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Acta Physica Polonica A

Atomic Number Fluctuations in Spinor Bose-Einstein Condensate with Dynamical Quantum Phase Transitions

Yaming Li, Yi Ding, Jianning Liu, Yixiao Huang

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We study atomic number fluctuations in a spinor Bose–Einstein condensate and use it to characterize behaviors of dynamical quantum phase transitions. We observe that the quench dynamics of the atomic number fluctuations exhibit a nonanalytical change with respect to a parameter in the final Hamiltonian and demonstrate that the atomic number fluctuations can be used to detect both the ground state phase diagram and the highest energy state quantum phase transition. We further analyze the dynamics of atomic number fluctuations for finite magnetization and show that the quantum fluctuations could also be used to probe the phase transitions of the highest energy level and the ground state.

DOI
10.12693/aphyspola.143.83

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We study atomic number fluctuations in a spinor Bose–Einstein condensate and use it to characterize behaviors of dynamical quantum phase transitions. We observe that the quench dynamics of the atomic number fluctuations exhibit a nonanalytical change with respect to a parameter in the final Hamiltonian and demonstrate that the atomic number fluctuations can be used to detect both the ground state phase diagram and the highest energy state quantum phase transition. We further analyze the dynamics of atomic number fluctuations for finite magnetization and show that the quantum fluctuations could also be used to probe the phase transitions of the highest energy level and the ground state.
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Dynamical quantum phase transitions are closely related to equilibrium quantum phase transitions for ground states. Here, we report an experimental observation of a dynamical quantum phase transition in a spinor condensate with correspondence in an excited state phase diagram, instead of the ground state one. We observe that the quench dynamics exhibits a nonanalytical change with respect to a parameter in the final Hamiltonian in the absence of a corresponding phase transition for the ground state there. We make a connection between this singular point and a phase transition point for the highest energy level in a subspace with zero spin magnetization of a Hamiltonian. We further show the existence of dynamical phase transitions for finite magnetization corresponding to the phase transition of the highest energy level in the subspace with the same magnetization. Our results open a door for using dynamical phase transitions as a tool to probe physics at higher energy eigenlevels of many-body Hamiltonians.
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Quantum phase transitions universally exist in the ground and excited states of quantum many-body systems, and they have a close relationship with the nonequilibrium dynamical phase transitions, which however are challenging to identify. In the system of spin-1 Bose-Einstein condensates, though dynamical phase transitions with correspondence to equilibrium phase transitions in the ground state and uppermost excited state have been probed, those taking place in intermediate excited states remain untouched in experiments thus far. Here we unravel that both the ground- and excited-state quantum phase transitions in spinor condensates can be diagnosed with dynamical phase transitions. A connection between equilibrium phase transitions and nonequilibrium behaviors of the system is disclosed in terms of the quantum Fisher information. We also demonstrate that near the critical points parameter estimation beyond the standard quantum limit can be implemented. This work not only advances the exploration of excited-state quantum phase transitions via a scheme that can immediately be applied to a broad class of few-mode quantum systems, but also provides a new perspective on the relationship between quantum criticality and quantum enhanced sensing.