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Chinese Optics Letters

Generation of optical frequency comb squeezed light field with TEM01 transverse mode

Nan Huo, Chihua Zhou Chihua Zhou, Hengxin Sun, Kui Liu, and Jiangrui Gao and Jiangrui Gao

Published Jan 1, 2016• 4 citations
Publisher

Abstract

Nonclassical optical frequency combs find tremendous utility in quantum information and high-precision quantum measurement.The characteristics of a type-I synchronously pumped optical parametric oscillator with the TEM 01 transverse mode below threshold are investigated and a squeezing of 0.7 dB for an optical frequency comb squeezed light field with the TEM 01 transverse mode is obtained under the pump power of 130 mW.This work has a promising application in three-dimensional space-time measurement.

DOI
10.3788/col201614.062702

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Nonclassical optical frequency combs find tremendous utility in quantum information and high-precision quantum measurement.The characteristics of a type-I synchronously pumped optical parametric oscillator with the TEM 01 transverse mode below threshold are investigated and a squeezing of 0.7 dB for an optical frequency comb squeezed light field with the TEM 01 transverse mode is obtained under the pump power of 130 mW.This work has a promising application in three-dimensional space-time measurement.
Multimode quantum light fields significantly enhance quantum state manipulation and communication capabilities by expanding the dimensionality of the Hilbert space. In this work, we elaborately design a non-horizontal cavity suitable for a Gouy phase-compensated synchronously pumped optical parametric oscillator. By injecting an optical frequency comb in HG 10 mode into the cavity as the seed, we demonstrate the simultaneous generation of a bright squeezed optical frequency comb in HG 10 mode and a vacuum squeezed optical frequency comb in HG 01 mode. The coexistence of amplitude quadrature squeezed fields in these two orthogonal first-order Hermite-Gaussian transverse modes also suggest the presence of quadrature entanglement between the two first-order Laguerre-Gaussian modes, LG 0 + 1 and LG 0 - 1 . This research underscores the capability of one-step generation of multi-transverse-mode squeezed optical frequency combs using a single cavity, marking a significant stride in the realm of quantum optics.
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.
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.
Quantum optical frequency combs are of great significance in the fields of quantum computing, quantum information, and high precision quantum measurement, which can be produced by using a degenerate type-I synchronously pumped optical parametric oscillator (SPOPO). When anisotropic crystal is used as a nonlinear medium in the SPOPO, the spatial walk-off effect will occur due to the birefringence effect, which cannot be ignored and will adversely affect the generation of squeezed state. In this work, we investigate the influence of spatial walk-off effect on the squeezing level of quantum optical frequency combs both theoretically and experimentally. A Ti∶sapphire mode-locked femtosecond pulsed laser which produces 130 fs pulse trains at 815 nm with a repetition rate of 76 MHz is utilized as a fundamental source. Its second harmonic at 407.5 nm is used to pump the collinear BiB3O6 (BIBO) crystal for generating the squeezed vacuum frequency comb. It is indicated that as the crystal length increases, the area of interaction between pump light and signal light decreases gradually. Thus the enhancement of squeezing is eventually limited by the spatial walk-off effect. According to the simulations, the squeezing level reaches a maximum value when the crystal length is 1.49 mm. The quantum properties of squeezed vacuum optical frequency combs obtained for four crystal lengths (0.5, 1.0, 1.5 and 2.0 mm) are subsequently measured experimentally. When the length of BIBO is 1.5 mm, the maximum vacuum squeezing of (3.6±0.2) dB is obtained, which is (7.0±0.2) dB after being corrected for detection loss. The experimental results are consistent with the numerical simulations. This study demonstrates that the spatial walk-off effect in nonlinear crystal is a significant factor affecting the quantum optical frequency comb, and the theoretical model presented in this paper can be used to provide a guideline for optimizing the experimental implementation.
The novel aspect of this study is grounded on the fact that squeezing spectrum of a finite set of super-modes operators can be below the standard quantum limit, giving a clear image that the system is a highly quantum multi-mode system. In fact, not only the super-mode of minimum threshold is perfectly squeezed at threshold but, further, all the other super-modes have nonclassical character and are significantly squeezed provided that their threshold is sufficiently close to the minimum one. It is concluded that synchronously pumped OPOs reveal to be very interesting devices for studying frequency combs at the quantum level. Their quantum multi-modal behavior could be exploited for generation of nonclassical states of the light used for implement optical time measurement of great sensitivity or quantum information protocols.