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arXiv:2001.02686 · Physical Review Letters

Observation of Dynamical Quantum Phase Transitions with Correspondence in an Excited State Phase Diagram

Tonghua Tian, H.-X. Yang, L.-Y. Qiu, Hongyu Liang, Yan-Bin Yang, Yong Xu, Luming Duan

Published Jan 31, 2020• 110 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.043001

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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.
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.
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We conduct an investigation on the dynamical quantum phase transition within an atom-molecule Bose–Einstein condensate. We explore the dynamics of atom-molecule conversion and utilize the fraction population of the atom as an order parameter for probing dynamical quantum phase transitions. It is shown that the quench dynamics of the atom presents a non-analytical change regarding the atom binding energy, and it is demonstrated that this dynamics can detect both the quantum phase transition at the ground state and at the highest energy level. Furthermore, we analyze the dynamics of the Loschmidt echo and present its connection with the dynamical quantum phase transitions.
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition between quantum fluctuations and mutual interactions among constituents of the system, not by thermal fluctuations; hence they can occur even at zero temperature. Examples of quantum phase transitions in many-body physics may be found in systems ranging from high-temperature superconductors to topological insulators. A quantum phase transition usually can be characterized by nonanalyticity/discontinuity in certain order parameters or divergence of the ground state energy eigenvalue and/or its derivatives with respect to certain physical quantities. Here in a circular one-dimensional spin model with Heisenberg XY interaction and no magnetic field, we observe critical phenomena for the n0=1/N→0n_0=1/N\rightarrow0n0​=1/N→0 Mott insulator caused by a qualitative change of the boundary condition. We demonstrate in the vicinity of the transition point a sudden change in ground-state properties accompanied by an avoided level-crossing between the ground and the first excited states. Notably, our result links conventional quantum phase transitions to microscopic boundary conditions, with significant implications for quantum information, quantum control, and quantum computing.