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arXiv:1602.01723 · Physical Review A

Cavity-induced chiral states of fermionic quantum gases

Ameneh Sheikhan, Ferdinand Brennecke, Corinna Kollath

Published Apr 8, 2016• 39 citations
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Abstract

We investigate ultracold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

DOI
10.1103/physreva.93.043609

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We investigate ultracold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.
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.
We consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density-matrix renormalization-group method, we obtain a rich steady-state diagram of self-organized steady states. Transitions between superfluid to Mott-insulating states occur, on top of which we can have Meissner, vortex liquid, and vortex lattice phases. Also a state that explicitly breaks the symmetry between the two legs of the ladder, namely, the biased-ladder phase, is dynamically stabilized. We investigate the influence that a trapping potential has on the stability of the self-organized phases.
We investigate the dynamics of fermionic atoms in a high-finesse optical resonator after a sudden switch on of the coupling between the atoms and the cavity. The atoms are additionally confined by optical lattices to a ladder geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity-assisted Raman process. At long times after the quantum quench the arising steady state can carry a chiral current. In this work we employ exact diagonalization techniques on small system sizes to study the dissipative attractor dynamics after the quench towards the steady state and deviations of the properties of the steady state from predictions obtained by adiabatically eliminating the cavity mode.
We propose two experimental setups for fermionic atoms in a high-finesse optical resonator in which either a superconducting state with sss-wave symmetry of the pairs or a 4kF4{k}_{F}4kF​ charge-density wave can self-organize. In order to stabilize the sss-wave pairing, a two component attractively interacting fermionic gas is confined to a one-dimensional chain structure by an optical lattice. The tunneling of the atoms along the chains is suppressed initially by an energy offset between neighboring sites. A Raman transition using the cavity mode and a transversal pump laser then reintroduces a cavity-assisted tunneling. The feedback mechanism between the cavity field and the atoms leads to a spontaneous occupation of the cavity field and of a state of the fermionic atoms which is dominated by sss-wave pairing correlations. Extending the setup to a quasi-one-dimensional ladder structure where the tunneling of atoms along the rungs of the ladder is cavity assisted, the repulsively interacting fermionic atoms self-organize into a 4kF4{k}_{F}4kF​ charge-density wave. We use adiabatic elimination of the cavity field combined with state-of-the-art density-matrix renormalization-group methods in finite systems in order to identify the steady-state phases of the system.
We propose how topologically nontrivial states can dynamically organize in a fermionic quantum gas that is confined to a two-dimensional optical lattice potential and coupled to the field of an optical cavity. The spontaneously emerging cavity field induces, together with coherent pump laser fields, a dynamical gauge field for the atoms. Upon adiabatic elimination of the cavity degree of freedom, the system is described by an effective Hofstadter model with a self-consistency condition that determines the tunneling amplitude along the cavity direction. The fermions are found to self-organize into topologically nontrivial states that carry an extended edge state for a finite system size. Due to the dissipative nature of the cavity field, the topological steady states are protected from external perturbations.
We propose that an artificial electromagnetic field can be engineered in the context of cold fermionic atoms that are coupled to a cavity mode via two-photon processes in a two-dimensional optical lattice. There is a standing-wave pump laser inducing the electric effect in one spatial direction, and a second running-wave laser beam generates the magnetic flux perpendicular to the lattice plane. In the static scenario, the bulk spectrum resembles the fractal structure of the Hofstadter butterfly and the edge mode spectrum indicates the occurrence of the quantum Hall phase. The Keldysh formulism is utilized to capture the time evolution. The back action between atoms and cavity field gives a picture of the time-dependent non-equilibrium dynamics. We find that the spontaneous emergence of the artificial electromagnetic field stimulates the Hall current, and the superradiant cavity field emerges without pump threshold. Moreover, the magnetic flux not only modify the bulk topology, but also drives a series of dynamical phase transitions.