Open Ising model perturbed by classical colored noise

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 inter-qubit interaction regime shows a metastable behaviour. 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. PACS numbers: 85.25.-j, 42.50.-p, 06.20.-f t 0 dsK(t, s)ρ(s), where ρ(t) is the system's density matrix operator and the two-time operator K(t, s) acts on the system's Hilbert space [16][17][18]. Secondly, local-in-time master equations derived from the time-convolutionless projection operator method [19,20]. The dynamic term in master equations is written in the form iHere the time-dependent decay rates γ i (t) can have temporarily negative values, which actually encode the system-evolution history. The practical usefulness of the former approach is limited due to the difficulty in the evaluation of the memory integral, and also the memory kernel alone does not guarantee the non-Markovian character [21]. In contrast, the latter approach is mathematically simple and has been widely applied to various non-Markovian problems [22][23][24][25].

Proposal for an active whispering-gallery microclock

“…In contrast, the white frequency noise (∝ f 0 ) governs the high-frequency (high-f ) regime and leads to the τ −1/2 -dependence of the fractional frequency stability, Both σ BN C,y (τ ) and σ WT C,y (τ ) are far above the fundamental limit σ TR C,y (τ ) that is imposed by the thermorefractive noise. According to the frequency spectral density (11), one may numerically generate the time-dependent detuning noise ∆ (t) of clock WGMs [52] and investigate the influence of ∆ (t) on the clock laser stability (see figures 3(a) and (b)).…”

From the open Heisenberg model to the Landau-Lifshitz equation

“…A suitable choice of the magnetic field B, the exchange coupling constants V ij αβ , and the topology of the system allows to understand the origin of magnetic ordering [2], phase transition [3], spin-wave excitations [4], lattice effects [5], to name a few. Furthermore, the Heisenberg dynamic is currently reproduced in different physical systems such as circuit quantum electrodynamics [6], cavity QED [7], superconducting devices [8], one-dimensional interacting spins [9], Rydberg atoms [10][11][12][13], and trapped ions [14,15]. Many of the previous setups deal with unavoidable relaxation processes induced by system-bath interactions, which is well understood in terms of the Lindblad master equation [16,17].…”

“…We use the term open Heisenberg model (OHM) to describe any system of N interacting spins with a Hamiltonian structure similar to Eq. ( 1) and subject to an interaction with an external bath [8,9,18].…”

“…Nevertheless, our approach is a new perspective that is useful for connecting the LL dynamics with the evolution of open quantum systems in the meanfield regime. The latter is particularly advantageous to future simulations of magnetic-like phenomena using quantum systems like trapped ions [14,15], superconducting devices [8] and cavity QED [7]. Moreover, it allows the study of more general environments exhibiting memory effects usually described as non-Markovian master equations [50].…”

Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time

“…Due to increased experimental and computational capabilities, non-Markovian systems are of great interest today. Among them there are such well-known systems as quantum dots [12][13][14][15], micromechanical resonators [16,17], superconducting qubits [18][19][20], and many others. Non-Markovian effects are ubiquitous in physics, chemistry, and biology and for systems interacting with either bosonic or fermionic reservoirs, like photosynthetic systems [21][22][23][24][25], molecular aggregates [26], molecular magnets [27], and solar cells [28].…”