quantum teleportation of photonic quantum bits by a hybrid technique[END_REF]. Recent technological advances have extended the generation and control of squeezed vacuum from a single mode to multiple modes, which enables a deterministic generation of large-scale multipartite entangled states [START_REF] Yokoyama | Ultra-large-scale continuous-variable cluster states multiplexed in the time domain[END_REF][START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF][START_REF] Chen | Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb[END_REF]. However, such quantum states intrinsically exhibit Gaussian statistics in electric field quadrature measurements. These Gaussian states have limitations to reach quantum advantages [START_REF] Mari | Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient[END_REF], e.g., entanglement distillation [START_REF] Eisert | Distilling Gaussian States with Gaussian Operations is Impossible[END_REF] and universal quantum computing [START_REF] Lloyd | Quantum computation over continuous variables[END_REF][START_REF] Menicucci | Universal quantum computation with continuous-variable cluster states[END_REF].

Non-Gaussian quantum states, on the other hand, are connected to exotic quantum fea-tures such as contextuality, which goes hand in hand with negative values of the Wigner function [START_REF] Spekkens | Negativity and Contextuality are Equivalent Notions of Nonclassicality[END_REF].

The hybrid approach, which combines continuous-variable and discrete-variable quantum information processing, provides a solution [START_REF] Andersen | Hybrid discreteand continuous-variable quantum information[END_REF]. Subtracting/adding a discrete number of photons [START_REF] Wenger | Non-Gaussian statistics from individual pulses of squeezed light[END_REF] can generate non-Gaussian states such as a local or non-local superposition of coherent states [START_REF] Ourjoumtsev | Generating optical Schrödinger kittens for quantum information processing[END_REF][START_REF] Ourjoumtsev | Preparation of non-local superpositions of quasi-classical light states[END_REF][START_REF] Sychev | Enlargement of optical Schrödinger's cat states[END_REF][START_REF] Serikawa | Generation of a Cat State in an Optical Sideband[END_REF][START_REF] Biagi | Entangling macroscopic light states by delocalized photon addition[END_REF] and hybrid entanglement [START_REF] Jeong | Generation of hybrid entanglement of light[END_REF][START_REF] Morin | Remote creation of hybrid entanglement between particle-like and wave-like optical qubits[END_REF]. Hitherto, this approach has only been successfully applied to a single-or two-mode quantum state, and the extension to highly multimode quantum states remains challenging due to the arduous task of maintaining coherence among multiple modes [START_REF] Averchenko | Multimode theory of singlephoton subtraction[END_REF].

To exploit the full potential of the large-scale entangled states that are generated by our source [START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF], it is essential that the hybrid approach is made compatible with multimode quantum states. The concept of our experiment is illustrated in Fig. 1(a). We choose photon subtraction as it generally leads to a stronger increase in entanglement than photon addition and is simpler to implement [START_REF] Das | Superiority of photon subtraction to addition for entanglement in a multimode squeezed vacuum[END_REF]. If we call ρ the density operator of an input multimode quantum state, the output state ρ-by a photon subtraction operator  becomes ρ-∝ Âρ  † , where  = k=0 c k âk .

(1) c k are complex numbers normalized as |c k | 2 = 1, and âk is the annihilation operator for mode k. Note that  is, in general, an annihilation operator in an arbitrary mode. The ability to experimentally control both the c k coefficient and the multimode resource ρ is the key to tailor non-Gaussian multimode states and to achieve non-Gaussian entanglement for building non-Gaussian quantum networks [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF][START_REF] Walschaers | Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States[END_REF].

In our experiment, the controlled generation of non-Gaussian multimode quantum states is performed using quantum frequency combs as a resource. Figure 1(b) shows the experimental setup, whose details are presented in Methods. The optical modes in which we implement Eq. ( 1) are time-frequency modes [START_REF] Ansari | Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings[END_REF]. The interest of these modes is that they are co-propagating in the same transverse mode, allowing for a large multimode quantum resource to keep its coherence and for the access to arbitrary superpositions of modes without constructing an interferometer. We populate these modes with a highly multimode Gaussian state through a parametric down conversion process [START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF]. Tailoring the measurement mode basis allows for the generation of versatile multipartite entangled states [START_REF] Cai | Multimode entanglement in reconfigurable graph states using optical frequency combs[END_REF]. We combine this resource with a time-frequency mode-dependent photon subtractor to de-Gaussify such multimode Gaussian states.

More specifically, our multimode Gaussian resource ρ is a set of independent squeezed vacua whose eigenmodes are conveniently approximated by time-frequency Hermite-Gaussian modes HG k . In order to implement the concepts of Eq. ( 1), we associate these modes with the annihilation operators âk . Hence, it remains to control the c k coefficients for the photon subtraction. As shown in Fig. 1(b), this is implemented through a mode-selective sumfrequency generation between the Gaussian resource ρ and a gate beam [START_REF] Ra | Tomography of a Mode-Tunable Coherent Single-Photon Subtractor[END_REF]. The non-linear interaction is designed such that pulse-shaping the gate allows for the control of the mode of photon subtraction [START_REF] Ansari | Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings[END_REF]. Finally, detection of a single photon in the up-converted beam heralds the subtraction of a photon in the desired mode from the Gaussian resource. The intensity of the gate governs the efficiency of the operation, and hence the heralding probability.

To characterize the resulting non-Gaussian multimode quantum state, we employ a homodyne detection that can control the mode of measurement by pulse-shaping the local oscillator. By virtue of these homodyne measurements, we show that our setup can generate a wide range of quantum states with key properties for the development of quantum technologies: negativity of the Wigner function on the one hand, and non-Gaussian entangled states on the other hand.

In the first column of Fig. 2(a), we first measure the input multimode squeezed vacua without photon subtraction (i.e., no gate field is applied). As expected, the measured state exhibits Gaussian distribution. This behavior changes drastically in the second column, ) with almost no effect on the mode in which the photon is actually subtracted. A completely analogous effect is observed when the photon is subtracted in EPR 1 . In striking contrast with the aforementioned separable input state, the effect of photon subtraction on an entangled state is not localized but is transferred to another mode.

In addition to generating Wigner functions that reach negative values, the results for these EPR state show that our setup is an ideal toolbox to study the interplay between non-Gaussianity and quantum entanglement. Cluster states, which form the backbone of measurement-based quantum computation [START_REF] Menicucci | Universal quantum computation with continuous-variable cluster states[END_REF], are a well-suited class of states to explore the rich entanglement structures in our quantum frequency combs [START_REF] Cai | Multimode entanglement in reconfigurable graph states using optical frequency combs[END_REF]. Upon photon subtraction in a given node and due to this cluster like correlation patterns, the non-Gaussian features will not remain concentrated in a single node but will spread among those linked to the photon-subtracted node [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF]. This implies that the negativity of the multimode Wigner function can generally not be retrieved from single-mode measurements (not even in the fully idealized pure state scenario). However, this interplay between non-Gaussianity and entanglement can be tested by measuring the propagation of non-Gaussian features through the cluster states using easily accessible higher order statistical properties such as the kurtosis and directly compared with theoretical predictions [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF].

We experimentally realize a four-mode linear cluster (LC) state and a four-mode square cluster (SC) state (see Methods), where we denote the four modes of the linear one as LC k (k = 0, 1, 2, 3) and the square one as SC k (k = 0, 1, 2, 3). We quantify the non-Gaussianity in each mode by evaluating the phase-averaged excess kurtosis (to compare with the kurtosis of 3 by a Gaussian distribution). This is obtained from the quadrature measurement outcomes

x 1 , x 2 , ..., x S where the measurement phase is randomized:

K ex = 1 S S s=1 x 4 s ( 1 S S s=1 x 2 s ) 2 -3 (2)
For a quantum state with zero mean ( â = â † = 0), which corresponds to all the quantum states in our experiment, a Gaussian state always exhibits K ex ≥ 0, thus K ex < 0 indicates a non-Gaussian state. Figure 3 shows excess kurtosis of the generated states. For the linear cluster state, excess kurtosis in each mode is initially close to zero. When a photon is subtracted in LC 3 , it is LC 2 in which excess kurtosis becomes highly negative (i.e. non-Gaussian) while those in the other modes remain close to zero. For photon subtraction in LC 2 , only LC 3 exhibits a significant negativity. We can concentrate more non-Gaussianity in LC 3 by subtracting a photon in a superposition of four modes, as shown in the last figure of Fig. 3(a). For the square cluster state, excess kurtosis without photon subtraction is close to zero in each mode. Photon subtraction in SC 0 , however, does not affect the distributions in its nearby modes (SC 1 and SC 3 ) much, but it introduces non-Gaussianity mostly in SC 2 which is two steps away from the mode of photon subtraction. This effect was predicted in [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF] and we note an excellent agreement between the measured kurtosis values and the theoretical values calculated from the measured input Gaussian states. Hence, even though the obtained values for the excess kurtosis are consistent with reported values for photonsubtracted thermal states [START_REF] Bogdanov | Multiphoton subtracted thermal states: Description, preparation, and reconstruction[END_REF], the hallmark of non-Gaussian correlation lies in the way that these non-Gaussian effects propagate through the nodes of the cluster state.

In the future, our approach can be used to generate a broader class of non-Gaussian states by subtracting multiple photons, either via a sequence of subtractors or by replacing the single-photon detector with a number-resolved subtraction scheme. In such a scenario, the success probability of the heralding will be a limiting factor, which could be significantly improved by a repeat-until-success scheme [START_REF] Marek | Loop-based subtraction of a single photon from a traveling beam of light[END_REF]. More generally, the availability of non-Gaussian multimode states will stimulate fundamental studies on non-Gaussian entanglement [START_REF] Park | Conditional superpositions of Gaussian operations on different modes of light[END_REF][START_REF] Katamadze | How quantum is the "quantum vampire" effect?: Testing with thermal light[END_REF] and quantumness [START_REF] Ježek | Experimental test of the strongly nonclassical character of a noisy squeezed single-photon state[END_REF][START_REF] Albarelli | Resource theory of quantum non-Gaussianity and Wigner negativity[END_REF] by going beyond the Gaussian realm, as well as applications in quantum technologies [START_REF] Lloyd | Quantum computation over continuous variables[END_REF][START_REF] Menicucci | Universal quantum computation with continuous-variable cluster states[END_REF][START_REF] Eisert | Distilling Gaussian States with Gaussian Operations is Impossible[END_REF][START_REF] Plick | Violating Bell inequalities with entangled optical frequency combs and multipixel homodyne detection[END_REF]. In particular, the observed nontrivial interplay between photon subtraction and cluster states, confirming recent theoretical predictions [START_REF] Walschaers | Tailoring Non-Gaussian Continuous-Variable Graph States[END_REF], provides an ideal avenue for future experimental studies of non-Gaussian entanglement and its applications. Input is a beam containing a Gaussian multimode quantum state ρ, which can be, in general, a multipartite entangled state. From the input state, we subtract a photon in a specific mode or in a coherent superposition of multiple modes by controlling the complex coefficient c k for each mode k. This process, described by an annihilation operator  in Eq. ( 1), is heralded by a registration of a photon at the single-photon detector (SPD). As a result, the output beam contains a non-Gaussian multimode quantum state ρ-. The inset inside each circle is the Wigner function of the reduced quantum state in the associated mode. (b) Experimental setup. A Ti:sapphire laser produces a beam made of a train of femtosecond pulses, which splits into three beams. One beam is up-converted via second harmonic generation in a second-order nonlinear crystal (NC 1 ), and then, pumps NC 2 for a parametric down-conversion process. Synchronously pumped optical parametric oscillator (SPOPO) amplifies the process, which generates twelve-mode squeezed vacua in welldefined time-frequency modes. Another beam is used as a gate for the photon subtractor, and its time-frequency mode is engineered by a pulse shaper (PS). Inside NC 3 , sum-frequency-interaction between the gate and the multimode squeezed vacua generates an up-converted beam, which is detected by SPD. A photon registration in SPD heralds photon subtraction from the multimode squeezed vacua. The resulting multimode quantum state is measured by homodyne detection with a time-frequency-engineered local oscillator (LO) using another PS. PD: photo diode; BS: beam splitter; θ: phase of LO. dot product between the samples and the double-sided-decaying-shape temporal mode of the SPOPO [START_REF] Neergaard-Nielsen | Generation of a Superposition of Odd Photon Number States for Quantum Information Networks[END_REF]. To reconstruct a Wigner function in Fig. 2, we collect 20,000 ∼ 30,000 quadrature outcomes. In the case of no photon subtraction, we monitor the variance of the quadrature outcomes. Phase dependance of the quadrature squeezing of the multimode

Gaussian state provides the phase information of the LO relative to this multimode light.

Preparation of entangled states. We prepare an entangled state by choosing a specific basis of modes in which quantum correlations among desired modes emerge [START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF][START_REF] Cai | Multimode entanglement in reconfigurable graph states using optical frequency combs[END_REF]. In the HG mode basis, even-order (odd-order) modes exhibit p-quadrature (x-quadrature) squeezed vacuum. To prepare an EPR entangled state, we use a basis of EPR 0 = 1 (the EPR criterion [START_REF] Bowen | Experimental Investigation of Criteria for Continuous Variable Entanglement[END_REF]). To prepare a linear cluster state, we use a basis of LC k (k = 0, 1, 2, 3) which is obtained by applying a unitary matrix U (LC) to the basis of HG k (k = 0, 1, 2, 3), where 2) for k = 0, 1, 2, and 3, respectively. Similarly, we prepare a square cluster state in the basis of SC k (k = 0, 1, 2, 3), which is obtained by applying a unitary matrix U (SC) to the HG basis, where

U (LC) =        -0.
U (SC) =        -0.

  where a single photon is subtracted in HG 0 : the multimode Wigner function becomes negative. More specifically, the reconstructed Wigner function in HG 0 reaches negative values (explicitly highlighted by W 0 ), while the Wigner functions in the other modes remain Gaussian, thus demonstrating the mode-selective operation of the photon subtractor. Similarly, when a photon is subtracted in HG 1 , we observe a non-Gaussian Wigner function only in HG 1 . Due to a larger optical loss in the input state for higher order modes than in HG 0 , the negativity of the Wigner function is unveiled only upon loss-correction, as shown in Extended Data Fig.1. Analogous results are obtained for the subtraction of a photon in the HG 2 mode, but due to higher losses the resulting Wigner function remains positive. The high quality of the photon subtraction process is emphasized in Fig.2by the high fidelity (F ) between experimental results and the ideal Wigner functions calculated by subtracting a photon from the corresponding input state.Furthermore, the versatility of the experimental setup allows for the computer controlled subtraction of a photon in an arbitrary superposition of modes from a multimode quantum state. As an example, we subtract a photon in a superposition of HG 0 and HG 1 modes, HG 0 -iHG 1 . We observe that the photon subtraction induces negativity in the Wigner function for this mode (first row of Fig.2(b)). On the other hand, in the orthogonal mode HG 0 + iHG 1 , a Gaussian Wigner function is obtained, and in a partially overlapping mode iHG 1 , an intermediate situation is obtained as expected, see Extended Data Fig.2. When we subtract a photon in a superposition of three modes HG 0 + iHG 1 +HG 2 , we similarly observe a non-Gaussian Wigner function in the same superposed modes (second row of Fig.2(b)), which remains positive due to the impurity of the input state.The flexibility of the setup allows us to extend photon subtraction to entangled input states. We first investigate an Einstein-Podolsky-Rosen (EPR) entangled state, which exhibits quantum correlations between two superposed modes: EPR 0 =HG 0 +HG 1 and EPR 1 =HG 0 -HG 1 (see Methods). The last two rows in Fig.2(b) show the experimentally obtained Wigner functions. Without photon subtraction, the reduced quantum state in each of EPR 0 and EPR 1 is a thermal state as expected. When a photon is subtracted in EPR 0 , the introduced non-Gaussian characteristics-including negativity of the Wigner function-appear in the other mode (EPR 1

FIG. 1 .

 1 Photon subtractor

FIG. 2 .FIG. 3 .

 23 FIG. 2. Wigner function reconstructed from experimental data. For a multimode quantum state, photon subtraction and measurement are conducted in (a) HG modes or in (b) superpositions of HG modes. The Wigner function of each mode is represented in the phase space of x and p axes, which are associated with quadrature operators x = â + â † and p = (â -â † )/i, respectively. The inset behind each Wigner function shows the experimentally obtained quadrature outcomes, where the horizontal and vertical axes represent the phase of local oscillator and a quadrature outcome, respectively; the quadrature outcome of one corresponds to the variance of the vacuum fluctuation. No correction of optical losses is made; for the results by optical loss correction, see Extended Data Fig. 1. W 0 = 2πW (0, 0) is the value of a normalized Wigner function at the origin, and F is the fidelity between an experimental Wigner function and the Wigner function by the ideal photon subtraction to the input state of the corresponding mode. Purities of the Wigner functions in (a), compared with the cases of the ideal photon subtraction, are presented in Extended Data Tab. 1. For measurements in modes EPR 0 and EPR 1 , the phase of a quadrature outcome is randomized since the associated quantum state is phase insensitive. Errors noted in parentheses are one standard deviations calculated by bootstrapping.

√ 2 ( 1 √ 2 (

 212 HG 0 + HG 1 ) and EPR 1 = HG 0 -HG 1 ). We have obtained ∆ 2 (x EPR 0 (6) < 4 (the Duan entanglement criterion[START_REF] Duan | Inseparability Criterion for Continuous Variable Systems[END_REF][START_REF] Simon | Peres-Horodecki Separability Criterion for Continuous Variable Systems[END_REF]) and ∆ 2 xEPR 1|0 ∆ 2 pEPR 1|0 = 0.71(4) < 1

.

  To check correlations among different modes, we use the four nullifiers associated with a linear cluster state[START_REF] Cai | Multimode entanglement in reconfigurable graph states using optical frequency combs[END_REF][START_REF] Van Loock | Building Gaussian cluster states by linear optics[END_REF], δ(LC)k = xkl V kl pl (Vkl is the adjacency matrix defining the topology of a cluster state, where V kl = 1 if k and l are connected, and 0 otherwise). They all exhibit a variance less than the vacuum fluctuation: ∆ 2 δ(LC) k / ∆ 2 δ(LC) k vacuum = 0.75(2), 0.67(2), 0.68(2), and 0.64(

Fig. 2 (. 1 .

 21 a). For comparison, the purity of a Wigner function by the ideal photon subtraction is provided in square brackets, which agrees well with the experimental result. Low purity in a photon-subtracted mode is attributed to a non-ideal input state [19]. No optical loss is corrected in the calculation. Errors noted in parentheses are one standard deviations calculated by bootstrapping. Wigner function reconstructed with optical loss correction. Optical loss only by the homodyne detection (12.5%) has been corrected. Comparing with Fig. 2, non-Gaussian Wigner functions show reduced W 0 . Errors noted in parentheses are one standard deviations calculated by bootstrapping.

. 2 .

 2 Effect of mode mismatch between photon subtraction and measurement. When a single photon is subtracted in HG 0 -iHG 1 , a Wigner function (without optical loss correction) is obtained in a measurement mode having (a) full match (HG 0 -iHG 1 ), (b) partial match (iHG 1 ), and (c) no match (HG 0 + iHG 1 ). Errors noted in parentheses are one standard deviations calculated by bootstrapping.

Extended Data Fig. 3 .

 3 Experimental covariance matrix. (a) is for x quadratures, seen from above, and (b) is for p quadratures, seen from below. Mode indexes are HG 0 , iHG 1 , HG 2 , and iHG 3 , where i is added for the odd-index HG modes to have p-squeezed vacua in all modes. For clarity, the vacuum noise (corresponding to the identity matrix) is subtracted from the covariance matrix. In the covariance matrix, variances of (x, p) quadratures are (2.8 dB, -1.8 dB) in mode 0, (2.1 dB, -1.6 dB) in mode 1, (1.6 dB, -1.0 dB) in mode 2, and (1.4 dB, -0.7 dB) in mode 3.

Table 1 .

 1 Purities of the Wigner functions in

		316 0.632 0.707	0.000	
		0.632i 0.316i 0.000 -0.707i -0.316 0.632 -0.707 0.000	     	.
		0.632i 0.316i 0.000 0.707i
	Each of the four nullifiers	δ(SC)

k associated with a square cluster state exhibits a variance less than the vacuum fluctuation: ∆ 2 δ(SC) k / ∆ 2 δ(SC) k vacuum = 0.72(2), 0.77(2), 0.61(2), and 0.75(2) for k = 0, 1, 2, and 3, respectively.

ACKNOWLEDGEMENTS This work is supported by the French National Research Agency projects COMB and SPOCQ, the European Union Grant QCUMbER (no. 665148). C.F. and N.T. are members of the Institut Universitaire de France. Y.-S.R. acknowledges support from the European Commission through Marie Sk lodowska-Curie actions (no. 708201) and the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1A6A3A03012129) and the Ministry of Science and ICT (NRF-2019R1C1C1005196). M.W. acknowledges funding through research fellowship WA 3969/2-1 from the German Research Foundation (DFG).

DATA AVAILABILITY

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

All authors contributed to scientific discussions.

COMPETING INTERESTS

The authors declare no competing interests.

METHODS

Experimental details. Non-Gaussian multimode quantum states are generated by several nonlinear interactions on femtosecond pulses, as described in Fig. 1. The fundamental light source is a Ti:Sapphire laser, which produces a train of pulses (duration: 90 fs, central wavelength: 795 nm) at a repetition rate of 76 MHz. The laser beam is split into three beams: one is used for generating a multimode Gaussian state, another for photon subtraction, and the third for the homodyne detection.

The first beam is up-converted to a femtosecond pulse having 397.5-nm central wavelength in NC 1 (0.2-mm-thick BiB 3 O 6 ) which is used as a pump for a parametric-down-conversion process in NC 2 (2-mm-thick BiB 3 O 6 ) inside a cavity, the SPOPO. The length of the SPOPO is locked to the length of the Ti-Sapphire laser via the Pound-Drever-Hall method, such that the train of pump pulses is synchronized with the down-converted pulses which circulate inside the SPOPO. Transmittance of the output coupler of the SPOPO is 50%. The light coming out through the output coupler is a multimode Gaussian state, containing roughly twelve squeezed vacua in orthogonal time-frequency modes [START_REF] Roslund | Wavelengthmultiplexed quantum networks with ultrafast frequency combs[END_REF][START_REF] Cai | Multimode entanglement in reconfigurable graph states using optical frequency combs[END_REF]. Among the twelve modes, we focus on the first four dominating modes, whose covariance matrix is given in Extended Data Fig. 3.

For photon subtraction, we perform sum-frequency interaction between the multimode Gaussian state and the second beam from the Ti-Sapphire laser (the gate; 1 mW power) inside NC 3 (2.5-mm-thick BiB 3 O 6 ). Detection of a single photon generated by the sumfrequency interaction heralds photon subtraction from the multimode squeezed vacua, where the time-frequency mode of the gate determines the photon subtraction mode [START_REF] Ra | Tomography of a Mode-Tunable Coherent Single-Photon Subtractor[END_REF]. To engineer the time-frequency mode of the gate, we employ a homemade pulse shaper whose core element is a spatial light modulator, having a spectral resolution of 0.2 nm. Conversion efficiency of the nonlinear interaction is 0.1 %, and we have typically 110 Hz of heralding rate with background noise of 6 Hz.

The last beam is used as the local oscillator (LO) of the homodyne detection to measure the generated quantum state. The measurement mode is the mode of the LO, which is engineered by another pulse shaper having a spectral resolution of 0.2 nm. For each event of photon subtraction, photocurrent difference between the two PDs is sampled every 2 ns during a 2-µs time window, and one quadrature outcome is obtained by calculating the


Alexei D Averin

Anton S Abel

Olga K Grigorova

V Gennadij

Yury N Latyshev

Alexander Yu Kotovshchikov

Alla G Mitrofanov

Irina P Bessmertnykh-Lemeune

Beletskaya

Gennadij V Latyshev

Yury N Kotovshchikov

Alexander Yu Mitrofanov

Alla Bessmertnykh-Lemeune

Irina P Beletskaya

Recent achievements in copper catalysis for C-N bonds formation

Keywords: Cu catalysis, amination, polyamines, adamantane, "click" reactions, steroids, immobilization

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The so-called renaissance of the Ullmann chemistry has become an important trend in the modern catalysis. The change of expensive palladium often associated with enough toxic phosphine ligands for a much cheaper copper boosted the search for new catalytic protocols in the formation of C-O, C-S and especially C-N bonds. The reviews covering the general aspects of the modern Ullmann chemistry are now abundant, they were published by Ma [1], Evano [2], Monnier [3], Jiang [START_REF] Jiang | Cu-catalyzed Ullmann-type C-heteroatom bond formation: the key role of dinucleating ancillary ligands[END_REF], Sambiago [START_REF] Sambiagio | [END_REF], a special chapter to this topic is dedicated in the recent comprehensive handbook [START_REF] Junge | Applied Homogeneous Catalysis with Organometallic Compounds: A Comprehensive Handbook in Three Volumes[END_REF]. Among the principal investigations in the field of the copper-mediated amination [7][8][9][10][11][12] and amidation [13,14] in last 15 years more specialized reviews can be cited [START_REF] Lee | Application of Copper-Mediated C-N Bond Formation in Complex Molecules Synthesis[END_REF][START_REF] Shaughnessy | Copper-Catalyzed Amination of Aryl and Alkenyl Electrophiles[END_REF]. Our own interest in the copper-catalyzed reactions exceeds the frames of purely Ullmann reactions due to a wide scope of various catalytic transformations promote by this metal and cover the following aspects: formation of C(sp 2 ) -P bonds [START_REF] Karlstedt | [END_REF][18][19], arylation with iodonium salts [20], formation of C-S and C-C bonds in the reactions with alkynes [21,22], use of the chiral Cu(II) complexes in the asymmetric addition reactions catalyzed by optically active Lewis acids [23][24][25][26], application of the heterogeneous copper catalysts like copper nanoparticles (CuNPs) [27] and copper-containing MOFs [28]. Our attention was also drawn by the Cu(I)-catalyzed Sonogashira coupling [29,30], formation of C-N bonds under the conditions of Chan-Lam-Evans reaction [31] or in the presence of poly(ethylene) glycols [32], the synthesis of polycyclic compounds [33]. As for reviews, the two approaches, via Pd-and Cu-catalyzed reactions in the C-N bond formation, were thoroughly compared in [34], while C-C and C-S bonds formation was overviewed in [35,36].

In the present mini-review the material is focused properly on the C-N bond formation catalyzed by copper complexes and deals with the amination of (hetero)aryl halides and CuAAC ("click") reactions applied for the conjugates syntheses. Historically we intensively studied the Pd(0)-catalyzed amination reactions with adamantane-containing amines [37][38][39][40][41][42][43] and linear polyamines [44][45][46][47][START_REF] Averin | Pd-catalyzed arylation of polyamines[END_REF]. Many efforts were done for the elaboration of the synthetic approaches to polyazamacrocycles [49][START_REF] Averin | Palladium-catalyzed amination reaction in the synthesis of nitrogen-and oxygen-containing macrocycles and macropolycycles[END_REF][51][52][53]. In this connection, the outline of the possibilities of the copper-catalyzed amination will serve as a timely complement to the acquired knowledge on the palladium-mediated synthetic approaches.

Cu(I)-catalyzed arylation of adamantane-containing amines

Scheme 1: Optimization of Cu-catalyzed arylation of adamantane-containing primary amine.

Our first goal was the search for the most efficient catalytic system for the aryaltion of the adamanatane-containing amines [54]. In the preliminary experiments we chose five primary amines 1-5 differing by the spatial hindrances at the amino groups and introduced them in the arylation with iodobenzene in the presence of [Cu]/L catalytic systems in which the nature of the copper source and the ligand was varied (Scheme 1). Among various sources of copper (CuI, Cu2O, CuO, CuOTf, CuOAc, CuBr*Me2S) the best results were shown by a traditional copper iodide, and in some cases cuprous and cupric oxides could be also used. The employed ligands L were as follows: L-proline (L1), N,N-dimethyl glycine (L2) (N,O-lgands), 2-isobutyrylcyclohexanone (L3), rac-BINOL (L4), ethylene glycol (L5) (O,O-ligands), 1,10-phenanthroline (L6), N,N'-dimethylethylenediamine (L7) (N,N-ligands). It was found out that L3 and L4 ligands provided the best yields of the arylation products. CuI/L3 or CuI/L4 catalytic systems were used further for the synthesis of various N-arylated derivatives of adamantyl-substituted primary amines. Cesium carbonate was always employed as a base and the reactions were run in DMF at 140 o C with 0.5 M concentrations of the reagents.

The application of para-substituted iodobenzenes in the couplings with the same amines 1-5 showed that the substituent strongly influenced the products yields (Scheme 2). The best results were observed for the reactions with piodotoluene while the most problematic reagent was p-iodoanisole due to a strong electron-donor effect of the methoxy group. Further investigations englobed a series of the amines 6-19 with more structural varieties, in all reactions rac-BINOL (L4) was used as the ligand (Scheme 3). In the majority of cases the yields of the products of arylation with para-substituted iodobenzenes were from moderate to high attaining 70-86% in the case of less sterically demanding amines, the increase in the spatial hindrances (especially in 9, 12, 13, 15) led to a decrease in the yields of the target products, and amine 14 was found to be the most problematic [55]. The method was successfully applied to adamantane-containing diamines 20 and 21 (Scheme 4). The reactions with the diamine 20 possessing the amino groups closer to the adamantane scaffold demonstrated greater dispersion of the yields and only L4 was helpful for its N,N'-diarylation. Products of the monoarylation were also obtained in some cases (R = Me, CF3, OMe). Diamine 21 was more reactive and both ligands, L3 and L4 allowed the synthesis of diarylated species in good to high yields [56].

Copper catalysis in the adamantane-containing amines heteroarylation

Scheme 5: Cu-catalyzed synthesis of N-pyridyl derivatives of adamantylated amines.

The heteroarylation of various adamantylated amines was explored using 2-iodo-and 3-iodopyridines (Scheme 5). Ligands L1-L4 were tested in these reactions and only L3 was found to be suitable for this purpose. 2-Iodopyridine was more reactive but the products were obtained in good yields for both isomeric halides. Nevertheless, when 2-iodopyridine was reacted with more strerically hindered amines such as 14 and 15, the yields of the target products decreased up to 15 and 36%, respectively [57]. It was found that the reaction also smoothly proceeded with more available 2-bromopyridines bearing fluoro-and trifluoromethyl substituents at the pyridine ring (Scheme 6). The yields of the target products were higher in the case of the amine 1 than with 4 what is in a good correspondence with the closer position of the amino group to the adamantane core in the case of 4. It was found possible to introduce sterically hindered 2-bromo-3-fluoropyridine in these reactions [58]. A variety of amines 1-8, 13, 16 and 17 were studied in the copper-mediated amination of 2-fluoro-5-iodopyridine (Scheme 7). Not only the reaction products attracted out attention as those bearing aminofluoropyridine -a promising pharmacophore, but also the problem of the competition of the catalytic substitution of the iodine and noncatalytic substitution of the fluorine atom. In the case of the equimolar ratio of the starting compounds the yields of the products of the catalytic amination were enough low and substantial amounts of the 2-aminopyridine derivatives were formed. However, with the application of 2 equiv. of starting amines the results improved drastically allowing almost quantitative synthesis of the target 5-amino-2-fluoropyridines [59]. Following our investigations on the application of palladium catalysis for the amination of various dichloro-, dibromo-and bromochloropyridines where the comparison with the Cu(I)-catalyzed amination of 2,5-dibromopyridine was done [60], we also demonstrated the possibilities of the copper-catalyzed amination with adamantylated amines with other dihalogenopyridines (Scheme 8). The same catalytic system was helpful for a selective substitution of the iodine atoms in 5-bromo-2-iodopyridine and 2-chloro-5-iodopyridine affording corresponding N-(5-bromopyridin-2-yl) and N-(2-chloropyridin-5-yl) substituted adamantylalkylamines in reasonable yields. Amines 1-6 were employed in the Cu(I)-catalyzed amination of another heterocyclic halide, i.e. 6-bromoquinoline (Scheme 9). The dependence of the reaction outcome on the steric hindrances at the amino group was enough clear, the best result (74% yield) was recorded in the case of the less sterically demanding amine 1. The attempts to use 2-or 4-chloroquinolines in the same reaction were not as successful and the yields did not surpass 30% due to numerous side reactions. Having acquired enough experience with the copper-catalyzed (hetero)arylation of monoamines, we thoroughly studied the possibilities of the N,N'-diarylation of di-and polyamines [61]. At first, a series of linear diamines was investigated which differ by the number of methylene groups between N atoms (Scheme 10). The reactions were run with different para-substituted iodobenzenes. Only ligands L1 and L3 were found to be suitable in these reactions, and L1 was superior to L3 in the reaction of ethylenediamine and pentane-1,5-diamine. In fact, for all these diamines the systems CuI/L1/PPh3 or CuI/L3/PPh3 provided the best yields of the diarylation products. The main by-products were the monoarylated derivatives, in some cases they were isolated as pure compounds. Such compounds became predominant in the reactions with the sterically hindered 2-fluoroiodobenzene (Scheme 11), and even the application of 20/40 mol% catalytic system could afford 10-18% yields of the N,N'-diarylated compounds. The introduction of the tri-and tetraamine in the similar reactions demonstrated that the CuI/L1/EtCN catalytic system was more efficient as it diminished the formation of the side products arising from the arylation of the secondary amino groups [62]. As a result, it was possible to introduce para-and meta-substituted iodobenzenes in the N,N'-diarylation process, though the product yields differed from low to high depending on the nature of the substituent in the aryl ring (Scheme 12). Naturally occurring polyamines can be equally transformed into their N,N'-diaryl derivatives and the application of the appropriate catalytic systems may improve the balance between the arylation of the primary and secondary amino groups (Scheme 13). The dependence of the target compounds yields on the nature of the substituent was also essential, the most problematic were the reactions with p-iodoanisole, which smoothly proceeded only in the presence of 20 mol% of the catalyst [61]. A thorough investigation of the N,N'-diarylation of the oxadiamines [63] revealed some peculiar details (Scheme 14). It was noted that usually the reactions with p-fluoro-and p-(trifluoromethyl)substituted iodobenzenes led to complete conversion of the starting amine but gave poor yields of the target compounds. On the other hand, it was possible to obtain excellent yields (over 90%) with meta-substituted derivatives. As for sterically hindered 2-fluoroiodobenzene, it afforded up to 77% yield of the diarylation product with the trioxadiamine provided 20 mol% catalyst was employed.

N,N'-diarylation of di-and polyamines using Cu(I) catalysis

Synthesis of N,N'-diheteroaryl derivatives of di-and polyamines in the presence of Cu(I) catalysts

In the case of the copper-catalyzed reactions of the diamines with 2-and 3-iodopyridines (Scheme 15) only ligands L3 and L4 proved to be suitable, though CuI/L3 catalytic system provided better results in the most of cases [64]. The longer is the diamine chain, the more difficult is the diheteroarylation and higher yields of the monopyridyl-substituted derivatives. The heteroarylation of the tri-and tetraamines was accomplished using 2-bromo-, 2-iodo-and 3-iodopyridines (Scheme 16). The main problem to be solved in these reactions was the diminishing of the amount of mono-and polyheteroarylated products to increase the yield of the target N,N'-dipyridyl compounds [65]. This was achieved by varying the catalytic system (ligands L1 or L2) and application of less active 2-bromopyridine, what helped to obtain corresponding products in yields up to 68-76%. In general, the increase in the number of ethylenediamine units in the molecules of polyamines led to an easier heteroarylation of the secondary amino groups while trimethylenediamine units disfavored diarylation and promoted the formation of the monopyridyl derivatives. Better results were obtained with the natural spermidine and spermine (Scheme 17). The use of 2-bromo-or 3iodopyridine in the presence of CuI/L3/DMF catalytic system and running the reaction at 110 o C allowed the synthesis of the corresponding N,N'-dipyridyl derivatives in 50-64% yields [64]. The introduction of the fluorophore groups like naphthalene and quinoline in polyamines is also possible via Cu(I)catalyzed amination (Scheme 18). Note that 1-iodo or 1-bromonaphthalenes possess lower reactivity in these reactions and gave mainly monoarylated derivatives, whereas 2-iodonaphtalene and 6-bromoquinoline were more reactive, especially in the reactions with the tetraamine [66]. The heteroarylation of the trioxadiamine with 2-and 3-iodopyridine proceeds easily in the presence of CuI/L3 system in DMF giving 57 and 73% yields, respectively, of the N,N'-dipyridyl derivatives (Scheme 18). It was shown possible to carry out the diheteroarylation of the same diamine with a series of substituted 2-bromopyridines bearing F and CF3 substituents. The yields were good in all cases, and the reaction with a sterically hindered 3-fluoro-2-bromopyridine provided the best 79% yield, probably, due to a suppression of the side reactions. We also demonstrated the possibility to introduce 3-bromo-and 3-iodothiophenes in the reactions with polyamines, the catalytic systems with L1 and L3 ligands were enough efficient (Scheme 20). However the yields were moderate, first of all, due to difficulties during the chromatographic isolation of the products [67].

Cu(I)-catalyzed C-N bond formation in the transformations of steroids

24-Amino derivatives of the cholanols were shown to participate in the Cu(I)-catalyzed amination: the reaction with p-iodotoluene catalyzed with CuI/L1 using K2CO3 as a base and run in DMSO at 110 o C provided almost quantitative yield of the desired product (Scheme 21), and the reactions with 1,3-diiodobenzene or 4,4'-diiodobiphenyl afforded bissteroid derivatives in quite reasonable yields [68]. This reaction is a rare example of the diamination of dihaloarenes in the presence of copper catalyst. The amination of 17-iodoandrosta-4,16-dien-3-one with indole demanded a search for the ligand able to suppress the catalytic reduction of the iodine (Scheme 22). 2,2,6,6-Tetramethylheptane-3,5-dione (DPM) was found to serve better than 8-hydroxyquinoline or cyclohexane-1,2-diamine, and using this catalytic system the amination with 5-substituted indoles and imidazole was carried out [69]. The same approach was successfully applied to the amination of another iodosubstituted steroid possessing the halogen atom at position 3 (Scheme 23). The scope of azoles was substantially enlarged, they included not only substituted indoles and imidazoles, but also pyrazoles, triazoles and carbazoles. In the case of 3-iodo-17-hydroxyandrostadiene the yields were excellent, and with the cholesterol derivatives they were from good to high.

Huisgen 1,3-dipolar cycloaddition in the formation of diverse conjugates

Copper-catalysed alkyne-azide cycloaddition (CuAAC, "click") is a novel synthetic tool with a remarkable practical and ecological impact and widely employed in the synthesis of many functional molecules including pharmaceuticals, dyes, sensors, and bioconjugates [START_REF] Lahann | Click Chemistry for Biotechnology and Materials Science[END_REF][START_REF] Castro | [END_REF][72][73][74][75][76][77]. This reaction allows to deliver sophisticated molecules or libraries of substituted 1,2,3-triazoles due to its selectivity, excellent functional compatibility, reliability and simplicity of experimental conditions. This reaction was employed by us for several purposes. The first is the synthesis of 5-iodo-1,2,3-triazoles in view of their further catalytic modifications employing a reactive C-I bond. The reactions of a variety of organic azides with several terminal acetylenes were conducted using CuI and TTTA ligand providing the desired products in yields from moderate to excellent and the modified protocol tolerated the presence of various functional groups [78]. (Scheme 24).

Scheme 24: Synthesis of 5-iodo-1,2,3-triazoles.

Then functionalisation of steroids bearing primary azido substituent in the side chains located at position 17 of the steroid scaffold was investigated (Scheme 25). The resulting triazolyl-substituted steroids were obtained in high to excellent yields using various terminal alkynes including those with hydroxyl groups [79]. Steroids with azido substituent at position 16 were also studied in CuAAC reaction(Scheme 26). The reactions of these more sterically hindered compounds proceeded more slowly and demanded the modification of the reaction conditions. The use of CuSO4•5H2O and NaAsc in aqueous THF (method A) allowed the reaction of azidosteroids with propargyl alcohol, while the catalytic system with Et3N (method B) appeared effective for both phenylacetylene and 1-hexyne. Finally, the catalytic system comprising CuSO4•5H2O, tris(benzyltriazolylmethyl)amine (TBTA) and NaAsc (method C) allowed to achieve complete conversion of azidosteroids and totally suppressed D-homo rearrangement process (Scheme 26).

Scheme 25: Synthesis of triazolyl derivatives from steroids bearing primary azido groups.

Scheme 26: Synthesis of triazolyl derivatives from steroids bearing secondary azido groups.

CuAAC reaction was successfully employed for the preparation of a series of steroid dipods and tripods based on the central phosphorus acids, comprising anion binding triazolium sites and hydrophobic cholane residues [80,81] Propargyl phosphorus esters first reacted with the steroid derivatives bearing azido group at various positions to obtain 1:1 conjugates and to optimize the reaction conditions (Scheme 27).

were applied for the preparation of the bile acid based tripods (Scheme 28). Good yields were obtained for 3β-, 3α-, and 24-cholanetriazolyl derivatives. Slightly higher yields were observed for lithocholic acid-based tripod in comparison with deoxycholic and cholic acid based products. Also we obtained a click adduct with 3-azidoacetoxycholane derivative. These di-and tripodal compounds in which steroidal units are organized around the phosphorus center via triazolyl linkers are of interest for anions binding studies.

Cu(I)-catalyzed 1,3-dipolar cycloaddition reactions were successfully used for the synthesis of porphyrin triads containing 1,2,3-triazole linkers. For this purpose two combinations of starting compounds were tried. The first reaction scheme employed 5,15-bis(ethynylphenyl) derivative of porphyrin with 2 equiv. of meso-(4-azidophenyl)substituted porphyrin (Scheme 29). The reaction conditions were adjusted to provide the high yield of the target trisporphyrin compound, the best were found to be CuI/DIPEA in THF-MeCN solution which gave 68% yield of this triad, a classical system (CuSO4/sodium ascorbate in DMF) provided slightly lower yield 60%. [82]. According to the second reaction route, 5,15-bis(4-azidophenyl)-substituted porphyrin was coupled with 2 equiv. of meso- (4-ethynylphenyl)porphyrin in the presence of CuI/DIPEA in THF-MeCN (Scheme 29) and it produced an isomeric porphyrin triad in a high 70% yield. It was also shown that a simpler porphyrin dyad could also be easily synthesized by reacting corresponding porphyrins under the same conditions.

Porphyrin triad of a star shape was successfully synthesized using the similar approach: 1,3,5-tri(ethynyl)benzene was reacted with 3 equiv. of meso-(4-azidophenyl)-substituted porphyrin and the target star-shaped triad was isolated in 30% yield (Scheme 30) [83]. It is to be mentioned that only zinc porphyrinates but not free porphyrin bases can participate in these reactions as the latter easily coordinate copper(II) hampering the catalytic reaction.

Heterogenized copper catalysis in C-N bond formation

In the last two decades, significant improvements in homogeneous Cu-catalyzed C-C and C-Het (Het . O, S, Se, N, P) cross-coupling reactions, additions to unsaturated C-C bonds, Huisgen 1,3-dipolar cycloaddition, and other organic transformations were reported. Homogeneous catalysts are well suited for increasing the reaction scope and the tuning the reaction rate and its selectivity. However, the separation of organic products from toxic copper compounds are particularly troublesome due to the exceptional coordination properties of this metal, which avidly bind a huge range of organic molecules containing oxygen and nitrogen donor sites. To overcome this drawback and open the route to industrial use of these catalytic reactions, the heterogenization of homogeneous copper catalysts are widely studied. A promising approach to robust catalytic materials is a direct immobilization of relevant copper complexes onto solid supports. For this purpose we developed a synthetic approach to phosphonate-substituted 1,10-phenanthroline derivatives [START_REF] Jiang | Cu-catalyzed Ullmann-type C-heteroatom bond formation: the key role of dinucleating ancillary ligands[END_REF], investigated their coordination [85,86] and catalytic properties of related copper(I) complexes [87]. These complexes are efficient catalyst for a wide range of catalytic reactions including C-N coupling and can be immobilized on titania oxide supports [88]. In order to investigate the possibilities of the heterogenized copper catalysts to promote various coupling reactions, at first the synthesis of Cu(I) complexes with 1,10-phenanthrolines with the phosphoryl groups at positions 2, 3, 4, and 5 was undertaken [87]. The efficiency of these complexes was studied in the model reaction of the diphenylamine arylation with the simplest iodobenzene. The complexes with 3-, 4-and 5-diethylphosphoryl substituted phenanthrolines were found to be of equal high efficiency (Scheme 31). Following these results, the free 3-diethoxyphosphoryl-1,10-phenanthroline ligand was grafted on the surface of hydrated mesoporouse titania followed by the complexation of copper ions, as shown in Scheme 32, to produce a heterogenized catalyst [88].

Scheme 32: Grafting of copper catalysts on the surface of hydrated mesoporous TiO2.

An excellent catalytic performance of the catalyst and its reusability in Huisgen 1,3-dipolar cycloaddition was demonstrated (Scheme 33). Moreover, this catalyst was found to be suitable for Sonogashira coupling and addition. Fairly low catalyst loading, simple recovery and reuse (up to ten times) of the solid were achieved in all studied reactions proceeding through principally different reaction pathways. This catalytic versatility of the copper catalyst is highly desirable for sustainable chemistry but still rarely reported owing to the challenge in the preparation of robust catalysts applicable for a wide range of experimental conditions. Scheme 33: Catalytic properties of the grafted copper(I) complex with 1,10-phenanthroline ligand.

We investigated the immobilization of copper nanoparticles (CuNPs) on various supports and used these solid catalysts in the C-N bond formation [89]. The model reaction included the amination of p-iodobenzonitrile with various azoles like imidazole, pyrazole, benzimidazole and indole (Scheme 34). TiO2 support was found to be the best among other tested (carbon, zeolite, montmorillonite-K10 clay) and the yields ranged from 59 to 90%. Using the model reaction with imidazole Cs2CO3 was found to be superior to K2CO3 as it provided almost quantitative yields on different supports. Using CuNPs/C catalyst we demonstrated the possibility to use it in three cycles without loss of efficiency.

Scheme 34: CuNPs on various supports in the aryalation of azoles.

Conclusions

As a result of our investigations in the field of the application of copper (I) catalysis in the formation of C-N bonds we may conclude that it can be seen as an efficient alternative to expensive Pd(0)-catalyzed amination in such fields as the amination of (hetero)aryl halides with adamantane-containing amines and various di-an polyamines. In the latter case we focused our attention at the N,N'-di(hetero)arylation and found out that this process is quite possible with the diamines, oxadiamines and polyamines. Comparing the efficiency of the Cu(I)-catalyzed amination with Pd-mediated processes, the advantage of the first is almost full absence of the side reactions of N,N-di(hetero)arylation of the primary amino groups in the majority of cases, on the other hand, steric hindrances become more important and may hamper the reactions. Also, in the case of diamines and oxadiamines the formation of monoarylated products may be more pronounced as well as the side reactions of the arylation of the secondary dialkylamino groups in polyamines. The right choice of the catalytic system helping to suppress side reactions and promoting the formation of the desired N,N'-diaryl derivatives is always important. The amination reactions catalyzed by Cu(I) complexes were extended to modifications of steroids with various N-containing heterocycles. Click reactions were successfully employed for the preparation of bis-and tris(steroid) systems (dipods and tripods) for further application in the anion binding studies. These reactions were also important in the synthesis of porphyrin triads of various architectures. Several heterogenized copper catalysts were also investigated to propose reusable catalytic systems.

Scheme 2 :

 2 Scheme 2: Cu(I)-catalyzed arylation of the adamantane-containing amines with para-substituted iodobenzenes.

Scheme 3 :

 3 Scheme 3: Expanding the scope of adamantylated amines in the copper-catalyzed arylation reaction.

Scheme 6 : 2 -

 62 Scheme 6: 2-Bromopyridines with fluorine-containing substituents in Cu(I)-catalyzed heteroarylation.

Scheme 7 :

 7 Scheme 7: Cu(I)-mediated heteroarylation of adamantane-containing amines with 2-fluoro-5-iodopyridine.

Scheme 8 :Scheme 9 :

 89 Scheme 8: Synthesis of N-(5-bromopyridin-2-yl) and N-(2-chloropyridin-5-yl)-substituted (adamantyl)alkylamines.

Scheme 10 :

 10 Scheme 10: Cu(I)-catalyzed N,N'-diarylation of the diamines.

Scheme 11 :

 11 Scheme 11: Arylation of linear diamines with 2-fluoroiodobenzene.

Scheme 12 :

 12 Scheme 12: Cu(I)-catalyzed N,N'-diarylation of the tri-and tetraamines.

Scheme 13 :

 13 Scheme 13: Cu(I)-catalyzed N,N'-diarylation of the naturally occurring tri-and tetraamines.

Scheme 14 :

 14 Scheme 14: Cu(I)-catalyzed N,N'-diarylation of the oxadiamines.

Scheme 15 :

 15 Scheme 15: Cu(I)-catalyzed N,N'-diheteroarylation of the diamines.

Scheme 16 :

 16 Scheme 16: Cu(I)-catalyzed N,N'-diheteroarylation of the tetraamines.

Scheme 17 :

 17 Scheme 17: Cu(I)-catalyzed N,N'-diheteroarylation of the naturally occurring tri-and tetraamines.

Scheme 18 :

 18 Scheme 18: Cu(I)-catalyzed N,N'-di(hetero)arylation using 1-and 2-halogenonaphthalenes and 6-bromoquinoline.

Scheme 19 :

 19 Scheme 19: Cu(I)-catalyzed N,N'-diheteroarylation of trioxadiamine with the 2-and 3-iodopyridine and fluorine-containing 2-bromopyridines.

Scheme 20 :

 20 Scheme 20: Cu(I)-catalyzed N,N'-diheteroarylation of the tetraamines with 3-halogenothiophenes.

Scheme 21 :

 21 Scheme 21: Cu(I)-catalyzed amination reaction in the functionalization of steroids and synthesis of steroid dyads.

Scheme 22 :

 22 Scheme 22: Cu(I)-catalyzed vinylation of indoles and imidazole using 17-iodoandrosta-4,16-dien-3-one.

Scheme 23 :

 23 Scheme 23: Cu(I)-catalyzed amination of 3-iodosteroids with various azoles.

Scheme 29 :Scheme 30 :

 2930 Scheme 29: Triazolyl linkers in the synthesis of the porphyrin triads.

Scheme 31 :

 31 Scheme 31:Copper catalysts comprising phosphonate-substituted 1,10-phenanthroline ligand.

Scheme 4: Cu(I)-catalyzed arylation of the adamantane-containing diamines with para-substituted iodobenzenes.

Scheme 27: Click reaction in the steroids modifications.

Scheme 28: Synthesis of dipodal and tripodal ligands -derivatives of cholanes -using click strategy.

Dipropargyl derivative appeared to be significantly less reactive than the monopropargyl-containing diphenylphosphinate, however, excellent yields were obtained when the temperature was raised to 60°C. The same conditions