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arXiv:2401.05921 · Physica Scripta

Universal dynamics of the entropy of work distribution in spinor Bose-Einstein condensates

Zhen-Xia Niu

Published Mar 5, 2025• 0 citations
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Abstract

Abstract Driving a quantum many-body system across the quantum phase transition (QPT) in the finite time has been concerned in different branches of physics to explore various fundamental questions. Here, we analyze how the underlying QPT affects the work distribution P (W ), when the control parameter of a ferromagnetic spinor Bose-Einstein condensates is tuned through the critical point in the finite time. We show that the work distribution undergoes a dramatic change with increasing the driving time τ. To capture the characteristics of the work distribution, we analyze the entropy of P (W ) and find three different regions in the evolution of entropy as a function of τ. Specifically, the entropy is insensitive to the driving time in the region of very short τ, while it exhibits a universal power-law decay in the region with intermediate value of τ. In particular, the power-law scaling of the entropy is according with the well-known Kibble-Zurek mechanism. For the region with large τ, the validity of the adiabatic perturbation theory leads to the entropy decay as τ-2 ln τ. Our results verify the usefulness of the entropy of the work distribution for understanding the critical dynamics and provide an alternative way to experimentally study nonequilibrium properties in quantum many-body systems.

DOI
10.1088/1402-4896/adbd03

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Abstract Driving a quantum many-body system across the quantum phase transition (QPT) in the finite time has been concerned in different branches of physics to explore various fundamental questions. Here, we analyze how the underlying QPT affects the work distribution P (W ), when the control parameter of a ferromagnetic spinor Bose-Einstein condensates is tuned through the critical point in the finite time. We show that the work distribution undergoes a dramatic change with increasing the driving time τ. To capture the characteristics of the work distribution, we analyze the entropy of P (W ) and find three different regions in the evolution of entropy as a function of τ. Specifically, the entropy is insensitive to the driving time in the region of very short τ, while it exhibits a universal power-law decay in the region with intermediate value of τ. In particular, the power-law scaling of the entropy is according with the well-known Kibble-Zurek mechanism. For the region with large τ, the validity of the adiabatic perturbation theory leads to the entropy decay as τ-2 ln τ. Our results verify the usefulness of the entropy of the work distribution for understanding the critical dynamics and provide an alternative way to experimentally study nonequilibrium properties in quantum many-body systems.
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 NNN ($\ensuremath{\nu},z$ are critical exponents and ddd the dimensionality). They are manifested by the excitation probability P\mathcal{P}P and the excess heat density Q\mathcal{Q}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 P\mathcal{P}P and Q\mathcal{Q}Q essentially being constants independent of $\ensuremath{\tau}$.
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.
The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.
Abstract Phase transitions in nonequilibrium dynamics of quantum many-body system, known as dynamical phase transitions (DPTs), play an important role for understanding various dynamical phenomena observed in different branches of physics. In general, there are two types of DPTs, the first one is characterized by distinct evolutionary behaviors of a physical observable, while the second one is marked by the vanishing overlap between the time-evolved and initial states. Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives in a spinor Bose–Einstein condensate (BEC), an ideal platform for investigating nonequilibrium dynamics. Utilizing the sudden quench process, we demonstrate that the system exhibits both types of DPTs as the control parameter is quenched through the critical value, referring to as the critical quenching. We show analytically how to determine the critical quenching via the semiclassical approach and carry out a detailed examination of both semiclassical and quantum signatures of DPTs. In particular, we reveal that the occurrence of DPTs is triggered by the separatrix in the underlying semiclassical system. Our findings offer deeper insights into the properties of DPTs and verify the usefulness of semiclassical analysis for studying DPTs in quantum systems with well-defined semiclassical limit.
Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both the dynamical steady-state-relaxation region and the phase-oscillation region. Based on various observables, two different values for the same quantum critical parameter are observed. This result is beyond a universal-scaling-law description of quantum phase transitions known as the Kibble-Zurek mechanism, and suggests that multiple quantum critical mechanisms are competing in many-body quantum phase transition experiments in inhomogeneous systems.
The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.