Noise spectroscopy of two-body loss as a probe of dynamical bulk viscosity in ultracold atomic gases

We show that the correlated noise of the two-body loss current provides access to the dynamical bulk viscosity in weakly dissipative quantum gases. Starting from the Lindblad equation for weak inelastic losses, we derive the loss-current operator. After subtracting the leading Poissonian shot-noise background, the remaining noise power spectrum of two-body loss current is found proportional to the equilibrium correlation function of the contact operator. Combining this result with the exact relation between contact correlations and bulk viscosity, we demonstrate the correspondence between the measurable loss-current noise and the bulk-viscosity. Our result identifies the higher-order fluctuation of two-body loss as a probe of dynamical bulk viscosity, whose measurement has remained elusive in experiments.