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We present the experimental implementation of simultaneous spatial multimode demultiplexing as a distance measurement tool. We first show a simple and intuitive derivation of the Fisher information in the presence of Poissonian noise. We then estimate the distance between two incoherent beams in both directions of the transverse plane, and find a perfect accordance with theoretical prediction, given a proper calibration of the demultiplexer. We find that, even though sensitivity is limited by the cross-talks between channels, we can perform measurements in 2 dimensions much beyond Rayleigh limit with a large dynamic.

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 study noise propagation dynamics in a femtosecond oscillator by injecting external noise on the pump intensity. We utilize a spectrally-resolved homodyne detection technique that enables simultaneous measurement of amplitude and phase quadrature noises of different spectral bands of the oscillator. To reveal the impact of added pump noise on the oscillator noise, we perform a modal analysis of the oscillator noise in which each mode corresponds to a particular temporal/spectral shape of the pulsed light. We compare this modal approach with the conventional noise detection methods and find the superiority of our method in particular unveiling a complete physical picture of noise distribution in femtosecond oscillator.

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.

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., Comment: 27 pages (incl. appendix), 6 figures

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states, and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyse the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

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.

A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cram\'er-Rao limit of detection without any assumptions on the nature of the light source.

The sensitivity of homodyne timing measurements with femtosecond lasers is only limited by the amplitude and phase noise. We describe a novel method to analyze the phase noise of a Ti:Sapph oscillator relative to the standard quantum limit. The broadband passive cavity used to this aim also filters lowest levels of classical noise at sidebands above 100kHz detection frequency. Leading to quantum limited carrier-envelope-phase noise at $\mu$s-timescales, it can improve the sensitivity of a highly sensitive, homodyne timing jitter measurement by 2 orders of magnitude.

We study in this paper the efficiency of different two-photon states of light to induce the simultaneous excitation of two atoms of different kinds when the sum of the energies of the two photons matches the sum of the energies of the two atomic transitions, while no photons are resonant with each individual transition. We find that entangled two-photon states produced by an atomic cascade are indeed capable of enhancing by a large factor the simultaneous excitation probability as compared to uncorrelated photons, as predicted some years ago by Muthukrishnan et al, but that several non-entangled, separable, correlated states, produced either by an atomic cascade or parametric down conversion, or even appropriate combinations of coher- ent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anti-correlation and not time correlation nor time-frequency entanglement.

We propose a direct and real-time ranging scheme using an optical frequency combs, able to compensate optically for index of refraction variations due to atmospheric parameters. This scheme could be useful for applications requiring stringent precision over a long distance in air, a situation where dispersion becomes the main limitation. The key ingredient is the use of a mode-locked laser as a precise source for multi-wavelength interferometry in a homodyne detection scheme. By shaping temporally the local oscillator, one can directly access the desired parameter (distance) while being insensitive to fluctuations induced by parameters of the environment such as pressure, temperature, humidity and CO$_2$ content.

The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology., Comment: 14 pages, 5 figures

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example in cluster state computation. They can be generated either by mixing different squeezed light sources using linear optical operations, or directly in a multimode optical device. In parallel, frequency combs are perfect tools for high precision metrological applications and for quantum time transfer. Synchronously Pumped Optical Parametric Oscillators (SPOPOs) have been theoretically shown to produce multimode non-classical frequency combs. In this paper, we present the first experimental generation and characterization of a femtosecond quantum frequency comb generated by a SPOPO. In particular, we give the experimental evidence of the multimode nature of the generated quantum state and, by studying the spectral noise distribution of this state, we show that at least three nonclassical independent modes are required to describe it.

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes.

We consider the problem of the measurement of very small displacements in the transverse plane of an optical image with a split photodetector. We show that the standard quantum limit for such a measurement, which is equal to the diffraction limit divided by the square root of the number of photons used in the measurement, cannot be overcome by use of ordinary single-mode squeezed light. We give the form of possible multimode nonclassical states of light, enabling us to enhance by orders of magnitude the resolution of such a measurement beyond the standard quantum limit., Comment: 9 pages

We study the transmission of a monochromatic "image" through a paraxial cavity. Using the formalism of self-transform functions, we show that a transverse degenerate cavity transmits the self-transform part of the image, with respect to the field transformation over one round-trip of the cavity. This formalism gives a new insight on the understanding of the behavior of a transverse degenerate cavity, complementary to the transverse mode picture. An experiment of image transmission through a hemiconfocal cavity show the interest of this approach., Comment: submitted to Phys. Rev. A

We describe an experiment showing a spontaneous symmetry breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type-II harmonic generation. It is based on a triply resonant dual cavity containing a type II phase matched $\chi^{(2)}$ crystal pumped at the fundamental frequency $\omega_0$. The pump beam generates in the cavity a second harmonic mode at frequency $2\omega_0$ which acts as a pump for frequency degenerate type II parametric down conversion. Under operating conditions which are precisely symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we have observed a breaking of the symmetry on the intensities of these two waves in agreement with the theoretical predictions., Comment: submitted

We have developed a new method based on two cavities containing $\chi^{(2)}$ media to reshape optical pulses by an all-optical technique. The system is entirely passive \emph{i.e.}, all the energy is brought by the incoming pulse and uses two successive optical cavities with independent thresholds. The output pulse is close to a rectangular shape. We show that this technique could be extended to high bit rates and telecommunication wavelength using very small cavities containing current nonlinear materials.