Effect of spatial walk-off on squeezing properties of quantum optical frequency combs

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.