Non-thermalization in trapped atomic ion spin chains

Abstract

Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Use of global interactions in efficient quantum circuit constructions

“…In fact, it has been calculated numerically that the power p 1.4 opt = renders the maximum quality for the set of parameters considered in [34]. Fortunately, p = 1.4 is within the limits p 0, 3 Î [ ] [11,31]. Motivated by the previous discussion, we next suggest an extended method of the power law approximation of the exponential drop off that is useful for quantum Fourier arithmetic circuits.…”

“…However, it is possible that ij c | | drops off as a function of the distance i j -| |. This may be natural given physical interaction strengths typically scale in the distance between qubits [31].…”

“…Unfortunately, the exponential drop off in the strength of the interaction appears to be unnatural. Instead, the decrease in the strength of the interaction as a power of the distance d as d p , where p 0, 3 Î [ ] [11,31] seems more realistic. This leads to the question of how well the desired exponential drop off can be approximated with such physical-level global gates.…”

Breakdown of ergodicity in quantum systems: from solids to synthetic matter

“…On the experimental side, this volume contains a review by Hess et al [22] on exploring non-ergodic phenomena in long-range interacting spin models realized by trapped ions. They observe a long-lived local memory of the out-of-equilibrium initial conditions and signatures of time crystal in the presence of quenched disorder.…”

Towards analog quantum simulations of lattice gauge theories with trapped ions

“…A unique feature of the trapped ion architecture is that global addressing of the ions using a few laser beams allows the realization of tunable longrange spin-spin interactions in the chain. With no need for individual addressability, systems of a few tens of ions have been successfully realized, and analog simulations of sizable quantum spin systems are made possible [63][64][65][66][67][68][69][70][71]. More complex quantum many-body systems, such as those described by gauge field theories, require either some degree of individual addressing or higherorder spin interactions among different species, as put forward in several proposals for simulating the relativistic Dirac equation [5,[72][73][74] a quantum field theory of scalar fields [75], and 1+1D QED [56,76].…”