Fig. 1. Theoretical model of double HBT scheme. B0, B1, B2, B3: Beamsplitter; D1, D2, D3, D4: Detector. The letters in parentheses L, N,K, et al, denote the photon numbers of splitting light paths, respectively.

Fig. 2. (a) Third-order, and (b) fourth-order photon correlations and of single-mode thermal state versus the mean photon number .

Fig. 3. (a) Second-order, (b) third-order, and (c) fourth-order photon correlations of single-mode squeezed vacuum state versus the squeezing parameter r.

Fig. 4. The third-order (blue hollow square) and fourth-order (red solid circle) photon correlations of Fock state versus the photon number: (a) , ; (b) , .

Fig. 5. Schematic illustration of the experimental setup (ISO, isolator; HWP, half-wave plate; PBS, polarized beam splitter; M1, M2, mirror; L, optical lens; RGGD, rotating ground glass disk; BS1, BS2, BS3, beam splitter; D1, D2, D3 and D4, single photon counting module, SPCM; DAS, data acquisition system).

Fig. 6. Measured (a) third-order and (b) fourth-order photon correlations of thermal state and coherent state versus the counting rate for resolution time of 2¹⁰ ns. The red and blue solid lines are the ideal results of the high-order photon correlations of thermal state and coherent state.

Fig. 7. Measured (a) third-order and (b) fourth-order photon correlations of thermal state and coherent state versus the resolution time for counting rate of 80 kc/s. The red and blue solid lines are the ideal results of the high-order photon correlations of thermal state and coherent state.

Fig. 8. Measured third-order photon correlation of thermal state versus delay times for resolution times of 2¹⁰ ns and counting rate of 80 kc/s. The blue dots and black solid curves are the experimental and theoretical results, respectively: (a) τ₂ = 0 μs; (b) τ₂ = –10 μs; (c) τ₂ = 10 μs. The peak value of g⁽³⁾ in Fig. (a) is .

Fig. 9. The fourth-order photon correlations of thermal state at complete time delays for (a) τ₃ = 0 μs, (b) τ₃ = –10 μs, (c) τ₃ = 10 μs. The peak value of g⁽⁴⁾ in Fig. (a) is .

Fig. 10. Measured fourth-order photon correlation of thermal state versus delay time τ₁ for resolution times of 2¹⁰ ns and counting rate of 80 kc/s. The dots are the experimental results, and the black solid curves are the theoretical fittings.