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arXiv:2404.10560 · Optics Letters

Few-mode squeezing in type-I parametric downconversion by complete group velocity matching

D. B. Horoshko, Mikhail I. Kolobov, Valentina Parigi, Nicolas Treps

Published Jun 21, 2024• 3 citations
arXivHTMLPDF

Abstract

Frequency-degenerate pulsed type-I parametric downconversion is a widely used source of squeezed light for numerous quantum optical applications. However, this source is typically spectrally multimode, and the generated squeezing is distributed between many spectral modes with a limited degree of squeezing per mode. We show that in a nonlinear crystal, where the condition of complete group velocity matching (GVM) for the pump and the signal is satisfied, the number of generated modes may be as low as two or three modes. We illustrate the general theory with the example of the MgO-doped lithium niobate crystal pumped at 775 nm and generating squeezed light at 1.55 µm. Our model includes the derivation of the degree of squeezing from the properties of the pump and the crystal and shows that 12 dB of squeezing can be obtained in a periodically poled crystal at a length of 80 mm.

DOI
10.1364/ol.528280

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Frequency-degenerate pulsed type-I parametric downconversion is a widely used source of squeezed light for numerous quantum optical applications. However, this source is typically spectrally multimode, and the generated squeezing is distributed between many spectral modes with a limited degree of squeezing per mode. We show that in a nonlinear crystal, where the condition of complete group velocity matching (GVM) for the pump and the signal is satisfied, the number of generated modes may be as low as two or three modes. We illustrate the general theory with the example of the MgO-doped lithium niobate crystal pumped at 775 nm and generating squeezed light at 1.55 µm. Our model includes the derivation of the degree of squeezing from the properties of the pump and the crystal and shows that 12 dB of squeezing can be obtained in a periodically poled crystal at a length of 80 mm.
Summary form only given. In aperiodically poled quasi-phase-matching (QPM) crystals, parametric down-conversion (PDC) can generate very broadband pulsed squeezed light. This is because each part of the crystal will generate squeezed light at a different frequency [1]. But the emission will be thus inhomogeneously broadened, and one requires special measures to eliminate the chirp accompanying the pulses. This can be done by placing a group-velocity dispersion material after the crystal [2] or by specially designing the nonlinear grating [3]. If the bandwidth of squeezed light is large enough, the squeezing and photon-number correlations, after the chirp is removed, will be “single-cycle”, with the correlation time comparable to one optical cycle [4].In this work, the first results on such broadband squeezing are demonstrated. In the 5-mm-long aperiodically poled MgO:LiNbO3 crystal we use, the QPM grating period changes from 7.38 μm to 8.91 μm. With this device, we generated bright twin beams through collinear frequency-nondegenerate high-gain PDC. The phase chirp was eliminated through the design of the nonlinear grating. The frequency bandwidth was measured to be 17 THz, a factor of 15 larger than in a periodically poled crystal. The correlation time was measured using non-phase matched sum frequency generation from the signal and idler beams. The dependence of the sum frequency intensity on the time delay between the signal and idler beams is shown in Fig.1. Fine-resolution scanning (b) shows a narrow peak, demonstrating a correlation time of 90 fs. It can be further reduced by using more advanced grating designs.
We report on an initial squeezing of 3.3 dB below the shot noise level, generated in bulk, quasi-phase-matched lithium niobate. This squeezing was generated by degenerate parametric amplification, at 1047 nm, of a mode-locked pulse train. We present a detailed comparison of the process performed in both the quasi-phase-matched material and in MgO:LiNbO3,{\mathrm{M}\mathrm{g}\mathrm{O}:\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{b}\mathrm{O}}_{3},MgO:LiNbO3​, which was phase matched using conventional birefringent methods. The single-pass gain measured was 2.5 from MgO:LiNbO3{\mathrm{M}\mathrm{g}\mathrm{O}:\mathrm{L}\mathrm{i}\mathrm{N}\mathrm{b}\mathrm{O}}_{3}MgO:LiNbO3​ and 3.9 from periodically poled lithium niobate (PPLN), although the former was affected by photorefractive damage. We directly recorded 1111%11 of noise reduction in the vacuum using the PPLN parametric amplifier, purely because the detection efficiency was so low in our experiment. The experimental data was fitted to a model which includes the initial squeezing level and the homodyne detector efficiency as free parameters. The observed squeezing agrees well with the a total detection efficiency of just 1616%16 and an initial squeezing level of 3.3 dB (53%) in PPLN.
Parametric down-conversion of light (PDC) in a quasi-phase-matched (QPM) nonlinear crystal can be spectrally very broad when the spatial frequency of periodical poling is linearly chirped. The present day technology makes possible the fabrication of chirped QPM crystals phase-matched for PDC in all optical spectrum. In the low-gain regime this allows for generation of biphotons with the correlation time of the order of a single optical cycle. A natural next step is the study of the PDC light produced by such a crystal in the high-gain regime, where PDC is widely used as a source of squeezed states of light. Up to now only a classical treatment of this regime was undertaken. In the present work we demonstrate a possibility to generate single-cycle squeezing in a chirped QPM nonlinear crystal with squeezing spectrum covering almost all the optical octave.
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.