Search

In 1935, Schrödinger introduced the word "entanglement" to describe a situation examined in the famous Einstein-Podolsky-Rosen paper published a few months before. The proper nature of quantum correlations that exist when a two-partite system is in an entangled state was a subject of controversy. In contrast to many other subjects, the debate about the nature of entanglement came quite recently to an end.

Léon Brillouin a été durant toute sa carrière au coeur des développements de la nouvelle physique quantique. Il lui a apporté des contributions majeures et originales, notamment en physique du solide. Il a participé à l’émergence d’une nouvelle discipline scientifique : l’informatique.

International audience; Le père jésuite Ignace Gaston Pardies, outre son activité d’enseignant dans les collèges jésuites comme celui de Clermont à Paris, a été au coeur des débats concernant la nature de la lumière, correspondant avec Newton, Leibniz, Huygens et bien d’autres savants européens. Avant Huygens, il a été le premier à proposer une théorie détaillée et argumentée basée sur la nature ondulatoire de la lumière. Malheureusement, son décès à l’âge de 36 ans a prématurément interrompu une carrière prometteuse.

Irène Curie nait à Paris en 1897. Elle est la fille ainée de Pierre Curie et Marie Sklodowska-Curie. Une année auparavant, Henri Becquerel a découvert un rayonnement étrange émis par les sels d’uranium. Marie décide d’en faire le sujet de ses travaux de thèse, bientôt suivie par Pierre, qui laisse de côté ses recherches sur le magnétisme.

Measuring the spectral properties of an optical frequency comb is among the most fundamental tasks of precision metrology. In contrast to general single-parameter measurement schemes, we demonstrate here single shot multi-parameter estimation of an optical frequency comb at and beyond the standard quantum limit. The mean energy and the central frequency as well as the spectral bandwidth of ultrafast pulses are simultaneously determined with a multi-pixel spectrally resolved (MPSR) apparatus, without changing the photonics architecture. Moreover, using a quantum frequency comb that intrinsically consists of multiple squeezed states in a family of Hermite–Gaussian spectral/temporal modes, the signal-to-noise ratios of the multiple spectral parameters estimation can surpass the standard quantum limit. Combining our multi-pixel detection scheme and the multimode entangled resource could find applications in ultrafast quantum metrology and multimode quantum information processing.

Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. We present both the experimental implementation of simultaneous spatial multimode demultiplexing as a distance measurement tool and the theoretical analysis of the actual sensitivity limits given the main experimental imperfection: cross-talks between channels. We demonstrate the distance estimation between two incoherent beams in both directions of the transverse plane, and find a perfect accordance with theoretical predictions, given a proper calibration of the demultiplexer. We show that, even though sensitivity is limited by the cross-talk between channels, we can perform measurements in two dimensions much beyond the Rayleigh limit over a large dynamic range. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and N.

International audience

A few decades ago, quantum optics stood out as a new domain of physics by exhibiting states of light with no classical equivalent. The first investigations concerned single photons, squeezed states, twin beams and EPR states, that involve only one or two modes of the electromagnetic field. The study of the properties of quantum light then evolved in the direction of more and more complex and rich situations, involving many modes, either spatial, temporal, frequency, or polarization modes. Actually, each mode of the electromagnetic field can be considered as an individual quantum degree of freedom. It is then possible, using the techniques of nonlinear optics, to couple different modes, and thus to build in a controlled way a quantum network in which the nodes are optical modes and that is endowed with a strong multipartite entanglement. In addition, such networks are easily reconfigurable and subject only to weak decoherence. They open indeed many promising perspectives for optical communications and computation. Because of the linearity of Maxwell equations a linear superposition of two modes is another mode. This means that a "modal superposition principle" exists hand in hand with the regular quantum state superposition principle. The purpose of the present review is to show the interest of considering these two aspects of multimode quantum light in a global way. Indeed using different sets of modes allows to consider the same quantum state under different perspectives: a given state can be entangled in one basis, factorized in another. We will show how to produce, characterize and tailor multimode quantum light. Finally we will describe some applications to quantum technologies, such as parameter estimation and measurement-based quantum computation., Review paper

Superresolution techniques based on intensity measurements after a spatial mode decomposition can overcome the precision of diffraction-limited direct imaging. However, realistic measurement devices always introduce finite crosstalk in any such mode decomposition. Here, we show that any nonzero crosstalk leads to a breakdown of superresolution when the number $N$ of detected photons is large. Combining statistical and analytical tools, we obtain the scaling of the precision limits for weak, generic crosstalk from a device-independent model as a function of the crosstalk probability and $N$. The scaling of the smallest distance that can be distinguished from noise changes from $N^{-1/2}$ for an ideal measurement to $N^{-1/4}$ in the presence of crosstalk., Comment: 5 + 6 pages, 5 + 3 figures

We have experimentally shown in a recent paper [Wang et al., Phys. Rev. A 95, 051802(R) (2017)] that a four-wave mixing (FWM) process in a Rb vapor with a spatially structured pump (SSP), consisting of a coherent combination of two tilted pump beams, can generate six well-separated bright beams that are quantum correlated. The experimental setup is compact, simple, phase insensitive, and easily scalable to a larger number of quantum correlated beams. For applications to quantum information processing, multipartite entanglement is needed in addition to quantum correlations. Very recently, we have also experimentally demonstrated the generation of the hexapartite entanglement from this SSP-based FWM process [Zhang et al., Phys. Rev. Lett. 124, 090501 (2020)]. The purpose of this theoretical paper is to extensively investigate the hexapartite entanglement properties by using different entanglement witnesses such as the van Loock-Furusawa criterion and the positivity under partial transposition criterion. We find that hexapartite entanglement is indeed present among the six beams. In addition, we also study the supermodes of this system using basis change.

Advanced quantum technologies require scalable and controllable quantum resources1,2. Gaussian states of multimode light, such as squeezed states and cluster states, are scalable quantum systems3–5, which can be generated on demand. However, non-Gaussian features are indispensable in many quantum protocols, especially to reach a quantum computational advantage6. 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 state7. To highlight the potential for continuous-variable quantum technologies, we first demonstrated the capability to generate negativity of the Wigner function in a controlled mode. Subsequently, we explored the interplay between non-Gaussianity and quantum entanglement and verify a theoretical prediction8 about the propagation of non-Gaussianity along the nodes of photon-subtracted cluster states. Our results demonstrate large-scale non-Gaussianity with great flexibility along with an ensured compatibility with quantum information protocols. This range of features makes our approach ideal to explore the physics of non-Gaussian entanglement9,10 and to develop quantum protocols, which range across quantum computing11,12, entanglement distillation13 and quantum simulations14. Continuous-variables quantum information processing requires non-Gaussian states and operations. The generation of non-Gaussian quantum states of a multimode field is now reported through a mode-selective photon-subtraction scheme

International audience; We present a single-pass source of broadband multimode squeezed light with potential application in quantum information and quantum metrology. The source is based on a type I parametric down-conversion (PDC) process inside a bulk nonlinear crystal in a non-collinear configuration. The generated squeezed light exhibits a spatio-temporal multimode behavior that is probed using a homodyne measurement with a local oscillator shaped both spatially and temporally. Finally we follow a covariance matrix based approach to reveal the distribution of the squeezing among several independent temporal and spatial modes. This unambiguously validates the multimode feature of our source.

We theoretically investigate the generation of two entangled beams of light in the process of single-pass type-I noncollinear frequency degenerate parametric downconversion with an ultrashort pulsed pump. We find the spatio-temporal squeezing eigenmodes and the corresponding squeezing eigenvalues of the generated field both numerically and analytically. The analytical solution is obtained by modeling the joint spectral amplitude of the field by a Gaussian function in curvilinear coordinates. We show that this method is highly efficient and is in a good agreement with the numerical solution. We also reveal that when the total bandwidth of the generated beams is sufficiently high, the modal functions cannot be factored into a spatial and a temporal parts, but exhibit a spatio-temporal coupling, whose strength can be increased by shortening the pump., Comment: accepted version, 19 pages, 10 figures

Quantum key distribution with continuous variables already uses advantageous high-speed single-mode homodyne detection with low electronic noise at room temperature. Together with continuous-variable information encoding to nonclassical states, the distance for secure key transmission through lossy channels can approach 300 km in current optical fibers. Such protocols tolerate higher channel noise and also limited data processing efficiency compared to coherent-state protocols. The secret key rate can be further increased by increasing the system clock rates, and, further, by a suitable frequency-mode-multiplexing of optical transmission channels. However, the multiplexed modes couple together in the source or any other part of the protocol. Therefore, multiplexed communication will experience crosstalk and the gain can be minuscule. Advantageously, homodyne detectors allow solving this crosstalk problem by proper data processing. It is a potential advantage over protocols with single-photon detectors, which do not enable similar data processing techniques. We demonstrate the positive outcome of this methodology on the experimentally characterized frequency-multiplexed entangled source of femtosecond optical pulses with natural crosstalk between eight entangled pairs of modes. As the main result, we predict almost 15-fold higher secret key rate. This experimental test and analysis of frequency-multiplexed entanglement source opens the way for the field implementation of high-capacity quantum key distribution with continuous variables., Comment: 14 pages, 5 figures; to be published in Photonics Research

We study the Bloch-Messiah reduction of parametric downconversion of light in the pulsed regime with a nondegenerate phase matching providing generation of twin beams. We find that in this case every squeezing eigenvalue has multiplicity at least two. We discuss the problem of ambiguity in the definition of the squeezing eigenmodes in this case and develop two approaches to unique determination of the latter. First, we show that the modal functions of the squeezing eigenmodes can be tailored from the Schmidt modes of the signal and idler beams. Alternatively, they can be found as a solution of an eigenvalue problem for an associated Hermitian squeezing matrix. We illustrate the developed theory by an example of frequency non-degenerate collinear twin beams generated in beta barium borate crystal. On this example we demonstrate how the squeezing eigenmodes can be approximated analytically on the basis of the Mehler's formula, extended to complex kernels. We show how the multiplicity of the eigenvalues and the structure of the eigenmodes are changed when the phase matching approaches the degeneracy in frequency., Comment: 18 pages, 9 figures, 1 theorem

Multipartite entanglement serves as a vital resource for quantum information processing. Generally, its generation requires complex beam splitting processes which limit scalability. A promising trend is to integrate multiple nonlinear processes into a single device via frequency or time multiplexing. The generated states in these schemes are useful for quantum computation. However, they are confined in one or two beams and hard to be spatially separated for applications in quantum communication. Here, we experimentally demonstrate a scheme to generate spatially separated hexapartite entangled states by means of spatially multiplexing seven concurrent four-wave mixing processes. In addition, we show that the entanglement structure characterized by subsystem entanglement distribution can be modified by appropriately shaping the pump characteristics. Such reconfigurability of the entanglement structure gives the possibility to target a desired multipartite entangled state for a specific quantum communication protocol. Our results here provide a new platform for generating large scale spatially separated reconfigurable multipartite entangled beams.

The experimental implementation of large multipartite entangled state in the time and frequency domain is realised via optical frequency comb and parametric process. We discuss the implementation of quantum complex networks and their non-Gaussian features

The first quantum-enhanced interferometric timing measurement with a squeezed optical frequency comb was demonstrated. The timing resolution at 2 MHz was improved from a shot-noise limited value of (2.8 ± 0.1) × 10−20 s to (2.4 ± 0.1) × 10−20 s.

We show the single-pass generation of entangled states featuring spatial-spectral quantum correlations via SPDC. They constitute multimode building blocks of dual-rail cluster states, which can be achieved via multiplexing in the time (pulsed) domain.

Accurate time-delay measurement has become a crucial issue for space positioning experiments which require increasing precision over large distances. The femtosecond frequency comb has been found to be a good source for its advantages of a large nonambiguity range and coherence length up to tens of kilometers or more. A scheme combining homodyne detection and frequency combs was proposed [B. Lamine et al., Phys. Rev. Lett. 101, 123601 (2008)] that leads to a timing sensitivity reaching the shot-noise limit; with a squeezed frequency comb as the input field, the measured timing sensitivity can be further improved to the level of the sub-shot-noise limit. Based on this scheme and a squeezed frequency comb that was measured to have a phase squeezing of 1.5 dB at an analyzing frequency of 2 MHz, a narrow-band interferometric timing measurement is implemented. The minimum measurable timing variation modulation at 2 MHz is reduced from a shot-noise-limited value of $(2.8\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s to $(2.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s.

We present an upconversion imaging experiment from the near-infrared to the visible spectrum. Using a dedicated broadband pump laser to increase the number of resolved elements converted in the image we obtain up to 56x64 spatial elements with a 2.7 nm wide pump spectrum, more than 10 times the number of elements accessible with a narrowband laser. Results in terms of field of view, resolution and conversion efficiency are in good agreement with simulations. The computed sensitivity of our experiment favorably compares with direct InGaAs camera detection.

Near-infrared imaging InGaAs sensors show lower performances in term of noise and sensitivity compared to silicon based cameras. Image frequency conversion from near-infrared to visible wavelengths by nonlinear parametric sumfrequency mixing in a χ(2) medium should increase detection performances in active imaging applied to long range target identification. For such applications, both energy conservation and phase matching conditions are ideally suited to efficient upconversion. Nevertheless, the available resolution still hampers the development of upconversion imagers. In this paper, we upconvert images provided by 1.5 μm collimated continuous wave lasers illuminating resolution targets and small objects. Using a 2.7 nm wide pump spectrum at 1064 nm, we resolve 56x64 spatial elements whereas we obtained only 16x19 spatial elements with a narrow spectrum pump laser at 1064 nm with the same beam diameter and 8x8 spatial elements with a 0.5 mm thick crystal. These results are compatible with long range target recognition. A laboratory scale experiment of active imaging of diffusive objects is shown as an illustration.

In this work, we investigate three different compact fibered systems generating vacuum squeezing that involve optical cavities limited by the end surface of a fiber and by a curved mirror and containing a thin parametric crystal. These systems have the advantage to couple squeezed states directly to a fiber, allowing the user to benefit from the flexibility of fibers in the use of squeezing. Three types of fibers are investigated: standard single-mode fibers, photonic-crystal large-mode-area single-mode fibers, and short multimode fibers taped to a single-mode fiber. The observed squeezing is modest (−0.56 dB, −0.9 dB, −1 dB), but these experiments open the way for miniaturized squeezing devices that could be a very interesting advantage in scaling up quantum systems for quantum processing, opening new perspectives in the domain of integrated quantum optics.

We study the quantum correlations induced by spontaneous parametric down-conversion (SPDC) of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the advantages of pump-shaping in real experiments we take into account the physical limitations of the pulse shaper., Updated title, improved presentation and figures, added references, corrected typos. Closer to the version accepted for publication

The nature of a quantum network, in particular in the continuous variable regime, is governed not only by the light quantum state but also by the measurement process. It can then be chosen after the light source has been generated. Multimode entanglement is not anymore an intrinsic property of the source but a complex interplay between source, measurement and eventually post processing. This new avenue paves the way for adaptive and scalable quantum information processing. However, to reach this ambitious goal, multimode degaussification has to be implemented. Single-photon subtraction and addition have proved to be such key operations, but are usually performed with linear optics elements on single-mode resources. We present a device able to perform mode dependant non Gaussian operation on a spectrally multimode squeezed vacuum states. Sum frequency generation between the state and a bright control beam whose spectrum has been engineered through ultrafast pulse-shaping is performed. The detection of a single converted photon heralds the success of the operation. The resulting multimode quantum state is analysed with standard homodyne detection whose local oscillator spectrum is independently engineered. The device can be characterized through quantum process tomography using weak multimode coherent states as inputs. Its single-mode character can be quantified and its inherent subtraction modes can be measured. The ability to simultaneously control the state engineering and its detection ensures both flexibility and scalability in the production of highly entangled non-Gaussian quantum states.

Single-photon subtracting operation plays important roles in photonic quantum information processing. For example, it enables distillation of entanglement, noiseless amplification of a quantum state, and enhancement of measurement precision. In particular, the non-Gaussian characteristic of the operation is essential for genuine speed-up and universality of continuous-variable quantum computing. Until now, implementation of single-photon subtraction has been limited on a single-mode or a two-mode quantum state, but recently, extension to multiple modes attracts attention [1, 2] in accordance with the availability of multimode quantum states [3].

The mid-infrared domain (MIR) has recently witnessed a renewed interest for a large range of demanding applications such as spectroscopic detection [1, 2]. However, this region still suffers from a lack of low noise, efficient and fast detectors contrary to the visible or near-infrared regions. This has led to the development of an alternative detection scheme based on sum frequency generation (SFG). This idea is as old as nonlinear optics but the limited efficiency of available nonlinear materials has hampered practical developments for a long time [3]. The advent of periodically poled lithium niobate (PPLN) and related crystals constituted a breakthrough for signal wavelengths in their transparency range, i.e. up to 4.5 μm [4].

We report an upconversion experiment using an orientation-patterned gallium arsenide (OP-GaAs) crystal to detect small mid-infrared signals on an InGaAs avalanche photodiode. A conversion efficiency up to 20% with a nonpolarized pulsed fiber pump is demonstrated. Our uncooled setup is favorably compared in terms of noise equivalent power, dynamic range, and response time to cryogenically cooled HgCdTe detectors. Its dependence on the polarization of both the pump and signal beams is also investigated.

An experimental scheme is introduced to measure multiple parameters that are encoded in the phase quadrature of a light beam. Using a modal description and a spectrally-resolved homodyne detection, it is shown that all of the information is collected simultaneously, such that a single measurement allows extracting the value of multiple parameters \emph{post-facto}. With a femtosecond laser source, we apply this scheme to a measurement of the delay between two pulses with a shot-noise limited sensitivity as well as extracting the dispersion value of a dispersive medium.

The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics. Quantum physics adds that the excitation within each mode is quantized in close analogy to the harmonic oscillator. A complete set of mode functions forms a basis with which any new modes can be reconstructed. In full generality each electromagnetic mode function in the four dimensional space-time is mathematically equivalent to a harmonic oscillator. The quantization of the electromagnetic field defines the excitation per mode and the correlation between modes. In classical optics there can be oscillations and stochastic fluctuations of amplitude, phase, polarization et cetera. In quantum optics there are in addition uncertain quantum field components, quantum correlations and quantized energies. Here, we present selected topics from classical to quantum optics. We start in the second chapter with the classical optics description of a light field and its spectral densities, their measurement and their interpretation. In the third chapter the quantum properties of a single light mode are reviewed as well as ways to measure these quantum properties. Gaussian states of a light mode are emphasized, i. e. states for which the Wigner function has a two dimensional Gaussian shape. The fourth chapter will be concerned with more than one mode presenting a unifying approach to quadratic Hamiltonians including phase conjugation which is related to time reversal.

We present a new multimode squeezed-states quantum source operating in a single pass regime suitable for cluster states and complex network generation.

We present the generation and characterization of a multimode non-gaussian state. We prepare squeezed vacua in multiple time-frequency modes, subtract a single photon, and then characterize the state by using mode-selective homodyne detection.

The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this contribution, we derive the truncated correlations, which are multimode generalisations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process, and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum., 27 pages (incl. appendix), 6 figures