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arXiv:1707.04123 · Physical Review A

Cavity-induced artificial gauge field in a Bose-Hubbard ladder

Catalin-Mihai Halati, Ameneh Sheikhan, Corinna Kollath

Published Dec 27, 2017• 26 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.96.063621

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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 consider theoretically ultracold interacting bosonic atoms confined to a wire geometry and coupled to the field of an optical cavity. A spin-orbit coupling is induced via Raman transitions employing a cavity mode and a transverse running-wave pump beam; the transition imprints a spatially dependent phase onto the atomic wave function. Adiabatic elimination of the cavity field leads to an effective Hamiltonian for the atomic degrees of freedom with a self-consistency condition. We map the spin-orbit coupled bosonic wire to a bosonic ladder in a magnetic field, by discretizing the spatial dimension. Using the numerical density-matrix renormalization group method, we show that in the continuum limit the dynamical stabilization of a Meissner superfluid is possible for parameters achievable by current experiments.
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 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 consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse cavity field, pumped by a laser beam in the transverse direction. Assuming a weak classical\mathit{classical}classical optical lattice added in the cavity direction, we model this system by a generalized Bose-Hubbard model, which is solved by means of bosonic dynamical mean-field theory. The complete phase diagram is established, which contains two novel self-organized quantum phases, lattice supersolid and checkerboard solid, in addition to conventional phases such as superfluid and Mott insulator. At finite but low temperature, thermal fluctuations are found to enhance the buildup of the self-organized phases. We demonstrate that cavity-mediated long-range interactions can give rise to stable lattice supersolid and checkerboard solid phases even in the regime of strong sss-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.
When placing an ultracold atomic gas inside a cavity, the light-matter coupling is enhanced and nonlinear atomic dynamics is generated, offering a promising platform for quantum simulation of models with short- and long-range interactions. Recently, superradiant self-organized phases for ultracold atomic gases inside a cavity, pumped by a blue detuned optical lattice, have been observed. Here, we explore the formation of quantum many-body phases of bosonic atoms inside an optical cavity, subject to transverse blue detuned pumping. We investigate the strongly interacting regime, which can be reached by tuning the s-wave scattering length using external fields. We analyze the interplay between superradiant self-organization with superfluid and Mott insulator phases, without the need of including higher lying bands, as the Wannier functions are dynamically linked to the cavity light via backaction. We observe different kinds of structural phase transitions driven by the light inside the cavity and the interplay with atomic collisions. We observe the mode softening at the critical points in the quantum phase transitions which can be measured in future experiments. We obtain our results within a full self-consistent theoretical framework, the light-matter density matrix renormalization group (DMRG), which employs the computation of light dependent Wannier functions for the full quantum optical lattice in combination with DMRG for the atomic dynamics. The methods introduced here can be used to analyze the effects of strong quantum correlations in strongly interacting light-matter systems.