Higher-order photon antibunching of phase-variable squeezed coherent state

Abstract

Squeezed state has important applications in quantum communication, quantum computing, and precision measurement. It has been used to improve the sensitivity and measurement accuracy of gravitational wave detectors. Up to now, squeezed state is prepared by optical parametric oscillators, four-wave mixing, and atom-optomechanical coupling. As a typical non-classical light, the photon statistics of squeezed state usually shows obvious bunching effect, but it can also show photon antibunching effect through interference or photon subtraction operation. More importantly, squeezed coherent state can be prepared by performing displacement operation on the squeezed state. In the case of certain displacement and squeezing operations, squeezed coherent state with obvious antibunching effect can be produced. The squeezed coherent state with photon antibunching effect can be employed to achieve super-resolution imaging beyond the diffraction limit, and the state exhibits good particle features which can suppress the multiphoton emission. Then it has become a research focus to study the antibunching effect and quantum statistical properties of squeezed coherent state at the single-photon level.<br>The photon antibunching effect can be characterized by the second-order photon correlation g<sup>(2)</sup>(τ), which is introduced by Glauber to determine the non-classical properties of the light field. Namely, the second-order photon correlation g<sup>(2)</sup> can be used as a metric to distinguish different lights. Hanbury Brown-Twiss (HBT) scheme is used experimentally to measure the second-order photon correlation. However, the second-order photon correlation g<sup>(2)</sup> can only reflect the variance of the photon-number statistical distribution. In order to obtain more information on photon statistical distribution and non-classical features, it is necessary to measure higher-order photon correlations. Then the study of higher-order photon correlations for different light fields has been carried out by extending the traditional HBT scheme and combining with multiplex single-photon detection technology, and the method is applied to ghost imaging, characterization of single-photon detectors, research on exciton dynamics, and analysis of NV center fluorescence emission. However, the research on photon statistics of the squeezed state is mainly focused on the second-order photon correlation and the effect of displacement amplitude on the statistical properties. The effect of squeezed phase on photon antibunching and higher-order photon correlation of squeezed coherent states with considering background noise and detection efficiency have not been investigated.<br>In this paper, we study high-order photon correlations and antibunching effect of phase-variable squeezed coherent state based on an extended HBT scheme. The photon statistics of the squeezed coherent state behaves prominent antibunching effect by adjusting the squeezing parameter r, displacement amplitude α and squeezing phase θ. The antibunching effect of the state can be obtained in a wide range of α-r parameter space when squeezing phase θ∈[0,π/2]. In an ideal case, the minimum antibunching values of the squeezed coherent state are g<sup>(2)</sup>=4.006×10<sup>-4</sup>, g<sup>(3)</sup>=1.3594×10<sup>-4</sup> and g<sup>(4)</sup>=6.6352×10<sup>-5</sup>. When the detection efficiency η=0.1 and background noise γ=10<sup>-6</sup>, the strong antibunching effect can still be observed, i.e. g<sup>(2)</sup>=0.1740, g<sup>(3)</sup>=0.0432, g<sup>(4)</sup>=0.0149. The results indicate that the antibunching effect of higher-order photon correlation has strong robustness to the experimental environment. In addition, the antibunching effect of the phase-variable squeezed coherent state is studied as functions of the measured mean photon number <n> and the squeezing degree S. When the measured mean photon number is much less than 1 and the squeezing parameter is less than 10<sup>-4</sup>, a prominent photon anti-bunching effect of g<sup>(n)</sup><<0.5 can still be obtained. The results show that the control of the squeezing phase θ can be used to prepare the squeezed coherent state with obvious antibunching effect, which have potentially important applications in quantum metrology and secure communication.