The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.
The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.
Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information.In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations.In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t = 0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Foss-Feig et al (2013 Phys.Rev. A 87 042101).Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g.Bloch vector and spin-squeezing dynamics.In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence 5
To create a more comprehensive understanding of nonequilibrium dynamics of open quantum many-body systems, we visit an exactly solvable example, that is a quenched transverse-field Ising chain coupled to Markovian baths, which act locally on the Jordan-Wigner fermionic space. Performing explicit calculations on the heat transfer, transverse magnetization, and kink density, we find that the imbalance of two opposite damping mechanisms play a crucial role in constructing a nontrivial nonequilibrium steady state accompanied with a dissipative quantum phase transition, also that the competition between unitary drive and decoherence does not necessarily lead to a quasi-stationary state or prethermalization under certain ordinary relaxation.
During the last decade the field of quantum information has seen considerable progress both
theoretically and experimentally. The building block of this theory is the so-called qubit,
the quantum counterpart of the classical bit. It turns out that spin degrees of freedom
of quantum particles are among the most promising candidates for quantum information
processing and computation. Thus, a deep understanding of the different processes that
govern the dynamics of these objects is of fundamental importance. For instance, the decoherence
process, caused the coupling of the qubits to their surrounding environment, is
the main obstacle to quantum information processing: it leads them to lose their quantum
coherence and thus behave classically. In addition, quantum systems exhibit correlations
that have no classical counterpart. This phenomenon is called entanglement and is the
vital resource for quantum teleportation and quantum computing. Decoherence and entanglement
dynamics were extensively studied within the framework of the Markovian
approximation using the master equation approach. However, due to the non-commuting
character of quantum observables, only few models are known to be exactly solvable.
Moreover, many spin systems display a strongly non-Markovian behavior. This thesis is
devoted to the development of new techniques for deriving the exact dynamics of spin
qubits, coupled through Heisenberg and/or Ising interactions to spin environments that
have internal dynamics. The basic idea behind these techniques is to use the underlying
symmetries exhibited by the Hamitonian operators of the composite systems. This allows
for the study of problems related to decoherence and entanglement.
Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of (9)Be(+) ions in a Penning trap. We verified entanglement in spin-squeezed states of up to 219 ions, directly observing 4.0 ± 0.9 decibels of spectroscopic enhancement, and observed states with non-Gaussian statistics consistent with oversqueezed states. The good agreement with ab initio theory that includes interactions and decoherence lays the groundwork for simulations of the transverse-field Ising model with variable-range interactions, which are generally intractable with classical methods.
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.