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Dynamical quantum phase transitions in an atom-molecule system

Yixiao Huang, Jialu Yin, Yuguo Su, En-Jia Ye, Zheng-Da Hu, Yi Ding

Published Dec 1, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1063/5.0240740

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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.
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.
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.
We study spin-nematic squeezing in a spinor Bose-Einstein condensate and use it to probe dynamical quantum phase transitions. We show that the quench dynamics of the spin-nematic squeezing exhibits a nonanalytical change with respect to a final quadratic Zeeman energy, and demonstrate that the squeezing detects not only the ground state phase diagram, but also the excited state quantum phase transition. We further analyze the dynamic stabilization of the system and present its relation to the dynamical quantum phase transitions. Our results are applicable to the spinor condensates with both of the sodium and rubidium atoms.
Identifying dynamical signatures of excited-state quantum phase transitions (ESQPTs) in experimentally realizable quantum many-body systems is helpful for understanding the dynamical effects of ESQPTs. In such systems, the highly controllable spinor Bose-Einstein condensates (BECs) offer an exceptional platform to study ESQPTs. In this work, we investigate the dynamical characteristics of the ESQPT in spin-1 BEC by means of the Loschmidt echo spectrum. The Loschmidt echo spectrum is an extension of the well-known Loschmidt echo and defined as the overlaps between the evolved state and the excited states of the initial Hamiltonian. We show that both the time-evolved and long-time-averaged Loschmidt echo spectrum undergo a remarkable change as the system passes through the critical point of the ESQPT. Moreover, the particular behavior exhibited by the Loschmidt echo spectrum at the critical point stands as a dynamical detector for probing the ESQPT. We further demonstrate how to capture the features of the ESQPT by using the energy distribution associated with the Loschmidt echo spectrum for time-evolved and long-time-averaged cases, respectively. Our findings contribute to a further verification of the usefulness of the Loschmidt echo spectrum for witnessing various quantum phase transitions in many-body systems and provide a different way to experimentally examine the dynamical consequences of ESQPTs.
A dynamical quantum phase transition can be characterized by a nonanalytic change in the quench dynamics when a parameter in the governing Hamiltonian is varied. Such a transition typically only shows up in long-time dynamics for extensive systems with short-range couplings. We analyze a model Hamiltonian of spin-1 particles with effectively infinite-range couplings and demonstrate that for this system the nonanalytic transition occurs for local observables in short-time durations even when the system is of a large size. We experimentally realize this model Hamiltonian and observe the dynamical quantum phase transition in an antiferromagnetic spinor Bose-Einstein condensate of around 105{10}^{5}105 sodium atoms. Our observations agree well with the theoretical prediction. We also analyze the scaling exponent near the dynamical phase transition and discuss its relation with the excited-state spectrum of the system.
We study Bose-Einstein condensates at the low-energy limit and show that their collective dynamics exhibit interesting quantum dynamical behavior. The system undergoes a dynamical quantum phase transition after a sudden quench into a properly distributed static force, provided its dispersion relation is linear. We corroborate the occurrence of a dynamical phase transition by calculating the Fisher zeros of the Loschmidt amplitude and showing that they cross the real time axis in the thermodynamic limit. A connection is established between the order of nonanalycity in the return rate function and the spectral density of the force. Furthermore, it is shown that a logarithmic or power-law scaling holds at the critical times depending on the displacement spectrum. The scaling behaviors are studied for three different cases. Eventually, a scheme for the quantum simulation of such a dynamical phase transition and its verification is proposed. We show that by taking into account the environmental effects the behavior remains observable.