We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.
We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.
We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components.One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly.This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas.Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment.As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat.Commun.4 1903) and show qualitative agreement with experimental results.
We determine the exact asymptotic many-body wavefunction of a spin-s Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at t=0+ and for arbitrary s. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-1/2 case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-1/2 case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.
We investigate the reduced dynamics of a qubit subject to correlated longitudinal and transverse noise arising from its coupling to a shared bosonic bath. The environmental fluctuations are characterized by a positive-semidefinite matrix-valued spectral density, whose complex off-diagonal elements encode correlations between dephasing and relaxation channels in the frequency domain. Within the second-order time-convolutionless framework, we derive closed time-local equations for the Bloch-vector components of the reduced density matrix. The numerical implementation is validated against the exact pure-dephasing solution and the established behavior of the transverse-coupling spin-boson model. When both noise channels are present, the cross-spectral terms couple the otherwise distinct dephasing and relaxation sectors, producing dynamics that cannot be reproduced by adding independent noise contributions. In particular, the correlations generate non-monotonic population relaxation and a transient revival of coherence following its initial decay. The strength, bandwidth, delay, and phase of the cross spectrum provide control parameters for the magnitude and temporal structure of these effects. Our results demonstrate that correlated multi-axis noise can redistribute coherence loss and energy relaxation in time, thereby providing finite temporal windows of enhanced coherence or suppressed relaxation within the weak-coupling regime.
We address the dynamics of entanglement and quantum discord for two noninteracting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e., coupled with an external environment characterized by a noise spectrum of the form $1/{f}^{\ensuremath{\alpha}}$. More specifically, we address systems in which the Gaussian approximation fails, i.e., mere knowledge of the spectrum is not enough to determine the dynamics of quantum correlations. We thus investigate the dynamics for two different configurations of the environment: in the first case, the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with fixed switching rates. In both cases, we found analytical expressions for the time dependence of entanglement and quantum discord, which may also be extended to a collection of fluctuators with random switching rates. The environmental noise is introduced by means of stochastic time-dependent terms in the Hamiltonian, and this allows us to describe the effects of both separate and common environments. We show that the non-Gaussian character of the noise may lead to significant effects, e.g., environments with the same power spectrum, but different configurations give rise to the opposite behavior for quantum correlations. In particular, depending on the characteristics of the environmental noise considered, both entanglement and discord display either a monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure of the environment, in addition to its noise spectrum, is relevant for the dynamics of quantum correlations and may be a valid starting point for the engineering of non-Gaussian colored environments.
We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], assuming that the qubit–bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.
In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is pseudo-Hermitian/PT symmetric, and as the strength of the coupling to the environment is increased, the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.