Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1204.2354 · New Journal of Physics

A time/frequency quantum analysis of the light generated by synchronously pumped optical parametric oscillators

Shifeng Jiang, Nicolas Treps, Claude Fabre

Published Apr 10, 2012• 23 citations
arXivHTMLPDF

Abstract

We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.

DOI
10.1088/1367-2630/14/4/043006

Related papers

Generation and characterization of multimode quantum frequency combs

R. Medeiros de Araújo, Olivier Pinel, Pu Jian +4 more

Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2011•2 citations

Quantum properties of ultra-short pulses generated by SPOPOs (multi-mode squeezing and entanglement)

Giuseppe Patera, Claude Fabre, LUGIATO, Luigi A.

This Thesis studies, from a theoretical point of view, the dynamical and quantum properties of a type I degenerate optical parametric oscillator which is synchronously pumped by a mode-locked laser (SPOPO). In recent past, SPOPOs have been used for generating ultra-short optical pulses of tunable wavelength and their temporal properties have been investigated. Having a huge number of degrees of freedom, the output field of a SPOPO needs to be characterized via a multimodal quantum analysis. Then, we first develop a multimode model of the device, obtaining the quantum equations for the intra-cavity field operators. Afterwards, we study the steady state solutions of the average values of the generated fields that are the solutions of an eigenvalue equation. Its spectrum gives information about the “useful” number of modes in which are concentrated almost all the dynamical and quantum properties of the intra-cavity field and which we call “super-modes”.Indeed, we show that not only the super-mode of minimum threshold is (ideally) perfectly squeezed at threshold, but that all the other super-modes have an important non-classical character provided that their thresholds are close enough to the minimum one. This circumstance gives the clear image that a SPOPO is a highly quantum multi-mode system. Finally, the last part of this Thesis is focused on the study of the output of a SPOPO from the point of view of the generation of highly multi-mode entangled states and their optimization by means of specific experimental configurations.

•Jan 1, 2008•2 citations

Experimental Generation and Characterization of Multimode Squeezed Light in a Synchronously Pumped Optical Parametric Oscillator

Edoardo Suerra, Francesco Canella, Dario Giannotti +3 more

Multimode squeezed light is a key resource for quantum technologies, enabling applications in boson sampling, quantum networks, and optical quantum computation [1],[2]. Parametric down-conversion in synchronously pumped optical parametric oscillators (SPOPOs) offers a versatile platform for generating multimode squeezed states across the time-frequency domain. In these systems, supermodes manifest as independent quantum states in the temporal domain and as frequency combs in the spectral domain [3]. Precise control of these states is crucial for quantum applications and requires an experimental setup capable of fine-tuning multiple parameters to optimize squeezing properties. In this work, we present an experimental setup for generating and characterizing multimode vacuum squeezed states using a SPOPO and a balanced homodyne detection scheme. Two spatial light modulators (SLMs) placed on the pump and local oscillator (LO) beams provide full control over their spectral properties, including amplitude and phase shaping. This flexibility allows us to optimize the experimental conditions and investigate squeezing dependence on key parameters such as the LO spectral detuning and bandwidth. By introducing a programmable$\pi$-phase shift to the LO via the SLM, we selectively probe the multimode structure, distinguishing between even and odd supermodes. Additionally, the SLM on the pump can introduce an arbitrary chirp, further enhancing control over the system. Our setup, schematized in Figure 1a, is based on a commercial mode-locked Yb-fiber laser operating at 93MHz, emitting pulses centered at 1035nm with a 10nm bandwidth. A portion of the radiation is frequency-doubled to 517.5nm via an LBO crystal to serve as the pump for the SPOPO, while the remaining part is used as the LO for homodyne detection after transmission through the SPOPO cavity, ensuring high beam quality. The SPOPO cavity is frequency-locked to the laser via a Pound-Drever-Hall technique, ensuring stable and optimized operation. Figure 1b presents representative measurements of squeezing levels as a function of the LO spectral bandwidth, showing how its symmetric or antisymmetric phase influences the detection of different supermodes and, consequently, the squeezing level depending on their structure. The measurements were performed using lithium niobate (LNB) nonlinear crystals of 3.0mm and 1.5mm lengths. Our setup allows for future investigations of dispersion effects on squeezing, thus far only theoretically predicted [4], by introducing chirped mirrors for dispersion compensation. Moreover, different nonlinear crystals, such as lithium niobate, beta barium borate (BBO), and lithium triborate (LBO) of various lengths, will be tested to explore the multimode properties of the squeezed states. These investigations will provide insights into the experimental conditions required to achieve single-mode squeezing, crucial for applications such as Gaussian Boson Sampling, with results to be presented at the conference.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 23, 2025•0 citations

Effect of group-velocity dispersion on the generation of multimode pulsed squeezed light in a synchronously pumped optical parametric oscillator

Valentin Averchenko, Danil Malyshev, K. S. Tikhonov

Abstract Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode femtosecond pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed time-domain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance due to temporal Gouy phase, as well as linear coupling between these supermodes. With perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the amplitudes of multiple supermodes given an arbitrary sub-threshold pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators.

arXiv:2407.18826•New Journal of Physics•Dec 1, 2024•2 citations

Quantum correlated pulses from a synchronously pumped optical parametric oscillator operating above threshold

Valentin Averchenko, Yu. M. Golubev, Claude Fabre +1 more

We perform the quantum analysis of the light emitted by a synchronously pumped optical parametric oscillator operating in the above threshold regime, i.e. when the peak power of pulsed pumping exceeds the threshold of continuous generation. We show that both regimes (below and above threshold) are realized at different times within each pulse of the signal field. We show that the quantum fluctuations of signal and pump pulses are correlated between nearby pulses at times that are placed in the same position relative to the center of the pulses, whereas fluctuations are totally not correlated at different times within the same pulse. The model also predicts the existence of cross-correlations between pump and signal pulses. It is shown theoretically that there is suppression of quantum noise at the frequencies multiple of the pulse repetition frequency in the spectra of phase quadratures of pump and signal fields measured by a balanced homodyne detection with a pulsed local oscillator.

arXiv:1104.1648•Apr 8, 2011•0 citations

Squeezing frequency combs

Germán J. de Valcárcel, Giuseppe Patera, Nicolas Treps +1 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.

arXiv:quant-ph/0605128•May 15, 2006•0 citations
We present in this paper a general model for determining the quantum properties of the light generated by a synchronously pumped optical parametric oscillator (SPOPO) operating below threshold. This model considers time and frequency on an equal footing, which allows us to find new quantum properties, related for example to the carrier envelope offset (CEO) phase, and to consider situations that are close to real experiments. We show that, in addition to multimode squeezing in the so-called ‘supermodes’, the system exhibits quadrature entanglement between frequency combs of opposite CEO phases. We have also determined the quantum properties of the individual pulses and their quantum correlations with the neighboring pulses. Finally, we determine the quantum Cramer–Rao limit for an ultra-short time delay measurement using a given number of pulses generated by the SPOPO.
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables [1]. They can be generated either by mixing different squeezed light sources using linear optical operations [2], or directly in a multimode optical device [3, 4]. Synchronously Pumped Optical Parametric Oscillators (SPOPO) — which correspond to an OPO pumped by a train of ultrashort pulses that are synchronized with the cavity round-trip time — have been theoretically shown to be promising devices for the generation of multimode nonclassical frequency combs, since a SPOPO is a sole optical cavity acting as an assembly of independent squeezers in a particular basis called the supermodes basis [5]. The supermodes are optical frequency combs with specific spectrum and phase profiles that are determined by the length of the intracavity nonlinear crystal and the pulse shape of the pump.
This Thesis studies, from a theoretical point of view, the dynamical and quantum properties of a type I degenerate optical parametric oscillator which is synchronously pumped by a mode-locked laser (SPOPO). In recent past, SPOPOs have been used for generating ultra-short optical pulses of tunable wavelength and their temporal properties have been investigated. Having a huge number of degrees of freedom, the output field of a SPOPO needs to be characterized via a multimodal quantum analysis. Then, we first develop a multimode model of the device, obtaining the quantum equations for the intra-cavity field operators. Afterwards, we study the steady state solutions of the average values of the generated fields that are the solutions of an eigenvalue equation. Its spectrum gives information about the “useful” number of modes in which are concentrated almost all the dynamical and quantum properties of the intra-cavity field and which we call “super-modes”.Indeed, we show that not only the super-mode of minimum threshold is (ideally) perfectly squeezed at threshold, but that all the other super-modes have an important non-classical character provided that their thresholds are close enough to the minimum one. This circumstance gives the clear image that a SPOPO is a highly quantum multi-mode system. Finally, the last part of this Thesis is focused on the study of the output of a SPOPO from the point of view of the generation of highly multi-mode entangled states and their optimization by means of specific experimental configurations.
Multimode squeezed light is a key resource for quantum technologies, enabling applications in boson sampling, quantum networks, and optical quantum computation [1],[2]. Parametric down-conversion in synchronously pumped optical parametric oscillators (SPOPOs) offers a versatile platform for generating multimode squeezed states across the time-frequency domain. In these systems, supermodes manifest as independent quantum states in the temporal domain and as frequency combs in the spectral domain [3]. Precise control of these states is crucial for quantum applications and requires an experimental setup capable of fine-tuning multiple parameters to optimize squeezing properties. In this work, we present an experimental setup for generating and characterizing multimode vacuum squeezed states using a SPOPO and a balanced homodyne detection scheme. Two spatial light modulators (SLMs) placed on the pump and local oscillator (LO) beams provide full control over their spectral properties, including amplitude and phase shaping. This flexibility allows us to optimize the experimental conditions and investigate squeezing dependence on key parameters such as the LO spectral detuning and bandwidth. By introducing a programmableπ\piπ-phase shift to the LO via the SLM, we selectively probe the multimode structure, distinguishing between even and odd supermodes. Additionally, the SLM on the pump can introduce an arbitrary chirp, further enhancing control over the system. Our setup, schematized in Figure 1a, is based on a commercial mode-locked Yb-fiber laser operating at 93MHz, emitting pulses centered at 1035nm with a 10nm bandwidth. A portion of the radiation is frequency-doubled to 517.5nm via an LBO crystal to serve as the pump for the SPOPO, while the remaining part is used as the LO for homodyne detection after transmission through the SPOPO cavity, ensuring high beam quality. The SPOPO cavity is frequency-locked to the laser via a Pound-Drever-Hall technique, ensuring stable and optimized operation. Figure 1b presents representative measurements of squeezing levels as a function of the LO spectral bandwidth, showing how its symmetric or antisymmetric phase influences the detection of different supermodes and, consequently, the squeezing level depending on their structure. The measurements were performed using lithium niobate (LNB) nonlinear crystals of 3.0mm and 1.5mm lengths. Our setup allows for future investigations of dispersion effects on squeezing, thus far only theoretically predicted [4], by introducing chirped mirrors for dispersion compensation. Moreover, different nonlinear crystals, such as lithium niobate, beta barium borate (BBO), and lithium triborate (LBO) of various lengths, will be tested to explore the multimode properties of the squeezed states. These investigations will provide insights into the experimental conditions required to achieve single-mode squeezing, crucial for applications such as Gaussian Boson Sampling, with results to be presented at the conference.
Abstract Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode femtosecond pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed time-domain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance due to temporal Gouy phase, as well as linear coupling between these supermodes. With perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the amplitudes of multiple supermodes given an arbitrary sub-threshold pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators.
We perform the quantum analysis of the light emitted by a synchronously pumped optical parametric oscillator operating in the above threshold regime, i.e. when the peak power of pulsed pumping exceeds the threshold of continuous generation. We show that both regimes (below and above threshold) are realized at different times within each pulse of the signal field. We show that the quantum fluctuations of signal and pump pulses are correlated between nearby pulses at times that are placed in the same position relative to the center of the pulses, whereas fluctuations are totally not correlated at different times within the same pulse. The model also predicts the existence of cross-correlations between pump and signal pulses. It is shown theoretically that there is suppression of quantum noise at the frequencies multiple of the pulse repetition frequency in the spectra of phase quadratures of pump and signal fields measured by a balanced homodyne detection with a pulsed local oscillator.
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.