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arXiv:1806.09269 · Physical Review Applied

Observation of a Dynamical Quantum Phase Transition by a Superconducting Qubit Simulation

Xue-Yi Guo, Chao Yang, Yu Zeng, Yi Peng, He-Kang Li, Hui Deng, Yi-Rong Jin, Shu Chen, Dongning Zheng, Heng Fan

Published Apr 24, 2019• 135 citations
arXivHTMLPDF

Abstract

Quantum information helping condensed matter research: A dynamical quantum phase transition can occur during the time evolution of a suddenly quenched quantum system, in analogy to the nonanalyticity of the free-energy density at the critical temperature of a macroscopic system. The authors succeed in observing such a transition in a quantum simulation of the quench dynamics of a many-body system. This computational experiment shows that quantum phase transitions of many-body systems can be simulated successfully using a single superconducting qubit, by varying the control parameter over the range of momenta as the qubit's spin-1/2 state evolves on the Bloch sphere.

DOI
10.1103/physrevapplied.11.044080

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Quantum information helping condensed matter research: A dynamical quantum phase transition can occur during the time evolution of a suddenly quenched quantum system, in analogy to the nonanalyticity of the free-energy density at the critical temperature of a macroscopic system. The authors succeed in observing such a transition in a quantum simulation of the quench dynamics of a many-body system. This computational experiment shows that quantum phase transitions of many-body systems can be simulated successfully using a single superconducting qubit, by varying the control parameter over the range of momenta as the qubit's spin-1/2 state evolves on the Bloch sphere.
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.
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.
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.
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Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.