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arXiv:2008.02431 · Physical Review A

Symmetry breaking in binary Bose-Einstein condensates in the presence of an inhomogeneous artificial gauge field

S. Sahar S. Hejazi, Juan Polo, Rashi Sachdeva, Thomas Busch

Published Nov 9, 2020• 21 citations
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Abstract

The ground state of interacting two-component Bose-Einstein condensates in the presence of an inhomogeneous artificial gauge potential is found to exhibit symmetry breaking in the phase separated regime. This theoretical work explains that this behavior arises as a consequence of the competition between the interaction and the rotational energies.''

DOI
10.1103/physreva.102.053309

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The ground state of interacting two-component Bose-Einstein condensates in the presence of an inhomogeneous artificial gauge potential is found to exhibit symmetry breaking in the phase separated regime. This theoretical work explains that this behavior arises as a consequence of the competition between the interaction and the rotational energies.''
We consider a two-component immiscible Bose-Einstein condensate with dominating intra-species repulsive density-density interactions. In the ground-state phase of such a system only one condensates is present. This can be viewed as a spontaneous breakdown of Z2\mathbb{Z}_2Z2​ symmetry. We study the phase diagram of the system at finite temperature beyond mean-field approximation. In the absence of rotation, we show that the system undergoes a first order phase transition from this ground state to a miscible two-component normal fluid as temperature is increased. In the presence of rotation, the system features a competition between vortex-vortex interaction and short range density-density interactions. This leads to a rotation-driven "mixing" phase transition in a spatially inhomogeneous state with additional broken U(1)\mathrm{U}(1)U(1) symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and Z2\mathbb{Z}_2Z2​ phase transitions split. This results in the formation of an intermediate state which breaks only Z2\mathbb{Z}_2Z2​ symmetry. It represents two phase separated normal fluids with density imbalance.
We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic (BBB) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.
We analyze the spontaneous symmetry breaking (SSB) induced by one specific component of a linearly coupled binary Bose-Einstein condensate (BEC). The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and with a double-well (DW) potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground-states were obtained, and an induced asymmetry in the partner field was observed. In this sense, we properly demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between atomic species, as well as the appearance of the Josephson and SSB phases.
The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge'' symmetry. This symmetry is manifested by a superfluid velocity us{\mathbf{u}}_{s}us​ (or gauge field) generated by the Berry phase of the spin field. In ``static'' traps, us{\mathbf{u}}_{s}us​ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\ensuremath{\Omega}}}_{c1}$, and can lead to vortex ground states.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.