Dynamics of the modified Kibble-Żurek mechanism in antiferromagnetic spin-1 condensates

Abstract

We investigate the dynamics and outcome of a quantum phase transition from an antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We explicitly demonstrate double universality in dynamics within experiments with various quench time. Furthermore, we show that spin domains created in the nonequilibrium transition constitute a set of mutually incoherent quasicondensates. The quasicondensates appear to be positioned in a semiregular fashion, which is a result of the conservation of local magnetization during the post-selection dynamics.

Nonadiabatic quantum phase transition in a trapped spinor condensate

“…[22]. Moreover, the antiferromagnetic 2C state remains dynamically stable, up to a critical field b c > b 1 [12]. Consequently, the system driven adiabatically across the phase boundary b 1 , from the 2C phase into the separated phase, remains in the initial 2C state up to b 2 , when the 2C state becomes dynamically unstable towards the phase separation.…”

“…We consider the quantum phase transition from an antiferromagnetic to a phase-separated state by increasing an external magnetic field. In our previous work [11][12][13] we demonstrated the modification of the KZ mechanism due to the conservation of a magnetization in the system. Initially, the quantum phase transition develops in the usual way.…”

“…Stability analysis of the initial 2C+ρ + state, which is based on the Bogoliubov transformation for the uniform system [12] treated with the LDA, gives…”

“…In the pure ρ 0 phase, we denote the local chemical potential of the m f = 0 atoms (the cost of adding another m f = 0 particle to the ρ 0 phase) by μ 0 , and in the 2C phase by μ 2C . At the critical point the chemical potential difference μ = μ 2C − μ 0 is exactly zero and becomes positive in the phase-separated regime increasing to the first order in the small parameter μ(x,t) ∼ (x,t), so linearly with magnetic field according to (12). Therefore, we approximate the velocity gradient as…”

“…Based on stability conditions for the coexistence of two phases, it is possible to reach r dependence of critical magnetic fields. Here we follow our previous analysis [12] …”