  We theoretically investigate the time- and frequency-domain two-particle
correlations of a driven dissipative Bose-Hubbard model (BHM) at and near a
dissipative phase transition (DPT). We compute Hanbury Brown-Twiss (HBT) type
two-particle temporal correlation function $g^2(\tau)$ which, as a function of
time delay $\tau$, exhibits oscillations with frequencies determined by the
imaginary part of Liouvillian gap. As the gap closes near a transition point,
the oscillations at that point dies down. For parameters slightly away from the
transition point, the HBT correlations show oscillations from super-bunching to
anti-bunching regimes. We show that the Fourier transform of HBT correlations
into frequency domain provide information about DPT and Liouvillian dynamics.
We numerically solve the many-body Lindblad master equation and calculate
Wigner distribution of the system in steady state to ascertain DPT.Below
certain drive strength, the Fourier transform shows a two-peak structure while
above that strength it exhibits either a Lorenzian-like single-peak structure
or a structure with two-dips. The width of the single-peak structure is minimum
at the phase transition point and the peak of this structure always lies at
zero frequency. The positions of the two symmetrical peaks in case of two-peak
structure are given by the imaginary parts of the Liouvillian gap while their
half width at half maximum (HWHM) is given by the real part of the gap. The
positions and the widths of the two dips are also related to low lying
eigenvalues of the Liouvillian operator. We discuss quantum statistical
properties of the model in terms of the HBT correlation function and its
Fourier transform.
