Superradiance Induced Particle Flow via Dynamical Gauge Coupling

We study fermions that are gauge coupled to a cavity mode via Raman-assisted hopping in a one-dimensional lattice. For an infinite lattice, we find a superradiant phase with an infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the nonequilibrium dynamics including fluctuation effects. The short-time dynamics is dominated by superradiance, while the long-time behavior is governed by cavity fluctuations. We show that the steady state in the finite lattice is not unique and can be understood in terms of coherent bosonic excitations above a Fermi surface in real space.

Figure 1

The setup for cavity-assisted hopping on a lattice. A large energy offset $\delta$ prevents direct tunneling between neighboring sites. The atoms can hop by a cavity-assisted Raman process, absorbing a pump photon at ${\omega }_p$ (solid green arrow) and emitting a photon at ${\omega }_p-\delta$ into the cavity (red dashed arrow). This emission is detuned from the cavity mode ${\omega }_c$ by $\mathrm{\Delta }\ll \delta$. Cavity losses are described by $\kappa$.

Figure 2

Mean field band structure and momentum distribution of fermions. (a) No pumping field, $\lambda =0$. (b) Nonzero pumping strength, $\lambda \ne 0$. Here $k=-\theta$ is the minimum of the band.

Figure 3

The nonequilibrium dynamics of the cavity mode and the fermions. (a) The cavity field occupation ${|\alpha (t)|}^2$; (b) the phase of $\alpha (t)$; (c) the center of mass of the fermions; (d) the total current of the fermions. The inset shows the current beyond the mean field, $J^{\mathrm{cl}}+J^{\mathrm{qu}}$. The blue dashed lines are the mean field results with lattice length $L=20$, particle number $N=5$, detuning $\mathrm{\Delta }/\kappa =0.5$, and $\lambda /\kappa =0.5$. The red solid lines are the results beyond the mean field by solving Eq. (6) with the same parameters.

Figure 4

(a),(b) The density distribution and the absolute value of the single-particle density matrix of the initial state. (c),(d) The final density distribution and density matrix of fermions (beyond the mean field) after a long-time evolution $\kappa t=10^3$. (e),(f) The final density distribution and density matrix of hard-core bosons starting from the same initial state. Blue dashed lines are the mean field results, while the red solid lines are the solutions beyond the mean field. The lattice length is $L=20$, particle number $N=5$, detuning $\mathrm{\Delta }/\kappa =0.5$, and $\lambda /\kappa =0.5$.