Topological condensate in an interaction-induced gauge potential

Abstract

We systematically investigate the ground state and elementary excitations of a Bose-Einstein Condensate within a synthetic vector potential, which is induced by the many-body effects and atomlight coupling. For a sufficiently strong inter-atom interaction, we find the condensate undergoes a Stoner-type ferromagnetic transition through the self-consistent coupling with the vector potential. For a weak interaction, the critical velocity of a supercurrent is found anisotropic due to the density fluctuations affecting the gauge field. We further analytically demonstrate the topological ground state with a coreless vortex ring in a 3D harmonic trap and a coreless vortex-antivortex pair in a 2D trap. The circulating persistent current is measurable in the time-of-flight experiment or in the dipolar oscillation through the violation of Kohn theorem.Introduction: Gauge fields play an important role in the modern particle physics, mediating interaction between elementary particles. In condensed matter physics, the gauge fields bring many important phenomena, such as integer/factional quantum Hall effects[1, 2], Laughlin liquids [3] and Hofstadter butterfly spectrum[4], etc. In quantum gas systems, artificial gauge fields can be also generated for neutral atoms in the rotating frame [5,6], or by the atom-light coupling with spatial dependent laser fields [7][8][9] or detuning [10,11]. The latter opens up a new possibility to study many-body physics with gauge potential, and is extended to investigate the spin-orbital coupling problems in similar experiments [12].Besides of the generating by external lasers, it was theoretically proposed that the gauge field can be induced by dipole-dipole interaction between two dipolar or Rydberg atoms [13][14][15]. For many-body systems, some interesting dynamics [16] and excitations[17] within a densitydependent gauge field were investigated in a 1D system. However, considering the finite temperature effects and quantum fluctuations, it is certainly more realistic and demanding to investigate many-body properties in higher dimensional systems, where the effective gauge field may further introduce topological defects and more interesting many-body physics not observable in 1D systems.In this Letter, we systematically investigate the ground state and excitation properties of a (pseudo) spin-1/2 condensate with the interaction-induced gauge field in 2D and 3D systems. We find several new many-body properties: (i) For a sufficiently strong inter-atom interaction, the condensate can have a Stoner-type ferromagnetism through the self-consistent coupling with the synthetic field. (ii) In the weak interaction limit, we calculate the Bogoliubov excitation spectrum of a superfluid current, and show that the critical velocity for dynamical instability becomes anisotropic in space due to density fluctuations within the gauge field. (iii) In a harmonic trap, we show analytic solutions of the condensate ground state, and find a coreless vortex ring around the gauge field

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

“…where C is an arbitrary integration constant. Substituting equation (32) into (39), and then substituting again to remove a factor of ẋ 1 , leads to the mechanical energy equation,…”

“…This has led to the realization of vortex states [34] as well as spin-orbit coupling [35]. Interest was recently focused on schemes for generating gauge potentials with an effective back-action between the matter and the gauge potential [36,37], which leads to a number of novel phenomena, including the violation of the Kohn's theorem [38,39], and unconventional vortex dynamics [40,41]. Very recently, the first experimental realization of a dynamical gauge theory in a trapped ion system was shown [42] .…”

Stability of matter-wave solitons in a density-dependent gauge theory

“…Recently, proposals have appeared which center around the engineering of density-dependent gauge potentials which feature a back-action between the matter-field and the gauge potential [54,55]. The condensate dynamics in these models can be greatly modified, including collective modes which violate Kohn's theorem [56][57][58][59], unconventional vortex dynamics [60,61], and the emergence of chiral solitons which feature non-integrable collision dynamics [62]. Very recently, experiments have appeared in which a dynamical gauge theory was realised in trapped ion systems [63] and a density-dependent synthetic gauge field in a Bose-Einstein condensate loaded into a two-dimensional lattice [64].…”

Vortex dynamics in superfluids governed by an interacting gauge theory

“…The resulting gauge field is not dynamical in a field theoretic sense, but it does become density dependent and therefore provides a back-action between the synthetic gauge potential and the superfluid. This results in a current nonlinearity in the equation of motion for the superfluid with dramatic consequences for the transport properties of the system [1,27,28]. A more complete understanding of the vortex dynamics in such a system will provide important insight into phenomena such as drag forces and superfluidity of the chiral gas.We start by briefly introducing the concept of a synthetic nonlinear gauge potential.…”