Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

We propose how a fermionic quantum gas confined to an optical lattice and coupled to an optical cavity can self-organize into a state where the spontaneously emerging cavity field amplitude induces an artificial magnetic field. The fermions form either a chiral insulator or a chiral liquid carrying chiral currents. The feedback mechanism via the dynamical cavity field enables robust and fast switching in time of the chiral phases, and the cavity output can be employed for a direct nondestructive measurement of the chiral current.

Figure 1

Setup for generating cavity-induced artificial magnetic fields. (a) Fermionic atoms in an optical standing-wave cavity are subjected to an optical lattice potential, which creates an array of ladders with tunneling amplitude $J_{\parallel }$ along the legs. The bare tunneling along the rungs is strongly suppressed by a potential offset $\mathrm{\Delta }$ between neighboring wells. (b) Cavity-assisted Raman processes induced by two running-wave pump beams restore tunneling along the rungs with a dynamically induced amplitude $J_{\perp }$ and imprint a phase $\phi$ onto the tunneling of atoms around a plaquette.

Figure 2

(a) Real part of the cavity field $\alpha =⟨a⟩$ and (b) induced chiral current $⟨J_c⟩$ versus the pump strength $A\propto {\tilde{\mathrm{\Omega }}}^2$ for different fillings $n$. The lines show the results obtained by the adiabatic elimination of the cavity mode. For $n=1/2$ for intermediate values of $A$, two different solutions exist. Symbols represent the corresponding expectation values of the steady state obtained from exact diagonalization ($L=3$) with open boundary conditions and a maximum photon number of up to 25 [37] with $\hslash \kappa =0.05J_{\parallel }$ and $\hslash {\delta }_{cp}=J_{\parallel }$. Only the steady state that maximizes the real part of the expectation value of the photon field is shown.

Figure 3

(a) Time evolution of the chiral current $⟨J_c(t)⟩$ obtained by exact diagonalization for $N=2$, $L=2$, $\hslash {\delta }_{cp}=J_{\parallel }$ with open boundary conditions and a maximum photon number of up to 15 [37]. Horizontal lines mark the corresponding steady-state values $⟨J_c(t=\infty )⟩$. (b) Time scale $\tau$ versus $\kappa$ obtained from a linear fit of $\log (⟨J_c(t)⟩-⟨J_c(t=\infty )⟩)$. The shaded region represents the standard deviation of the fit.