Engineering many-body dynamics with quantum light potentials and measurements

Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterize these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunneling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.

Figure 1

Ultracold atoms trapped in an optical lattice scatter incident light into optical cavities. The cavity-mediated light-matter interactions induce correlated atomic dynamics that are tunable through the optical geometry. Detection of the leaked photons enables a selective suppression of these processes, through the measurement backaction effect. This allows the atomic dynamics to be engineered for quantum simulation purposes.

Figure 2

Schematic displaying the regions and associated interaction strengths of cavity-mediated density-density interactions. The flexibility in the geometry of the cavity modes allows for the strength of the long- and short-range processes to be tuned independently.

Figure 3

The cavity fields can also induce tunable correlated tunneling processes, which may be classified according to the relationship between the two tunneling atoms: (1) pair tunneling; (2) pair exchange; (3) effective next-nearest neighbor tunneling; (4) and (5) effective pair processes; and (6) general long-range correlated tunneling.

Figure 4

The correlated tunneling processes may be used to simulate superexchange interactions. Here, a superlattice is used to divide the system into a series of double-well potentials, each containing an atom of each of two spin species (denoted by their color). The superlattice potential and strong repulsive interactions allow only pair exchange processes to take place, between atoms in the same double well, mimicking superexchange dynamics. These correlated tunnelings are indicated by arrows of the same color.

Figure 5

Illustration of the allowed processes in the presence of measurement-induced dynamical constraints requiring fixed occupation number difference between even and odd sites ($\mathrm{\Delta }N=N^{\left(\mathrm{odd}\right)}-N^{\left(\mathrm{even}\right)}$). These allowed processes must conserve the total occupation difference between even and odd sites, and include: (a) nearest-neighbor tunneling; (b) effective nearest-neighbor tunneling; (c) pair exchange; and (d) long-range correlated tunneling events that preserve total mode occupations.

Figure 6

Dynamical constraints imposed by measurement of the light allows for selective engineering of atomic dynamics for use in quantum simulation. By designating some sites as reservoir modes, (a) effective pair processes and (b) generalized Dicke models can be realized. The highlighting of sites indicates the contribution of their occupation to the measurement value (green positive, blue negative), which is fixed by the quantum Zeno effect. In both cases, the measurement operator is given by $D_{\mathrm{\Pi }0}=N_{\mathrm{Res}1}-N_{\mathrm{Res}2}$). Tunneling events constrained to only occur simultaneously because of the constraints are indicated by identically colored arrows.

Figure 7

Ground-state average occupation $\langle n_1\rangle$ of the generalized Dicke model, showing a change in the superradiance phase transition point when varying ${\lambda }_1/{\lambda }_2$. In the standard Dicke model, the transition occurs at ${\lambda }_1={\lambda }_2=\mu /2$; here we find the general boundary at ${\lambda }_1+{\lambda }_2\approx \mu$. We use ${\mu }_1={\mu }_2=\mu$, and a maximum occupation of 20 for each mode.

Figure 8

Setup for the two-species generalized Dicke model. Combining two setups for the one-species generalized Dicke model, with a mutual synthetic light mode, allows the introduction of another atomic species. Circles represent the simulated modes, squares the reservoirs. The required measurements made are of occupation differences $R_{L_1}-R_A$ and $R_{L_2}-R_B$, which correlate certain tunneling events, as indicated by arrows the same color.