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Physical Review Letters

Decoherent Dynamics of a Two-Level System Coupled to a Sea of Spins

Jiushu Shao, Peter Hänggi A

Published Dec 28, 1998• 88 citations
Publisher

Abstract

The dynamics of a two-level system which is coupled to an environmental sea of infinitely many spin-1/2 particles is investigated by use of the resolvent operator approach. Only at zero temperature does this spin-spin-bath model exhibit identical behavior as the more familiar spin-boson model. It is found that increasing temperature favors coherent dynamics. At high temperatures, the spin-spin-bath model for an Ohmic spectral density sustains a coherent dynamics if the dissipation coefficient $\ensuremath{\alpha}$ is sufficiently small, i.e., $\ensuremath{\alpha}<1/2$; while the decoherence exhibits pure exponential decay if $\ensuremath{\alpha}>1/2$.

DOI
10.1103/physrevlett.81.5710

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The Journal of Chemical Physics•Jul 13, 2012•30 citations
The dynamics of a two-level system which is coupled to an environmental sea of infinitely many spin-1/2 particles is investigated by use of the resolvent operator approach. Only at zero temperature does this spin-spin-bath model exhibit identical behavior as the more familiar spin-boson model. It is found that increasing temperature favors coherent dynamics. At high temperatures, the spin-spin-bath model for an Ohmic spectral density sustains a coherent dynamics if the dissipation coefficient \ensuremathα\ensuremath{\alpha}\ensuremathα is sufficiently small, i.e., \ensuremathα<1/2\ensuremath{\alpha}<1/2\ensuremathα<1/2; while the decoherence exhibits pure exponential decay if \ensuremathα>1/2\ensuremath{\alpha}>1/2\ensuremathα>1/2.
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 dynamical behavior of a two-level system coupled linearly to a dissipative bath of two-level systems whose tunneling splittings and coupling parameters are distributed according to an Ohmic spectrum is studied using numerical path integral methods as well as the noninteracting blip approximation for an equivalent harmonic environment characterized by a scaled spectral density. Comparisons with the behaviors of the conventional spin-boson model of similar coupling strength reveal a weaker quenching of coherence in the present case. Finally, the boundary in parameter space between coherent and incoherent dynamics is mapped.
We consider the quantum dynamics of two spin-1/2 systems, each coupled to a bath of oscillators, so that a bath-mediated coupling is generated between the spins. We find that the interactions destroys any coherent motion of the 2 spins, even if the coupling of each spin to the bath is quite weak, unless the interaction is extremely small. This is because the dynamic mutual bias between the spins blocks any coherent transitions between nearly degenerate states. In many quantum measurement operations this means that decoherence effects will be much stonger during the actual measurement
Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.
We report an anomalous decoherence phenomenon of a quantum dissipative system in the framework of a stochastic decoupling scheme along with a hierarchical equations-of-motion formalism without the usual Born-Markov or weak-coupling approximations. It is found that the decoherence of a two-qubit spin-boson model can be reduced by increasing the bath temperature in strong-coupling regimes. For the weak-coupling situation, we find that the bath temperature may enhance the decoherence. This result is contrary to the common recognition that a higher bath temperature always induces a more severe decoherence and suggests that a decoherence dynamical transition occurs in this two-qubit spin-boson model. We also demonstrate that the critical transition point can be characterized by the behavior of the frequency spectrum of the quantum coherence indicator.
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.