Dynamic hysteresis from bistability in an antiferromagnetic spinor condensate

Abstract

We study the emergence of hysteresis during the process of quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 Bose Einstein condensate of ultracold atoms. We explicitly demonstrate the appearance of a hysteresis loop with various quench times showing that it is rate-independent for large magnetizations only. In other cases scaling of the hysteresis loop area is observed, which we explain by using the Kibble-Zurek theory in the limit of small magnetization. The effect of an external harmonic trapping potential is also discussed.PACS numbers: 03.75. Kk, 03.75.Mn, 67.85.De, 67.85.Fg The classic example of hysteresis is the relation of the applied magnetic field to the magnetization in solid-state ferromagnetic materials. Hysteresis can also occur in different situations as a product of a fundamental physical mechanism like a phase transition, or a result of imperfections or degradations. Hysteresis occurs in two forms: rate-dependent and rate-independent. In the rateindependent case, two or more metastable energy states are separated by an energy barrier. When an external driving force moves the system from one metastable state to another, the system exhibits the history-dependent behavior. The rate-independent hysteresis of supercurrent in a rotating, superfluid Bose-Einstein condensate was observed and has been proclaimed as a milestone in the advancement of atomtronic circuitry [1][2][3]. A recent experiment [4] has also demonstrated the rate-independent hysteresis when a Bose-Einstein condensate is placed in a double-well potential. On the other hand, the observation of rate-dependent hysteresis could provide insight into the out-of-equilibrium dynamics of the system.Spinor condensates are composed of N atoms in several Zeeman components with a given hyperfine spin F and magnetic numbers m F . The global ground state of the F = 1 system is classified as ferro-or antiferromagnetic, depending on the sign of spin-dependent interactions. The magnetization longitudinal with respect to magnetic field M is approximately conserved in the system and acts as an independent external parameter. This conservation law comes from the spin rotational symmetry of contact interactions when dipole-dipole interactions are neglected. Consequently, in contrast to solid-state magnetic materials, classical hysteresis is impossible in spinor F = 1 condensates. However, a weak magnetic field drives the system to the transition from an antiferromagnetic ground state to a state where domains of atoms with different spin projections separate [5]. The phase transition is specific due to the region of bistability in which the antiferromagnetic and phase separated states are both metastable [6].In this paper, we investigate the emergence of hysteresis from bistability during the phase transition in an antiferromagnetic spin-1 condensate. The system is al-ready recognized as useful for quantum technology tasks, however hysteresis was not been examined up to now. By employing numerical simulations within...

Flemish Strings of Magnetic Solitons and a Nonthermal Fixed Point in a One-Dimensional Antiferromagnetic Spin-1 Bose Gas

“…individually [57][58][59][60], undergo pair-annhilation by forming Flemish strings. While there are a number of studies for quench dynamics of an AF spinor Bose gas [26,[61][62][63][64][65][66][67][68][69][70][71], universal thermalization through Flemish strings has never been reported.…”