Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

Figure 1

(a) Fermions trapped in a superlattice and subject to a spatially modulated dissipative lattice (red), which causes atomic loss and breaks the parity symmetry with respect to the dashed line. The total atom number is measured by a site-resolved detector. (b) The top (black) and bottom (blue) bands of the effective Hamiltonian (4) for $\gamma =0$, $h=J$ (dashed curves), and $\gamma /h=1/2$ (solid curves). (c) Unconditional (left-most panel) and full-counting (other panels) equal-time correlations for different numbers $n$ of quantum jumps with $N=L/2=61$ and $\gamma =h/2=0.5J$. White dashed lines represent the light cone associated with the Lieb-Robinson bound.

Figure 2

(a) Unequal- and (b) equal-time correlations plotted for $N=L/2=61$ and $\gamma =h/2=0.5J$. The white dashed lines indicate the Lieb-Robinson bound. (c) An illustration of how the correlation is carried by quasiparticles propagating at velocities $v_{\mathrm{LR}}$ and $3v_{\mathrm{LR}}$. (d) The effective band populations for different times $J^{\prime }t=0^{+}$ (postquench state), 4, and 8.

Figure 3

(a) The current averaged over the time interval between $t=15/J^{\prime }$ and $20/J^{\prime }$ plotted against the strength of dissipation $\gamma$ for different on site potentials $h$. The inset shows a gain-loss situation for a positive particle current. (b) The time evolutions of entanglement entropy of a chain of length 20, starting from a product state (the ground state of $\widehat{H}$ with $h=\infty$). We vary a postquench parameter $\gamma$ from 0.0 to 0.5 (top to bottom) with step 0.1 and $\gamma =h/2$ held fixed. The inset magnifies the short-time regime showing the oscillatory behavior due to the time-dependent effective band populations.