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. Currently, squeezed state can be 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 present photon antibunching effect through interference or photon subtraction operation. More importantly, squeezed coherent state is 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 focus for studying the antibunching effect and quantum statistical properties of squeezed coherent state at a single-photon level.

The photon antibunching effect can be characterized by the second-order photon correlation g⁽²⁾(τ), which is introduced by Glauber to determine the non-classical properties of the light field. Namely, the second-order photon correlation g⁽²⁾ can be used as a metric to distinguish different lights. Hanbury Brown-Twiss (HBT) scheme is used to measure the second-order photon correlation experimentally. However, the second-order photon correlation g⁽²⁾ can reflect only the variance of the photon-number statistical distribution. In order to obtain more information about the photon statistical distribution and non-classical features, it is necessary to measure higher-order photon correlations. Then the higher-order photon correlations for different light fields are studied by extending the traditional HBT scheme and combining with multiplex single-photon detection technology. This method can be applied to ghost imaging, characterization of single-photon detectors, research of exciton dynamics, and analysis of NV center fluorescence emission. However, the research on photon statistics of the squeezed state focuses mainly 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 background noise and detection efficiency taken into consideration, have not been investigated.

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 manifests 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⁽²⁾ = 4.006 × 10^–4, g⁽³⁾ = 1.3594 × 10^–4 and g⁽⁴⁾ = 6.6352 × 10^–5. When the detection efficiency η = 0.1 and background noise γ = 10^–6, the strong antibunching effect can still be observed, specifically, g⁽²⁾ = 0.1740, g⁽³⁾ = 0.0432, g⁽⁴⁾ = 0.0149. The results indicate that the antibunching effect of higher-order photon correlation has strong robustness against the experimental environment. In addition, the antibunching effect of the phase-variable squeezed coherent state is studied as a function 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^–4, a prominent photon anti-bunching effect of g⁽ⁿ⁾ \ll 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 has potentially important applications in quantum metrology and secure communication.