Exact calculation of phonon effects on spin squeezing

Abstract

Theoretical models of spins coupled to bosons provide a simple setting for studying a broad range of important phenomena in many-body physics, from virtually mediated interactions to decoherence and thermalization. In many atomic, molecular, and optical systems, such models also underlie the most successful attempts to engineer strong, long-ranged interactions for the purpose of entanglement generation. Especially when the coupling between the spins and bosons is strong---such that it cannot be treated perturbatively---the properties of such models are extremely challenging to calculate theoretically. Here, exact analytical expressions for nonequilibrium spin-spin correlation functions are derived for a specific model of spins coupled to bosons. The spatial structure of the coupling between spins and bosons is completely arbitrary, and thus the solution can be applied to systems in any number of dimensions. The explicit and nonperturbative inclusion of the bosons enables the study of entanglement generation (in the form of spin squeezing) even when the bosons are driven strongly and near-resonantly, and thus provides a quantitative view of the breakdown of adiabatic elimination that inevitably occurs as one pushes towards the fastest entanglement generation possible. The solution also helps elucidate the effect of finite temperature on spin squeezing. The model considered is relevant to a variety of atomic, molecular, and optical systems, such as atoms in cavities or trapped ions. As an explicit example, the results are used to quantify phonon effects in trapped ion quantum simulators, which are expected to become increasingly important as these experiments push towards larger numbers of ions.

13 pages, 12 figures

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
• Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence
• Demagnetization dynamics of non-interacting trapped fermions

Cited by in corpus (13)

• Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
• Trapped Ion Quantum Information Processing with Squeezed Phonons
• Origin of the slow growth of entanglement entropy in long-range interacting spin systems
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Simulating generic spin-boson models with matrix product states
• Superradiant to subradiant phase transition in the open system Dicke model: Dark state cascades
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Realization of programmable Ising models in a trapped-ion quantum simulator
• Bilayer crystals of trapped ions for quantum information processing
• Driving Spin-Boson Models From Equilibrium Using Exact Quantum Dynamics
• Quantum Simulation of Non-perturbative Cavity QED with Trapped Ions
• Parametric Amplification of Spin-Motion Coupling in Three-Dimensional Trapped-Ion Crystals