Universal behaviors for the dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates

Haoxiang Yang, Tian Tian, Liyuan Qiu +7 more

Zachary Glassman, Donald P. Fahey, Ryan Wilson +2 more

Ming Xue, Shuai Yin, Li You

We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the equilibrium state and in the dynamics when the quadratic Zeeman shift is swept linearly. Three distinct dynamical regions are identified for different sweeping time scales ($\ensuremath{\tau}$) when compared to the time scale ${\ensuremath{\tau}}_{\mathrm{KZ}}\ensuremath{\sim}{N}^{(1+\ensuremath{\nu}z)/\ensuremath{\nu}d}$ decided by external driving in a system with finite size $N$ ($\ensuremath{\nu},z$ are critical exponents and $d$ the dimensionality). They are manifested by the excitation probability $\mathcal{P}$ and the excess heat density $\mathcal{Q}$. The adiabatic region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}2}$ follows from the adiabatic perturbation theory when $\ensuremath{\tau}>{\ensuremath{\tau}}_{\mathrm{KZ}}$, while the nonadiabatic universal region of $\mathcal{P}\ensuremath{\sim}\mathcal{Q}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ in the thermodynamic limit is described by the Kibble-Zurek mechanism when ${\ensuremath{\tau}}_{\mathrm{KZ}}>\ensuremath{\tau}>$ the time scale given by initial gap. The Kibble-Zurek scaling hypothesis is augmented with finite-size scaling in the latter region and several experimentally falsifiable features for the finite system we consider are predicted. The region of the fastest sweeping is found to be nonuniversal and far from equilibrium, with $\mathcal{P}$ and $\mathcal{Q}$ essentially being constants independent of $\ensuremath{\tau}$.

Tuoxin Li, Xiao Luo, Juncheng Wei +1 more

Abstract A central goal in condensed matter and modern atomic physics is the exploration of quantum phases of matter. Spinor Bose–Einstein condensates are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. This was explored by Sadler et al. in spinor condensates, rapidly quenched across a quantum phase transition to a ferromagnetic state. In this paper, we provide a mathematical justification for this phenomenon by completely classifying the ground state of ferromagnetic spin‐F Bose–Einstein condensates in ring traps as well as analyzing their asympototic behavior on the number of atoms and total magnetization. In particular, our classification results show the validity of single‐mode approximation (SMA) phenomenon first observed by Law et al.

Matthew T. Wheeler, Hayder Salman, Magnus O. Borgh

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.

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