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arXiv:1908.01494 · Physical Review A

Open Ising model perturbed by classical colored noise

Deshui Yu, Rainer Dumke

Published Aug 26, 2019• 9 citations
arXivHTMLPDF

Abstract

We investigate the non-Markovian dynamics of an open Ising model simulated by a superconducting circuit. The quantum many-body system is weakly coupled to a white, pink- or blue-colored environment. The relaxation of the system in the strong interqubit interaction regime shows a metastable behavior. In comparison with the dissipative system in the Markovian limit, the negative memory of the blue-colored noise weakens the system's relaxation. However, for the pink-colored noise the relaxation rate of the system is enhanced due to the positive memory effect. The understanding of quantum many-body systems responding to different colored noise fields is necessary for designing the environment of superconducting qubits in a large scale quantum processor.

DOI
10.1103/physreva.100.022124

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We investigate the non-Markovian dynamics of an open Ising model simulated by a superconducting circuit. The quantum many-body system is weakly coupled to a white, pink- or blue-colored environment. The relaxation of the system in the strong interqubit interaction regime shows a metastable behavior. In comparison with the dissipative system in the Markovian limit, the negative memory of the blue-colored noise weakens the system's relaxation. However, for the pink-colored noise the relaxation rate of the system is enhanced due to the positive memory effect. The understanding of quantum many-body systems responding to different colored noise fields is necessary for designing the environment of superconducting qubits in a large scale quantum processor.
We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by k-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N^{-2k} with the system size N. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.
We analyzed the effect of colored noise on the negativity dynamics of a hybrid system consisting of a qubit–qutrit and not interacting, prepared from the start in an entangled one-parameter state and acting with noise in local and non-local environments. In this pink and brown noise we investigated two different situations: in the first situation, the noise is produced by a bistable oscillator with an unknown exchange rate; however, in the second situation, the noise is generated by a set of bistable oscillators. We found that entanglement decreases with time to zero, and undergoes the phenomenon of sudden death and rebirth. The pink noise is more prone to entanglement than the brown noise and the non-local environment is more prone to entanglement than the local one. When the number of fluctuators is increased, entanglement decays faster and finally, for certain parameters of the initial state, the subsystems are not affected by the noise.
We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by kkk-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as N−2kN^{-2k}N−2k with the system size NNN. Our proposal can be readily implemented on a variety of quantum platforms including optical lattices, superconducting circuits and trapped ions.
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.
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.
Non-Markovian environments with finite memory pose significant challenges for simulating open quantum many-body dynamics. Here, we employ the Lindblad-pseudomode approach to investigate a transverse-field Ising chain collectively coupled to a structured bosonic environment with a Lorentzian noise spectrum. The pseudomode representation enables an efficient treatment of strong system-bath coupling and non-Markovian memory effects. We show that the common environment induces effective long-range spin interactions, leading to bath-induced localization and enhanced ferromagnetic ordering beyond the behavior of the isolated chain. Our findings elucidate how structured environments can fundamentally alter many-body dynamics and demonstrate the utility of pseudomode methods for exploring strongly coupled open quantum systems beyond the Markovian regime.