Nicolas Treps | Sorbonne University (original) (raw)
Papers by Nicolas Treps
We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomi... more We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomic ensemble using a pair of quantum-correlated atomic ensembles. We show how to prepare this pair of ensembles using quasiperfect quantum state transfer processes between light and atoms. Our protocol relies on optical joint measurements of the atomic ensemble states and magnetic feedback reconstruction.
Physical Review Letters, 2007
We present the key elements required for continuous variable parallel quantum information protoco... more We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear 2 material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.
Physical Review Letters, 2002
Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement ... more Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.
Optics Letters, 2006
We consider the problem of measurement of optical transverse profile parameters and their conjuga... more We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multi-mode analysis, we introduce the concept of detection noise-modes. For Gaussian beams, displacement and tilt are a pair of transverse profile conjugate variables. We experimentally demonstrate their optimal encoding and detection with a spatial homodyning scheme. Using higher order spatial mode squeezing, we show the sub-shot noise measurements for the displacement and tilt of a Gaussian beam.
Physical Review A, 2005
A light beam is said to be position squeezed if its position can be determined to an accuracy bey... more A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.
Physical Review Letters, 2008
Exchanging light pulses to perform accurate space-time positioning is a paradigmatic issue of phy... more Exchanging light pulses to perform accurate space-time positioning is a paradigmatic issue of physics. It is ultimately limited by the quantum nature of light, which introduces fluctuations in the optical measurements and leads to the so-called Standard Quantum Limit (SQL) [1, 2, 3]. We propose a new scheme combining homodyne detection and mode-locked femtosecond lasers that lead to a new SQL in time transfer, potentially reaching the yoctosecond range (10 −21 − 10 −24 s).
Journal of The European Optical Society-rapid Publications, 2006
We demonstrate quantum correlations in the transverse plane of continuous wave light beams by pro... more We demonstrate quantum correlations in the transverse plane of continuous wave light beams by producing −4.0 dB, −2.6 dB and −1.5 dB of squeezing in the TEM00, TEM10 and TEM20 Hermite-Gauss modes with an optical parametric amplifier, respectively. This has potential applications in quantum information networking, enabling parallel quantum information processing. We describe the setup for the generation of squeezing and analyze the effects of various experimental issues such as mode overlap between pump and seed and nonlinear losses.
Journal of Modern Optics, 2006
We study experimentally parametric amplification in the continuous regime using a transversedegen... more We study experimentally parametric amplification in the continuous regime using a transversedegenerate type-II Optical Parametric Oscillator operated below threshold. We demonstrate that this device is able to amplify either in the phase insensitive or phase sensitive way first a single mode beam, then a multimode image. Furthermore the total intensities of the amplified image projected on the signal and idler polarizations are shown to be correlated at the quantum level.
Physical Review A, 2005
We study the transmission of a monochromatic "image" through a paraxial cavity. Using the formali... more 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 selftransform 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.
Physical Review A, 2004
We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing a... more We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing at very low noise sideband frequencies produced by a single type-II, self-phase-locked, frequency degenerate optical parametric oscillator below threshold. The generated two-mode squeezed vacuum state is preserved for noise frequencies as low as 50 kHz. Designing simple setups able to generate non-classical states of light in the kHz regime is a key challenge for high sensitivity detection of ultra-weak physical effects such as gravitational wave or small beam displacement.
IEEE Journal of Selected Topics in Quantum Electronics, 2003
We investigate continuous variable quantum teleportation. We discuss the methods presently used t... more We investigate continuous variable quantum teleportation. We discuss the methods presently used to characterize teleportation in this regime, and propose an extension of the measures proposed by Grangier and Grosshans [1], and Ralph and Lam [2]. This new measure, the gain normalized conditional variance product ¢ , turns out to be highly significant for continuous variable entanglement swapping procedures, which we examine using a necessary and sufficient criterion for entanglement. We elaborate on our recent experimental continuous variable quantum teleportation results [3], demonstrating success over a wide range of teleportation gains . We analyze our results using fidelity; signal transfer, and the conditional variance product; and a measure derived in this paper, the gain normalized conditional variance product.
Journal of Optics B-quantum and Semiclassical Optics, 2002
We propose and demonstrate a system that produces squeezed vacuum using a pair of optical paramet... more We propose and demonstrate a system that produces squeezed vacuum using a pair of optical parametric amplifiers. This scheme allows the production of phase sidebands on the squeezed vacuum which facilitate phase locking in downstream applications. We observe strong, stably locked, continuous wave vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative resonator configuration to overcome low frequency squeezing degradation caused by the optical parametric amplifiers.
Nature Photonics, 2009
. . f 0 f 0 / 2 p + 0.5 1.0 1.5 V ( ) x+y f / 2 phase shift p , , V ( ) x y f , , -Variance (line... more . . f 0 f 0 / 2 p + 0.5 1.0 1.5 V ( ) x+y f / 2 phase shift p , , V ( ) x y f , , -Variance (linear) I=0.82 0.02 + -I= Fig. 1: Results for inseparability. Measurement of the variance for the sum
Physical Review Letters, 2003
We report the first experimental demonstration of conditional preparation of a non-classical stat... more We report the first experimental demonstration of conditional preparation of a non-classical state of light in the continuous variable regime. Starting from a non-degenerate OPO which generates above threshold quantum intensity correlated signal and idler "twin beams", we keep the recorded values of the signal intensity only when the idler intensity falls inside a band of values narrower than its standard deviation. By this very simple technique, we generate a sub-Poissonian state 4.4 dB (64%) below shot noise from twin beams exhibiting 7.5 dB (82%) of noise reduction in the intensity difference. PACS numbers: 42.50 Dv, 42.65.Yj A well-known technique to generate a single photon state from quantum correlated photons ("twin photons") is to use the method of conditional measurement: if one labels and the two modes in which the twin photons are emitted, it consists in retaining in the information collected on mode (1) only the counts occurring when a photon is detected in mode (2) (within a given time window ∆T ). This method has been widely and very successfully used over the past decades, firstly with twin photons generated by an atomic cascade [1], then by using the more efficient technique of parametric down conversion . Various protocols have been proposed to use conditional preparation in order to generate other kinds of non-classical states, for example Schrödinger cat states using a squeezed vacuum state transmitted through a beamsplitter and a measurement conditioned by the counts detected on the reflected port . In a similar way, teleportation of a quantum state of light can be achieved by using conditional measurements [4] and the degree of entanglement can be improved by photon subtractions . In cavity QED, conditional measurements on the atomic state have also led to the experimental generation of non-classical photon states [6].
Optics Express, 2010
A self-imaging resonator can be simultaneously resonant for many transverse modes and therefore a... more A self-imaging resonator can be simultaneously resonant for many transverse modes and therefore allows cavity build-up for images of various shapes. The stability properties of such a cavity are reviewed. We have used this device for the first time to enhance the efficiency of second harmonic generation of weak images. We characterize the global and local efficiency of the second harmonic generation, and discuss its limitation due to the spatial bandwidth of the cavity and the diffraction along the crystal length.
Entangling the Spatial Properties of Laser Beams
Science, 2008
Position and momentum were the first pair of conjugate observables explicitly used to illustrate ... more Position and momentum were the first pair of conjugate observables explicitly used to illustrate the intricacy of quantum mechanics. We have extended position and momentum entanglement to bright optical beams. Applications in optical metrology and interferometry require the continuous measurement of laser beams, with the accuracy fundamentally limited by the uncertainty principle. Techniques based on spatial entanglement of the beams could overcome this limit, and high-quality entanglement is required. We report a value of 0.51 for inseparability and 0.62 for the Einstein-Podolsky-Rosen criterion, both normalized to a classical limit of 1. These results are a conclusive optical demonstration of macroscopic position and momentum quantum entanglement and also confirm that the resources for spatial multimode protocols are available.
Pattern formation in optical parametric oscillators
Physical Review A, 2001
We have observed transverse pattern formation in type-II continuous-wave triply resonant optical ... more We have observed transverse pattern formation in type-II continuous-wave triply resonant optical parametric oscillators (OPOs). Different kinds of cavities with degenerate transverse modes have been studied: confocal, concentric, semiconcentric, and planar. We have ...
Physical Review A, 2006
We have developed the full theory of a synchronously pumped type I optical parametric oscillator ... more We have developed the full theory of a synchronously pumped type I optical parametric oscillator (SPOPO). We derive expressions for the oscillation threshold and the characteristics of the generated mode-locked signal beam. We calculate the output quantum fluctuations of the device, and find that, in the degenerate case (coincident signal and idler set of frequencies), perfect squeezing is obtained when one approaches threshold from below for a well defined "super-mode', or frequency comb, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
Physical Review A, 2010
We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes,... more We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes, either spatial or temporal, generates both below and above threshold a multimode non-classical state of light consisting of squeezed vacuum states in all the non-oscillating modes. We confirm this prediction by an experiment dealing with the degenerate TEM01 and TEM10 modes. We show the conservation of non-classical properties when the threshold is crossed. The experiment is made possible by the implementation of a new method to lock the relative phase of the pump and the injected beam.
Physical Review A, 2005
We study theoretically and experimentally the quantum properties of a type II frequency degenerat... more We study theoretically and experimentally the quantum properties of a type II frequency degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode gaussian states, illustrated in terms of covariance matrix. We report on the experimental generation of two-mode squeezed vacuum on non-orthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e. quantum correlations and anticorrelations on orthogonal quadratures. A half-sum of squeezed variances as low as 0.33 ± 0.02, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.
We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomi... more We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomic ensemble using a pair of quantum-correlated atomic ensembles. We show how to prepare this pair of ensembles using quasiperfect quantum state transfer processes between light and atoms. Our protocol relies on optical joint measurements of the atomic ensemble states and magnetic feedback reconstruction.
Physical Review Letters, 2007
We present the key elements required for continuous variable parallel quantum information protoco... more We present the key elements required for continuous variable parallel quantum information protocols based on spatial multimode quantum correlations. We describe techniques for encoding, combining and detecting spatial quantum information with high efficiency in the individual transverse modes. Until now, the missing feature for the implementation of such protocols was the generation of squeezing in higher order transverse Hermite-Gauss modes. We experimentally demonstrate squeezing in selective modes by fine-tuning the phase matching condition of the nonlinear 2 material and the cavity resonance condition of an optical parametric amplifier. Combined, these results open the way to practical multimode optical quantum information systems.
Physical Review Letters, 2002
Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement ... more Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.
Optics Letters, 2006
We consider the problem of measurement of optical transverse profile parameters and their conjuga... more We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multi-mode analysis, we introduce the concept of detection noise-modes. For Gaussian beams, displacement and tilt are a pair of transverse profile conjugate variables. We experimentally demonstrate their optimal encoding and detection with a spatial homodyning scheme. Using higher order spatial mode squeezing, we show the sub-shot noise measurements for the displacement and tilt of a Gaussian beam.
Physical Review A, 2005
A light beam is said to be position squeezed if its position can be determined to an accuracy bey... more A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.
Physical Review Letters, 2008
Exchanging light pulses to perform accurate space-time positioning is a paradigmatic issue of phy... more Exchanging light pulses to perform accurate space-time positioning is a paradigmatic issue of physics. It is ultimately limited by the quantum nature of light, which introduces fluctuations in the optical measurements and leads to the so-called Standard Quantum Limit (SQL) [1, 2, 3]. We propose a new scheme combining homodyne detection and mode-locked femtosecond lasers that lead to a new SQL in time transfer, potentially reaching the yoctosecond range (10 −21 − 10 −24 s).
Journal of The European Optical Society-rapid Publications, 2006
We demonstrate quantum correlations in the transverse plane of continuous wave light beams by pro... more We demonstrate quantum correlations in the transverse plane of continuous wave light beams by producing −4.0 dB, −2.6 dB and −1.5 dB of squeezing in the TEM00, TEM10 and TEM20 Hermite-Gauss modes with an optical parametric amplifier, respectively. This has potential applications in quantum information networking, enabling parallel quantum information processing. We describe the setup for the generation of squeezing and analyze the effects of various experimental issues such as mode overlap between pump and seed and nonlinear losses.
Journal of Modern Optics, 2006
We study experimentally parametric amplification in the continuous regime using a transversedegen... more We study experimentally parametric amplification in the continuous regime using a transversedegenerate type-II Optical Parametric Oscillator operated below threshold. We demonstrate that this device is able to amplify either in the phase insensitive or phase sensitive way first a single mode beam, then a multimode image. Furthermore the total intensities of the amplified image projected on the signal and idler polarizations are shown to be correlated at the quantum level.
Physical Review A, 2005
We study the transmission of a monochromatic "image" through a paraxial cavity. Using the formali... more 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 selftransform 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.
Physical Review A, 2004
We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing a... more We report on the experimental demonstration of strong quadrature EPR entanglement and squeezing at very low noise sideband frequencies produced by a single type-II, self-phase-locked, frequency degenerate optical parametric oscillator below threshold. The generated two-mode squeezed vacuum state is preserved for noise frequencies as low as 50 kHz. Designing simple setups able to generate non-classical states of light in the kHz regime is a key challenge for high sensitivity detection of ultra-weak physical effects such as gravitational wave or small beam displacement.
IEEE Journal of Selected Topics in Quantum Electronics, 2003
We investigate continuous variable quantum teleportation. We discuss the methods presently used t... more We investigate continuous variable quantum teleportation. We discuss the methods presently used to characterize teleportation in this regime, and propose an extension of the measures proposed by Grangier and Grosshans [1], and Ralph and Lam [2]. This new measure, the gain normalized conditional variance product ¢ , turns out to be highly significant for continuous variable entanglement swapping procedures, which we examine using a necessary and sufficient criterion for entanglement. We elaborate on our recent experimental continuous variable quantum teleportation results [3], demonstrating success over a wide range of teleportation gains . We analyze our results using fidelity; signal transfer, and the conditional variance product; and a measure derived in this paper, the gain normalized conditional variance product.
Journal of Optics B-quantum and Semiclassical Optics, 2002
We propose and demonstrate a system that produces squeezed vacuum using a pair of optical paramet... more We propose and demonstrate a system that produces squeezed vacuum using a pair of optical parametric amplifiers. This scheme allows the production of phase sidebands on the squeezed vacuum which facilitate phase locking in downstream applications. We observe strong, stably locked, continuous wave vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative resonator configuration to overcome low frequency squeezing degradation caused by the optical parametric amplifiers.
Nature Photonics, 2009
. . f 0 f 0 / 2 p + 0.5 1.0 1.5 V ( ) x+y f / 2 phase shift p , , V ( ) x y f , , -Variance (line... more . . f 0 f 0 / 2 p + 0.5 1.0 1.5 V ( ) x+y f / 2 phase shift p , , V ( ) x y f , , -Variance (linear) I=0.82 0.02 + -I= Fig. 1: Results for inseparability. Measurement of the variance for the sum
Physical Review Letters, 2003
We report the first experimental demonstration of conditional preparation of a non-classical stat... more We report the first experimental demonstration of conditional preparation of a non-classical state of light in the continuous variable regime. Starting from a non-degenerate OPO which generates above threshold quantum intensity correlated signal and idler "twin beams", we keep the recorded values of the signal intensity only when the idler intensity falls inside a band of values narrower than its standard deviation. By this very simple technique, we generate a sub-Poissonian state 4.4 dB (64%) below shot noise from twin beams exhibiting 7.5 dB (82%) of noise reduction in the intensity difference. PACS numbers: 42.50 Dv, 42.65.Yj A well-known technique to generate a single photon state from quantum correlated photons ("twin photons") is to use the method of conditional measurement: if one labels and the two modes in which the twin photons are emitted, it consists in retaining in the information collected on mode (1) only the counts occurring when a photon is detected in mode (2) (within a given time window ∆T ). This method has been widely and very successfully used over the past decades, firstly with twin photons generated by an atomic cascade [1], then by using the more efficient technique of parametric down conversion . Various protocols have been proposed to use conditional preparation in order to generate other kinds of non-classical states, for example Schrödinger cat states using a squeezed vacuum state transmitted through a beamsplitter and a measurement conditioned by the counts detected on the reflected port . In a similar way, teleportation of a quantum state of light can be achieved by using conditional measurements [4] and the degree of entanglement can be improved by photon subtractions . In cavity QED, conditional measurements on the atomic state have also led to the experimental generation of non-classical photon states [6].
Optics Express, 2010
A self-imaging resonator can be simultaneously resonant for many transverse modes and therefore a... more A self-imaging resonator can be simultaneously resonant for many transverse modes and therefore allows cavity build-up for images of various shapes. The stability properties of such a cavity are reviewed. We have used this device for the first time to enhance the efficiency of second harmonic generation of weak images. We characterize the global and local efficiency of the second harmonic generation, and discuss its limitation due to the spatial bandwidth of the cavity and the diffraction along the crystal length.
Entangling the Spatial Properties of Laser Beams
Science, 2008
Position and momentum were the first pair of conjugate observables explicitly used to illustrate ... more Position and momentum were the first pair of conjugate observables explicitly used to illustrate the intricacy of quantum mechanics. We have extended position and momentum entanglement to bright optical beams. Applications in optical metrology and interferometry require the continuous measurement of laser beams, with the accuracy fundamentally limited by the uncertainty principle. Techniques based on spatial entanglement of the beams could overcome this limit, and high-quality entanglement is required. We report a value of 0.51 for inseparability and 0.62 for the Einstein-Podolsky-Rosen criterion, both normalized to a classical limit of 1. These results are a conclusive optical demonstration of macroscopic position and momentum quantum entanglement and also confirm that the resources for spatial multimode protocols are available.
Pattern formation in optical parametric oscillators
Physical Review A, 2001
We have observed transverse pattern formation in type-II continuous-wave triply resonant optical ... more We have observed transverse pattern formation in type-II continuous-wave triply resonant optical parametric oscillators (OPOs). Different kinds of cavities with degenerate transverse modes have been studied: confocal, concentric, semiconcentric, and planar. We have ...
Physical Review A, 2006
We have developed the full theory of a synchronously pumped type I optical parametric oscillator ... more We have developed the full theory of a synchronously pumped type I optical parametric oscillator (SPOPO). We derive expressions for the oscillation threshold and the characteristics of the generated mode-locked signal beam. We calculate the output quantum fluctuations of the device, and find that, in the degenerate case (coincident signal and idler set of frequencies), perfect squeezing is obtained when one approaches threshold from below for a well defined "super-mode', or frequency comb, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.
Physical Review A, 2010
We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes,... more We show that an Optical Parametric Oscillator which is simultaneously resonant for several modes, either spatial or temporal, generates both below and above threshold a multimode non-classical state of light consisting of squeezed vacuum states in all the non-oscillating modes. We confirm this prediction by an experiment dealing with the degenerate TEM01 and TEM10 modes. We show the conservation of non-classical properties when the threshold is crossed. The experiment is made possible by the implementation of a new method to lock the relative phase of the pump and the injected beam.
Physical Review A, 2005
We study theoretically and experimentally the quantum properties of a type II frequency degenerat... more We study theoretically and experimentally the quantum properties of a type II frequency degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode gaussian states, illustrated in terms of covariance matrix. We report on the experimental generation of two-mode squeezed vacuum on non-orthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e. quantum correlations and anticorrelations on orthogonal quadratures. A half-sum of squeezed variances as low as 0.33 ± 0.02, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.