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Physical Review A

Kibble-Zurek scalings of continuous magnetic phase transitions in spin-1 spin-orbit-coupled Bose-Einstein condensates

Shuyuan Wu, Yongguan Ke, Jiahao Huang, Chaohong Lee

Published Jun 13, 2017• 12 citations
Publisher

Abstract

We investigate the universal dynamics of a continuous magnetic phase transition from a unmagnetized phase to a ferromagnetic phase in a spin-1 spin-orbit-coupled Bose-Einstein condensate. When the system approaches the critical point, the Landau critical velocity gradually decreases to zero and so the correlation length diverges. Therefore, during the slow passage through the critical point, ferromagnetic domains are spontaneously created according to the Kibble-Zurek mechanism. Through calculating the Bogoliubov excitations, we give the Landau critical velocity and the correlation length, from which we derive the Kibble-Zurek scalings. Furthermore, we numerically simulate the critical spatial-temporal dynamics of the bifurcation delay and spontaneous domain formation, and extract the universal scaling exponents. The numerical scalings extracted from the critical spatial-temporal dynamics are very consistent with the scalings derived from the correlation length.

DOI
10.1103/physreva.95.063606

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We investigate the universal dynamics of a continuous magnetic phase transition from a unmagnetized phase to a ferromagnetic phase in a spin-1 spin-orbit-coupled Bose-Einstein condensate. When the system approaches the critical point, the Landau critical velocity gradually decreases to zero and so the correlation length diverges. Therefore, during the slow passage through the critical point, ferromagnetic domains are spontaneously created according to the Kibble-Zurek mechanism. Through calculating the Bogoliubov excitations, we give the Landau critical velocity and the correlation length, from which we derive the Kibble-Zurek scalings. Furthermore, we numerically simulate the critical spatial-temporal dynamics of the bifurcation delay and spontaneous domain formation, and extract the universal scaling exponents. The numerical scalings extracted from the critical spatial-temporal dynamics are very consistent with the scalings derived from the correlation length.
Abstract We investigate the universal spatiotemporal dynamics in spin–orbit coupled Bose–Einstein condensates which are driven from the zero-momentum phase to the plane-wave phase. The excitation spectrum reveals that, at the critical point, the Landau critical velocity vanishes and the correlation length diverges. Therefore, according to the Kibble–Zurek mechanism, spatial domains will spontaneously appear in such a quench through the critical point. By simulating the real-time dynamics, we numerically extract the static correlation length critical exponent and the dynamic critical exponent z from the scalings of the temporal bifurcation delay and the spatial domain number. The numerical scalings consist well with the analytical ones obtained by analyzing the excitation spectrum.
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.
According to the famous Kibble-Zurek mechanism (KZM), the universality of spontaneous defect generation in continuous phase transitions (CPTs) can be understood by the critical slowing down. In most CPTs of atomic Bose-Einstein condensates (BECs), the universality of spontaneous defect generations has been explained by the divergent relaxation time associated with the nontrivial gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge fields, their spontaneous superfluidity breakdown is resulted from the divergent correlation length associated with the zero Landau critical velocity. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown obeys the KZM. The Kibble-Zurek scalings are derived from the Landau critical velocity which determines the correlation length. In further, the critical exponents are numerically extracted from the critical spatial-temporal dynamics of the bifurcation delay and the spontaneous vortex generation. Our study provides a general way to explore and understand the spontaneous superfluidity breakdown in CPTs from a single-well dispersion to a double-well one, such as, BECs in synthetic gauge fields, spin-orbit coupled BECs, and BECs in shaken optical lattices.
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.
According to the famous Kibble-Zurek mechanism (KZM), the universality of spontaneous defect generation in continuous phase transitions (CPTs) can be understood by the critical slowing down. In most CPTs of atomic Bose-Einstein condensates (BECs), the universality of spontaneous defect generations has been explained by the divergent relaxation time associated with the nontrivial gapless Bogoliubov excitations. However, for atomic BECs in synthetic gauge fields, their spontaneous superfluidity breakdown results from the divergent correlation length associated with the zero Landau critical velocity. Here, by considering an atomic BEC ladder subjected to a synthetic magnetic field, we reveal that the spontaneous superfluidity breakdown obeys the KZM. The Kibble-Zurek scalings are derived from the Landau critical velocity which determines the correlation length. Furthermore, the critical exponents are numerically extracted from the critical spatiotemporal dynamics of the bifurcation delay and the spontaneous vortex generation. Our study provides a general way to explore and understand the spontaneous superfluidity breakdown in CPTs from a single-well dispersion to a double-well one, such as BECs in synthetic gauge fields, spin-orbit-coupled BECs, and BECs in shaken optical lattices.
Spontaneous spin vortex formation in a magnetic phase transition of a trapped spin-1 Bose-Einstein condensate is investigated based on mean-field theory. In a harmonic trapping potential, an inhomogeneous atomic density leads to spatial variations of the critical point, magnetization time, and spin correlation length. The Kibble-Zurek phenomena are shown to emerge even in such inhomogeneous spinor condensates, when the quench of the quadratic Zeeman energy is fast enough. For slow quench, the magnetized region gradually expands from the center of the trap, pushing out spin vortices, which hinders the Kibble-Zurek mechanism from occurring. The case of a toroidal trapping potential is also discussed.