The bunching and antibunching effects of optical fields reflect the spatiotemporal correlations of photons, serving as key indicators to distinguish quantum statistics between classicality and non-classicality, and playing an essential role in quantum information processing and precision measurement. In this paper, we investigate the super-bunching and antibunching effects of the full-time-delay higher-order coherence function g⁽ⁿ⁾ for squeezed thermal states and squeezed number states based on a multi-cascaded Hanbury Brown–Twiss single-photon detection scheme.
Under ideal conditions, the high-order coherence of squeezed thermal states and squeezed number states is analyzed with varying compression parameter r, average photon numberα, and squeezed photon number n. The results indicate that when the compression parameter $r \in[0,1]$, the squeezed thermal state exhibits a significant super-bunching effect, with super-bunching values of each order given by g⁽²⁾= 9.98×10⁵,g⁽³⁾= 8.98×10⁶,g⁽⁴⁾= 8.96×10¹²,g⁽⁵⁾= 2.24×10¹⁴.The squeezed number state exhibits a continuous transition from antibunching to bunching behavior, with coherence degrees at various orders given as g⁽²⁾∈[1.60×10^-5, 1.09], g⁽³⁾∈[9.02×10^-6, 1.16], g⁽⁴⁾∈[4.75×10^-6, 1.22], g⁽⁵⁾∈[9.39×10^-6, 1.30]）．
Simultaneously, the study analyzed the high-order photon coherence of squeezed thermal states and squeezed number states under experimental conditions, taking into account background noise γ and detection efficiency η．When detection efficiency is relatively low and background noise is substantial, the higher-order coherence of squeezed thermal states with smaller average photon number α is disturbed by background noise, yet still maintains good super-bunching characteristics; however, when the average photon number α becomes large, limited by the dead time of single-photon detectors, it is challenging to accurately obtain all the information of the squeezed number state light field, resulting in measurement results that deviate from the ideal values. When the average photon number is α=0.5, the super-bunching effects reach their maximum values of g⁽²⁾= 2.149、g⁽³⁾= 6.389和g⁽⁴⁾= 23.228, corresponding respectively to the squeezing degrees S⁽²⁾= 5.47、S⁽²⁾= 4.86和S⁽²⁾= 4.43. Furthermore, by adjusting the number of squeezed photons η and the squeezing degree S of the squeezed number state light field, a continuous and wide-ranging variation of the high-order coherence function can be achieved, transitioning from anti-bunching to super-bunching effects. Additionally, under conditions of high environmental noise and low detection efficiency, higher-order coherence exhibits greater sensitivity to variations in optical field parameters compared to lower-order coherence. Furthermore, squeezed number states with multi-photon characteristics are less susceptible to disturbances from background noise, demonstrating stronger robustness.
In addition, the variation characteristics of the high-order photon coherence function of the squeezed thermal state light field under full time-delay conditions were investigated. The full time-delay high-order coherence g⁽ⁿ⁾ of the squeezed thermal state light field near the coherence time range $\tau_{\mathrm{STS}}$ is significantly higher than that of the classical thermal state light field. Even when a significant time delay is introduced in one of the optical paths, partial synchronization among photons can still maintain a certain correlation strength. Although unsynchronized photons lead to an overall reduction in coherence, the coherence remains higher than the theoretical predictions for thermal states under identical conditions.
Building on the theoretical framework established in this work, future experiments may focus on adjusting the pump power, intracavity loss, and crystal temperature of optical parametric amplifiers to jointly control the squeezing degree and mean photon number, enabling stable generation of squeezed thermal states across different parameter regimes. Additionally, precise measurement of higher-order coherence could be achieved using cascaded HBT detection systems with multiple inputs and high temporal resolution.
In summary, by considering environmental noise, detection efficiency, and time delay, and through the regulation of the average photon number, the number of squeezed photons, and the squeezing parameter. This approach enables the preparation of super-bunching squeezed thermal states and squeezed number states whose higher-order coherence can be continuously tuned over a wide range, facilitating efficient quantum state preparation and manipulation, as well as high-resolution quantum imaging.