Multiparticle quantum dynamics under real-time observation

Recent developments in quantum gas microscopy open up the possibility of real-time observation of quantum many-body systems. To understand the dynamics of atoms under such circumstances, we formulate the dynamics under a real-time spatially resolved measurement and show that, in an appropriate limit of weak spatial resolution and strong atom-light coupling, the measurement indistinguishability of particles results in complete suppression of relative positional decoherence. As a consequence, quantum correlation in the multiparticle dynamics persists under a minimally destructive observation. We numerically demonstrate this for ultracold atoms in an optical lattice. Our theoretical framework can be applied to the feedback control of quantum many-body systems which may be realized in subwavelength-spacing lattice systems.

Figure 1

Schematic illustration of (a) distinguishable and (b) indistinguishable signals. If the signals coming from multiple particles cannot be distinguished, the relative positional coherence in the multiparticle dynamics can be preserved and a superposition of more than one relative position is allowed [(b) bottom]. If the signals are distinguishable, the relative position can take on a single value at each instant of time [(a) bottom]. On the other hand, the center-of-mass position behaves the same way for both cases.

Figure 2

Schematic geometry of the system. Atoms trapped in an optical lattice (bottom, blue dots) are illuminated by an off-resonant probe light. A scattered photon is diffracted through a lens and detected on the screen. This induces the measurement backaction that causes the reduction of the wave function according to the outcome $X$ and a spatial resolution $\sigma$.

Figure 3

Real-time quantum dynamics of two particles under continuous observation. (a) Unitary time evolution. Without measurement backaction, quantum statistics hardly affects the atomic density. Quantum dynamics subject to the measurement backaction is shown for (b) distinguishable particles, (c) bosons, and (d) fermions, calculated for $\mathrm{\Gamma }=2.0$. Owing to the absence of the relative positional decoherence, (c) bunched and (d) anticorrelated quantum walks persist, whereas distinguishable particles exhibit uncorrelated random walks (b).

Figure 4

Diffusive regime of two-particle quantum dynamics under continuous observation. (a) Variance of the relative distance divided by the elapsed time. Distinguishable particles (solid curve) show rapid convergence to $2D_c/J$ (dashed line). Bosons (blue dashed curve) and fermions (red dash-dotted curve) exhibit a stronger diffusion and a weaker diffusion, respectively, than distinguishable particles. A typical realization of the atomic density is shown for (b) bosons and (c) fermions. The results are calculated with $\mathrm{\Gamma }=16.0$ and averaged over ${10}^3$ realizations.