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arXiv:2602.07438

Non-Markovianity in a dressed qubit with local dephasing

Saima Bashir, Muzaffar Qadir Lone, Prince A Ganai

quant-phcond-mat.quant-gasSubmitted Feb 7, 2026• Announced Feb 10, 2026• 0 citations
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Abstract

We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable perturbatively. Applying time-convolutionless master equation within the polaron frame, we investigate decoherence dynamics of the dressed qubit within the singlet-triplet basis of the system for a wide range of bath spectral densities. It is shown that the coherence persists for longer time scales for large coupling values and shows non-monotonic behaviour reflecting the presence of non-Markovianity in the dynamics. Non-Markovianity, characterized by coherence revivals and non-monotonic decay patterns, emerges distinctly depending on the bath spectrum and coupling strengths. Systems coupled to sub-Ohmic baths, whether both or in combination with another type, display pronounced memory effects at relatively small values of couplings. In contrast, combinations involving Ohmic and super-Ohmic baths exhibit noticeable non-Markovianity only at higher couplings.

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Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.
We investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.
We study decoherence in an interacting qubit system described by infinite range Heisenberg model (IRHM) in a situation where the system is coupled to a bath of local optical phonons. Using perturbation theory in polaron frame of reference, we derive an effective Hamiltonian that is valid in the regime of strong spin-phonon coupling under nonadiabatic conditions. It is shown that the effective Hamiltonian commutes with the IRHM upto leading orders of perturbation and thus has the same eigenstates as the IRHM. Using a quantum master equation with Markovian approximation of dynamical evolution, we show that the off-diagonal elements of the density matrix do not decay in the energy eigen basis of IRHM.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
We study the entanglement (measured by negativity) evolution and the non-Markovianity for the dynamical process of a spin-S system embedded in dephasing environments. The exact analytical solution is presented, which shows that the decoherence function governs the evolutions of coherence, entanglement, and the non-Markovianity of the corresponding dynamical processes. For Ohmic and sub-Ohmic reservoirs, the negativity decreases monotonically in time and the corresponding dynamics is Markovian. While for super-Ohmic reservoirs with non-monotonic decoherence function, the negativity appears as the phenomenon of revival and the corresponding dynamics is non-Markovian. The relation between non-Markovianity and the system dimension is studied.
We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for STz{S}_{T}^{z}STz​ (the zzz component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the polaron dynamics through a non-Markovian quantum master equation, we find that the system manifests a small amount of decoherence that decreases both with increasing nonadiabaticity and with enhancing strength of coupling; whereas, under the Markovian approximation, the polaronic system exhibits a decoherence-free behavior. For the situation where both spins are coupled to the same phonon bath, we also show that the system is decoherence-free in the subspace where STz{S}_{T}^{z}STz​ is fixed. To suppress decoherence through quantum control, we employ a train of $\ensuremath{\pi}$ pulses and demonstrate that unitary evolution of the system can be retained. We propose realization of a weakly decohering charge qubit from an electron in an oxide-based (tunnel-coupled) double-quantum-dot system.