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arXiv:1502.01817 · Physical Review Letters

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

Corinna Kollath, Ameneh Sheikhan, Stefan Wolff, Ferdinand Brennecke

Published Feb 12, 2016• 103 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.116.060401

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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 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 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.
Although Weyl semimetals have been extensively studied for exploring rich topological physics, the direct observation of the celebrated chiral magnetic effect (CME) associated with the so-called dipolar chiral anomaly has long intrigued and challenged physicists, still remaining elusive in nature.Here we propose a feasible scheme for experimental implementation of ultracold atoms that may enable us to probe the CME with a pure topological current in an artificial Weyl semimetal.The paired Weyl points with the dipolar chiral anomaly emerge in the presence of the well-designed spin-orbital coupling and laser-assisted tunneling.Both of the two artificial fields are readily realizable and highly tunable via current optical techniques using ultracold atoms trapped in threedimensional optical lattices, providing a reliable way for manipulating Weyl points in the momentum-energy space.By applying a weak artificial magnetic field, the system processes an auxiliary current originated from the topology of a paired Weyl points, namely, the pure CME current.This topological current can be extracted from measuring the center-of-mass motion of ultracold atoms, which may pave the way to directly and unambiguously observe the CME in experiments.
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.
Ultracold fermionic atoms placed in a synthetic magnetic field arrange themselves in Landau levels. We theoretically study the optomechanical interaction between the light field and collective excitations of such fermionic atoms in synthetic magnetic field by placing them inside a Fabry-Perot cavity. We derive the effective Hamiltonian for particle hole excitations from a filled Landau level using a bosonization technique and obtain an expression for the cavity transmission spectrum. Using this we show that the cavity transmission spectrum demonstrates cold atom analog of Shubnikov‐de Haas oscillation in electronic condensed matter systems. We discuss the experimental consequences for this oscillation for such a system and the related optical bistability. By allowing an ultracold atomic ensemble to interact with a selected mode of a high-finesse cavity it is possible to probe the quantum many-body state of such an ultracold atomic system. The resulting cavity optomechanics or cavity quantum electrodynamics with ultracold atoms has recently witnessed a significant development [1]. The experimental successes include the coupling of collective density excitation of an ultracold bosonic condensate with a single-cavity mode and observation of the coupled dynamics through cavity transmission [2], a strongly coupled cavity mode with a highly localized ultracold atomic condensate trapped inside a single antinode of a cavity field [3], demonstration of strong ultracold atomcavity-coupling-induced optical nonlinearity even at low photon density [4], and selected atom-photon coupling of a single atomic ensemble in a multiensemble system [5 ]t o name a few. In another development, there has been significant experimental and theoretical progress in studying the effect of optically induced artificial or synthetic gauge field [6] on such neutral atoms, making it a playground for quantum simulation of phenomena that occur when an electronic condensed matter system is placed in a real magnetic field. The experimental achievements in this direction include the observation of vortices, Abrikosov vortex lattice in trapped ultracold atomic superfluid initially by achieving the synthetic magnetic field through the rotation of the trap [7], and later by Raman laser induced spatially varying coupling of the hyperfine states of such ultracold atoms [8]. A more recent development in this direction includes the creation of optical flux lattices [9], realization of spin-orbit coupling for such neutral ultracold bosonic [10] and fermionic atoms [11] with the possibility of creating ultracold atomic analogs of topological condensed matter phases [12]. This Letter aims to combine these two developments by considering a system of such ultracold atoms trapped inside a high-finesse Fabry-Perot cavity interacting with
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.