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arXiv:1811.11045 · Physical Review A

Cavity-induced spin-orbit coupling in an interacting bosonic wire

Catalin-Mihai Halati, Ameneh Sheikhan, Corinna Kollath

Published Mar 7, 2019• 15 citations
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Abstract

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.

DOI
10.1103/physreva.99.033604

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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 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 realize the dynamical 1D spin-orbit coupling (SOC) of a Bose-Einstein condensate confined within an optical cavity. The SOC emerges through spin-correlated momentum impulses delivered to the atoms via Raman transitions. These are effected by classical pump fields acting in concert with the quantum dynamical cavity field. Above a critical pump power, the Raman coupling emerges as the atoms superradiantly populate the cavity mode with photons. Concomitantly, these photons cause a backaction onto the atoms, forcing them to order their spin-spatial state. This SOC-inducing superradiant Dicke phase transition results in a spinor-helix polariton condensate. We observe emergent SOC through spin-resolved atomic momentum imaging and temporal heterodyne measurement of the cavity-field emission. Dynamical SOC in quantum gas cavity QED, and the extension to dynamical gauge fields, may enable the creation of Meissner-like effects, topological superfluids, and exotic quantum Hall states in coupled light-matter systems.
We study the spin-orbit-coupled ultracold Bose-Einstein condensate placed in a single-mode Fabry-P\'erot cavity. The cavity introduces a quantum optical lattice potential which dynamically couples with the atomic degrees of freedom and realizes a generalized modified Bose-Hubbard model whose zero-temperature phase diagram can be controlled by tuning the cavity parameters. In the noninteracting limit, where the atom-atom interaction is set to 0, the resulting atomic dispersion shows interesting features such as a bosonic analog of Dirac points, a cavity-controlled Hofstadter spectrum which bears the hallmark of pseudospin-1/2 bosons in the presence of Abelian and non-Abelian gauge fields (the latter due to spin-orbit coupling) in a cavity-induced optical lattice potential. In the presence of atom-atom interaction, using a mapping to a generalized Bose-Hubbard model of spin-orbit-coupled bosons in a classical optical lattice, we show that the system realizes a host of quantum magnetic phases whose magnetic order can be detected from the cavity transmission. This provides an alternative approach to detecting quantum magnetism in ultracold atoms. We discuss the effects of cavity-induced optical bistability on these phases and their experimental consequences.
We consider an atom inside a ring cavity, where a plane-wave cavity field together with an external coherent laser beam induces a two-photon Raman transition between two hyperfine ground states of the atom. This cavity-assisted Raman transition induces effective coupling between atom’s internal degrees of freedom and its center-of-mass motion. In the meantime, atomic dynamics exerts a back-action to cavity photons. We investigate the properties of this system by adopting a mean-field and a full quantum approach, and show that the interplay between the atomic dynamics and the cavity field gives rise to intriguing nonlinear phenomena.
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.
The orbital degree of freedom plays an important role in understanding exotic phenomena of strongly correlated materials. In this work, we study strongly correlated ultracold bosonic gases coupled to a high-finesse cavity, pumped by a blue-detuned laser in the transverse direction. By controlling the reflection of the pump laser, we find that atoms can be selectively transferred to the odd-parity ppp-orbital band or to the even-parity ddd-orbital band of a two-dimensional square lattice, accompanied by pronounced cavity-photon excitations. By interacting with the cavity field, atoms self-organize to form stable higher-orbital superfluid and Mott-insulating phases with orbital-density waves, as a result of cavity-induced orbital-flip hoppings. Our study opens a route to manipulate orbital degrees of freedom in strongly correlated quantum gases via coupling to optical cavities.