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arXiv:1309.6107 · Physical Review B

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

Emilia Witkowska, Jacek Dziarmaga, Tomasz Świsłocki, Michał Matuszewski

Published Aug 20, 2013• 18 citations
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Abstract

We investigate the dynamics and outcome of a quantum phase transition from an antiferromagnetic to a phase-separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We explicitly demonstrate double universality in the dynamics within experiments with various quench times. 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 postselection dynamics.

DOI
10.1103/physrevb.88.054508

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We investigate the dynamics and outcome of a quantum phase transition from an antiferromagnetic to a phase-separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We explicitly demonstrate double universality in the dynamics within experiments with various quench times. 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 postselection dynamics.
We consider a phase transition from an antiferromagnetic to a phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We demonstrate the occurrence of two scaling laws, for the number of spin domain seeds just after the phase transition, and for the number of spin domains in the final, stable configuration. Only the first scaling can be explained by the standard Kibble-Żurek mechanism. We explain the occurrence of two scaling laws by a model including postselection of spin domains due to the conservation of condensate magnetization.
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.
It is shown that spin vortices are created through the Kibble-Zurek mechanism in the quantum phase transition of a spin-1 ferromagnetic Bose-Einstein condensate when the applied magnetic field is quenched to below a critical value. It is also shown that the spin correlation functions have finite correlation lengths, and that the magnetization at widely separated positions grows in random directions, resulting in spontaneous creation of spin vortices. We numerically confirm the scaling laws that the winding number of spin vortices is proportional to the square root of the length of a closed path and, for a slow quench, is proportional to ${\ensuremath{\tau}}_{\text{Q}}^{\ensuremath{-}1∕6}$ with ${\ensuremath{\tau}}_{\text{Q}}$ being the quench time. The relevance of spin conservation to the Kibble-Zurek mechanism is discussed.
Abstract Symmetry-breaking quantum phase transitions lead to the production of topological defects or domain walls in a wide range of physical systems. In second-order transitions, these exhibit universal scaling laws described by the Kibble–Zurek mechanism, but for first-order transitions a similarly universal approach is still lacking. Here, we propose a spinor Bose–Einstein condensate as a testbed system where critical scaling behaviour in a first-order quantum phase transition can be understood from generic properties. We demonstrate the applicability of the Kibble–Zurek mechanism for this transition to determine the critical exponents for: (1) the onset of the decay of the metastable state on short times scales, and (2) the number of resulting phase-separated ferromagnetic domains at longer times, as a one-dimensional spin-1 condensate is ramped across a first-order quantum phase transition. The predictions are in excellent agreement with mean-field numerical simulations and provide a paradigm for studying the decay of metastable states in experimentally accessible systems.
We present a method for investigating nonequilibrium dynamics of an ultracold system that is initially at thermal equilibrium. Our procedure is based on the classical fields approximation and appropriately prepared initial state for antiferromagnetic condensate with fixed magnetization. As an application of the method, we investigate the influence of thermal fluctuations on the quantum phase transition from an antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We find that at temperatures significantly lower than the critical condensation temperature Tc{T}_{c}Tc​ the scaling law for the number of created spin defects remains intact.
The famous Kibble-Zurek mechanism offers us a significant clue to study quantum phase transitions out of equilibrium. Here, we investigate an intriguing phenomenon of a spin-orbit coupled Bose-Einstein condensate by quenching the Raman coupling strength from a high-symmetry phase (nonmagnetic phase) to a low-symmetry phase (magnetic phase). When crossing the critical point, the fluctuation of momentum distribution leads to delayed bifurcation structures. Simultaneously, the domain information emerges in momentum space. Moreover, the universal scalings of spatiotemporal dynamics are extracted from the fluctuations and domains, which manifests homogeneous and inhomogeneous Kibble-Zurek power laws at different timescales. Our work demonstrates a paradigmatic study on the inhomogeneous Kibble-Zurek mechanism.