Parity-symmetry breaking and topological phases in a superfluid ring

Abstract

We study analytically the superfluid flow of a Bose-Einstein condensate in a ring geometry in presence of a rotating barrier. We show that a phase transition breaking a parity symmetry among two topological phases occurs at a critical value of the height of the barrier. Furthermore, a discontinuous (accompanied by hysteresis) phase transition is observed in the ordered phase when changing the angular velocity of the barrier. At the critical point where the hysteresis area vanishes, chemical potential of the ground state develops a cusp (a discontinuity in the first derivative). Along this path, the jump between the two corresponding states having a different winding number shows strict analogies with a topological phase transition. We finally study the current-phase relation of the system and compare some of our calculations with published experimental results. In the limit of a vanishing barrier, the state with topological defects adiabatically connect two rotation-invariant states with different winding number . A second-order phase transition takes place two times as a function of Ω [19], first as the system enters the state with topological defects from the first rotational-invariant state 1 and then as it leaves the former by entering the second rotational-invariant state 2 . This scenario changes in presence of any finite-size obstacle that breaks the rotational symmetry of the ring, wherein the topological defects are always dynamically unstable [20], so that, in general, two topologically different states cannot be adiabatically connected. This has been recently confirmed experimentally with a barrier moving inside a toroidal BEC [21], where hysteresis appears in the transition between states with different topological winding number. The unstable branch of the hysteresis loop corresponds to the state with topological defects, and the angular velocity at which the metastable state decays (through phase slippage [7]) into the ground state generalizes the Landau critical velocity to the weak-link case [16,20].In this manuscript, we show that with a barrier rotating at the angular velocity Ω c = /2mR 2 , with R and m the radius of the ring and the atomic mass, respectively, the ground state of the system becomes degenerate when the height of the barrier is smaller than a critical value V < V c . The degeneration arises from a parity symmetry breaking that provides two

Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link

“…More details can be found in the Supplemental Material of Ref. [25]. With these parameters, we find all possible stationary solutions, the plane wave solutions (PW) and the soliton solutions (SL), and we can then study the relationship between the current ( j) and the phase difference (γ), defined in Eq.…”

“…1, there exist two kinds of stationary solutions, which are called PW and SL solutions in Ref. [25], for a given winding number ℓ. Wherein, the PW solutions for ℓ = 0 (solid lines) can be found in a lager range for |v| ≤ v c1 , while the SL solutions (dashed lines) can only survive for v c ≤ |v| ≤ v c1 . The value of v c1 can be reduced to v c = π (in our case) by increasing the barrier height to V c , which indicates a continuous phase transition in Ref.…”

“…Novel phase transitions have been predicted in Ref. [25], with the help of an analytical solution for the ring-trapped BEC with a rotating weak link. A parity symmetry breaking between two topological phase states was suggested by changing the barrier height V crossing a critical value V c .…”

“…In this manuscript, we will explore the properties of the current-phase relations of a ring-trapped BEC interrupted by a rotating rectangular barrier with the analytical solutions in Ref. [25]. The effects of the periodic boundary condition and the finite size of the ring on the current-phase relations will be discussed.…”

Stationary states of Bose-Einstein condensed atoms rotating in an asymmetric ring potential

“…Motivated by the above remarks, we study the rotational properties of a Bose-Einstein condensed gas of atoms in the presence of an external potential [20][21][22][23][24][25][26][27][28][29]. We assume for simplicity that the atoms are confined in a ring potential, having in mind a very narrow annulus, or torus, where the transverse degrees of freedom are frozen.…”