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arXiv:2407.18826 · New Journal of Physics

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

Published Dec 1, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ad9be1

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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.
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.
An experimental investigation of intracavity dispersion effects in a synchronously pumped optical parametric oscillator (SPOPO) is presented. A flexible setup combining spectral and phase shaping of both pump and local oscillator fields with frequency-resolved balanced homodyne detection is employed to examine how intracavity dispersion influences squeezing. Different cavity configurations with varying finesse and dispersion conditions are studied, and the squeezing is measured as a function of pump power and local oscillator bandwidth. Contrary to expectations based on existing theoretical models, the measured squeezing levels remain essentially unchanged as dispersion varies. To account for these observations, a modeling approach is introduced in which intracavity dispersion is described as an effective spectral filtering occurring at the stage of SPOPO supermode generation. Within this framework, the filtering is incorporated directly into the interaction Hamiltonian of the nonlinear process. This perspective establishes a consistent experimental benchmark for the study of dispersion in SPOPOs and underscores the importance of spectral filtering in the interpretation of multimode squeezing experiments.
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.
We demonstrate experimentally the short pulse amplitude squeezed light from a singly resonant synchronously pumped optical parametric oscillator (SPOPO). The SPOPO operates in the frequency degenerate case and below threshold, with using a periodically poled potassium titanyl phosphate crystal. The pump laser is the second harmonic of a ultrashort mode-locked femtosecond pulse at 850 nm. The reduction of quantum noise of 2.58 dB is obtained experimentally. The squeezing extent is deduced to be 4.48 dB.
A synchronously pumped optical parametric oscillator (SPOPO) operating at 93 MHz is used to generate squeezed states at 1035 nm. The system features a counter-propagating beam at the same wavelength as the quantum state, which simultaneously actively stabilizes the cavity and, after transmission, acts as the local oscillator for homodyne detection. By deriving the local oscillator directly from the SPOPO cavity, the setup establishes an intrinsically excellent spatial mode overlap and high interference visibility, forming a distinctive self-referenced architecture. Two spatial light modulators enable precise spectral shaping of both the pump and the local oscillator in amplitude and phase, allowing investigation of the spectral properties of the generated states. The versatility of the setup further allows exploration of different SPOPO configurations, including regimes with varied finesse and escape efficiency. Representative measurements, including homodyne traces and squeezing levels as functions of pump power and local oscillator bandwidth, demonstrate the performance of the system. Theoretical simulations based on a multimode singular-value-decomposition model reproduce well the measured dependence of squeezing on pump power and LO bandwidth, confirming the accuracy of the description and the robustness of the setup. Measured squeezing levels up to − 3.3 dB are achieved, corresponding to − 5.7 dB at SPOPO output, evidencing the robustness and versatility of this platform for stable pulsed squeezed-light generation and advanced quantum optical applications.
The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.