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Journal of Physics B Atomic Molecular and Optical Physics

Prethermalization in an trapped ion spin chain with short interaction range

Ping Zou, Zhi‐Ming Zhang

Published May 31, 2018• 2 citations
Publisher

Abstract

Abstract The prethermalizaiton phenomenon in long-range interacting spin chains has been predicted in Gong and Duan (2013 New J. Phys. 15 113051) and experimentally observed in Neyenhuis et al (2017 Sci. Adv. 3 e1700672). The phenomenon disappears in short-range interacting spin chains in their scenario. Here we propose a scheme to observe prethermalization in short-range interacting spin chains by applying additional site-dependent potentials with global parity symmetry in the system. We study the time evolution of an effective XY model with a single-particle initially pumped, and consider several typical potential forms for the emergence of prethermalization. Through numerical calculations, we find that (1) depending on different dephasing speeds of the coherence between eigenstates, the spin chain may evolve up to three prethermal states at different time scales before relaxing to the thermal state; (2) an interesting excitation spreading phenomenon may occur along with prethermalization; and (3) with a special form of potentials, the long-time evolution of the system undergoes a transition from the absence to the presence of prethermal states by controlling the potential strength.

DOI
10.1088/1361-6455/aac945

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Abstract The prethermalizaiton phenomenon in long-range interacting spin chains has been predicted in Gong and Duan (2013 New J. Phys. 15 113051) and experimentally observed in Neyenhuis et al (2017 Sci. Adv. 3 e1700672). The phenomenon disappears in short-range interacting spin chains in their scenario. Here we propose a scheme to observe prethermalization in short-range interacting spin chains by applying additional site-dependent potentials with global parity symmetry in the system. We study the time evolution of an effective XY model with a single-particle initially pumped, and consider several typical potential forms for the emergence of prethermalization. Through numerical calculations, we find that (1) depending on different dephasing speeds of the coherence between eigenstates, the spin chain may evolve up to three prethermal states at different time scales before relaxing to the thermal state; (2) an interesting excitation spreading phenomenon may occur along with prethermalization; and (3) with a special form of potentials, the long-time evolution of the system undergoes a transition from the absence to the presence of prethermal states by controlling the potential strength.
Although statistical mechanics describes thermal equilibrium states, these states may or may not emerge dynamically for a subsystem of an isolated quantum many-body system. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale, and instead relax to quasi-stationary prethermal states that can be described by statistical mechanics, when approximately conserved quantities are included in a generalized Gibbs ensemble (GGE). We experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse-field Ising Hamiltonian following a sudden quench. For sufficiently long-range interactions, the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. However, the prethermal state in this case cannot be described by a standard GGE; it rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.
We propose an experimental scheme to observe prethermalization and a dynamic phase transition in a one-dimensional XY spin chain with long-range interactions and inhomogeneous lattice spacing, which can be readily implemented with a recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at an intermediate timescale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is shown to result from a non-trivial structure in the lower half of the energy spectrum. The dynamic behavior of the system is shown to cross different phases when the interaction range is continuously tuned, indicating the existence of a dynamic phase transition.
Nonequilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasistationary nonthermal plateaux are often observed at intermediate times. The paradigmatic example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state cannot escape the constraints imposed by the approximate integrability. We unveil a new mechanism of prethermalization, based on the presence of a symmetry of the prequench Hamiltonian, which is spontaneously broken at zero temperature and is explicitly broken by the postquench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasistationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full-time evolution is computed analytically, and the (nonintegrable) anisotropic next-nearest-neighbor Ising model, which is investigated numerically.
Recent progress in the study of many-body localization in strongly disordered interacting spin chains has emphasized the importance of distinguishing finite time prethermal behavior from long time and large volume asymptotics. We reexamine a reported nonergodic extended (NEE) regime in the interacting quasiperiodic Ganeshan-Pixley-Das Sarma model from this perspective, and propose that this regime is a prethermal feature. Indeed, we argue that the NEE regime may be identified through a change in the functional form of spin-spin autocorrelation functions, demonstrating that the NEE regime is distinguishable within intermediate-time dynamics. This is in contrast with existing conjectures relating the NEE regime to the presence of an asymptotic mobility edge in the single-particle spectrum. Thus, we propose a mechanism for the formation of an NEE regime which does not rely on asymptotic properties of the spin chain. Namely, we propose that the NEE regime emerges due to regularly spaced deep wells in the disorder potential. The highly detuned sites suppress spin transport across the system, effectively cutting the chain and producing a separation of timescales between the spreading of different operators. To support this proposal, we show that the NEE phenomenology also occurs in random models with deep wells but with no mobility edges, and does not occur in quasiperiodic models with mobility edges but with no deep wells. Our results support the broad conclusion that there is not a sharp distinction between the dynamics of quasiperiodically and randomly disordered systems in the prethermal regime. More specifically, we find that generic interacting quasiperiodic models do not have stable intermediate dynamical phases arising from their single-particle mobility edges, and that NEE phenomenology in such models is transient.
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (“qutrits”) with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.
We consider a chain of trapped ions to interact with each other via long-range interactions. This system can be used to simulate the long-range Ising model. We study the dynamics of quantum coherence of a single spin in the chain, where the spins are initially prepared in their upper states. The relaxation dynamics exhibits due to the genuine long-range interaction. The degree of quantum coherence of a single spin rapidly decreases and vanishes in the steady state. However, our numerical result suggests that the conventional spin chain model, which truncates the interactions between the distant spins, cannot show the relaxation dynamics. This implies that the usual truncation in approximating the long-range interaction is not applicable to describing the non-equilibrium dynamics. The effect of the interaction range on the relaxation dynamics is studied. The higher relaxation rate will show if a system has a longer range of interaction. However, it takes a longer relaxation time in the vicinity of infinite interaction range. We also examine the dynamics of quantum coherence of a block of spins. Our result may shed light on the relationship between long-range interaction and the coherence dynamics of a quantum many-body system.