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arXiv:1308.1764 · The Journal of Chemical Physics

Dynamics of a two-level system under the simultaneous influence of a spin bath and a boson bath

Ning Wu, Yang Zhao

Published Aug 7, 2013• 15 citations
arXivHTMLPDF

Abstract

We study dynamics of a two-level system coupled simultaneously to a pair of dissimilar reservoirs, namely, a spin bath and a boson bath, which are connected via finite interbath coupling. It is found that the steady-state population transfer in the two-level system increases with its coupling to the spin bath, while optimal transfer occurs at intermediate coupling in the transient process. If the two-level system is strongly coupled to the spin bath, the population transfer is unidirectional barring minor population oscillations of minute amplitudes. If the spin bath is viewed as an atomic ensemble, robust generation of macroscopic superposition states exists against parameter variations of the two-level system and the boson bath.

DOI
10.1063/1.4817336

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We study dynamics of a two-level system coupled simultaneously to a pair of dissimilar reservoirs, namely, a spin bath and a boson bath, which are connected via finite interbath coupling. It is found that the steady-state population transfer in the two-level system increases with its coupling to the spin bath, while optimal transfer occurs at intermediate coupling in the transient process. If the two-level system is strongly coupled to the spin bath, the population transfer is unidirectional barring minor population oscillations of minute amplitudes. If the spin bath is viewed as an atomic ensemble, robust generation of macroscopic superposition states exists against parameter variations of the two-level system and the boson bath.
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment, leading to an irreversible loss of coherence. The spin-boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath, but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains much less explored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteracting effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and transient quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel insight into the equilibration behavior of quantum devices operating in the ultra-strong coupling regime.
We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr\"odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment leading to an irreversible loss of coherence. The Spin-Boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains largely unexplored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteractive effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and non-equilibrium quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel opportunities to exploit coherence as a resource in quantum devices operating in the ultra-strong coupling regime.
The quantum dynamics of a two-level system coupled to an Ohmic spin bath is studied by means of the perturbation approach based on a unitary transformation. A scattering function xi(k) is introduced in the transformation to take into account quantum fluctuations. By the master equation within the Born approximation, nonequilibrium dynamics quantities are calculated. The method works well for the coupling constant 0<alpha<alpha(c) and a finite bare tunneling Delta. It is found that (i) only at zero temperature with small coupling or moderate one does the spin-spin-bath model display identical behavior as the well-known spin-boson-bath model; (ii) in comparison with the known results of spin-boson-bath model, the coherence-incoherence transition point, which occurs at alpha(c)=12[1+etaDelta/omega(c)], is temperature independent; and (iii) the nonequilibrium correlation function P(t)=tau(z)(t), evolves without temperature dependence, while tau(x)(t) depends on temperature. Both P(t) and tau(x)(t) not only satisfy their initial conditions, respectively, and also have correct long time limits. Besides, the Shiba relation and sum rule are exactly satisfied in the coherent regime for this method. Our results show that increasing temperature does not help the system suppress decoherence in the coherent regime, i.e., finite temperature does not favor the coherent dynamics in this regime. Thus, the finite-temperature dynamics induced by two kinds of baths (spin-bath and boson-bath) exhibit distinctly different physics.
The dynamics of a two-level system coupled to a spin bath is investigated via the numerically exact multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory. Consistent with the previous work on linear response approximation [N. Makri, J. Phys. Chem. B 103, 2823 (1999)], it is demonstrated numerically that this spin-spin-bath model can be mapped onto the well-known spin-boson model if the system-bath coupling strength obeys an appropriate scaling behavior. This linear response mapping, however, may require many bath spin degrees of freedom to represent the practical continuum limit. To clarify the discrepancies resulted from different approximate treatments of this model, the population dynamics of the central two-level system has been investigated near the transition boundary between the coherent and incoherent motions via the ML-MCTDH method. It is found that increasing temperature favors quantum coherence in the nonadiabatic limit of this model, which corroborates the prediction in the previous work [J. Shao and P. Hanggi, Phys. Rev. Lett. 81, 5710 (1998)] based on the non-interacting blip approximation (NIBA). However, the coherent-incoherent boundary obtained by the exact ML-MCTDH simulation is slightly different from the approximate NIBA results. Quantum dynamics in other physical regimes are also discussed.
We demonstrate an exact mapping of a class of models of two interacting qubits in thermal reservoirs to two separate problems of spin–boson-type systems. Based on this mapping, exact numerical simulations of the qubits dynamics can be performed, beyond the weak system–bath coupling limit and the Markovian approximation. Given the time evolution of the system population and coherences, we study as an application the dynamics of entanglement between the pair of qubits immersed in boson thermal baths, showing a rich phenomenology, including an intermediate oscillatory behavior, the entanglement sudden birth, sudden death and revival. We find that the occurrence of entanglement sudden death in this model depends on the portion of the zero and double excitation states in the subsystem initial state. In the long-time limit, analytic expressions are presented at weak system–bath coupling, for a range of relevant qubit parameters.