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arXiv:1204.4029 · Physical Review Letters

Persistence of Coherent Quantum Dynamics at Strong Dissipation

Denis Kast, Joachim Ankerhold

Published Jan 2, 2013• 92 citations
arXivHTMLPDF

Abstract

The quantum dynamics of a two-state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that a changeover from coherent to incoherent relaxation does not occur for a broad class of spectral distributions. In nonequilibrium coherences associated with substantial system-reservoir entanglement exist even when strong dissipation forces the thermodynamic state of the system to behave almost classically. This may be of relevance for current experiments with nanoscale devices.

DOI
10.1103/physrevlett.110.010402

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The quantum dynamics of a two-state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that a changeover from coherent to incoherent relaxation does not occur for a broad class of spectral distributions. In nonequilibrium coherences associated with substantial system-reservoir entanglement exist even when strong dissipation forces the thermodynamic state of the system to behave almost classically. This may be of relevance for current experiments with nanoscale devices.
The quantum dynamics of pairs of two-level systems immersed in dissipative reservoirs with sub-Ohmic spectral distributions is studied by means of numerically exact path integral Monte Carlo methods. It is shown that this class of reservoirs, relevant for generic properties of strongly non-Markovian environments with possible realizations in solid state structures at cryogenic temperatures, supports bipartite entanglement in broad ranges of parameter space and even for broken symmetries and in the presence of thermal noise. The sensitivity of the creation of entanglement in nonequilibrium on the initial preparations of the reservoir is investigated in detail.
The dissipative quantum dynamics of a two-level system interacting with a structured reservoir consisting of a damped harmonic mode is investigated by means of the numerically exact path integral Monte Carlo method. This approach provides benchmark results in a broad range of parameter space, in particular, in those domains which are not accessible by approximate methods and alternative numerical schemes, that is, strong coupling between system and harmonic mode and from low to high temperatures. For low temperatures the numerical data are quantitatively in agreement with the noninteracting blip approximation only in the regimes of very weak and very strong coupling. It turns out that the entangled dynamics of the two-level system and the harmonic mode is relatively robust so that its signatures are observable up to relatively strong friction and high temperatures. Nonequilibrium initial preparations of the reservoir with respect to the initial state of the system give rise, for strong interactions, to a stepwise decay of the population, thus displaying coherent dynamics of the bath. The impact of an additional Ohmic bath coupled directly to the two-level system is studied as well, including the case where both reservoirs carry different temperatures.
The standard approach for path-integral Monte Carlo simulations of open quantum systems is extended as an efficient tool to monitor the time evolution of coherences (off-diagonal elements of the reduced density matrix) also for strong coupling to environments. Specific simulations are performed for two-level systems embedded in Ohmic and sub-Ohmic reservoirs in the domains of coherent and incoherent dynamics of the polarization. In the latter regime, the notorious difficulty to access the long-time regime is overcome by combining simulations on moderate time scales with iteratively calculated initial densities. This allows us to extract relaxation rates for sub-Ohmic environments at finite temperatures and over a broad range of couplings and to compare them to analytical predictions. The time evolution of the von Neumann entropy provides insight into the quantum phase transition at thermal equilibrium from a delocalized to a localized state at zero temperature.
The decoherence of a two-state system coupled with a sub-Ohmic bath is investigated theoretically by means of the perturbation approach based on a unitary transformation. It is shown that the decoherence depends strongly and sensitively on the structure of environment. Nonadiabatic effect is treated through the introduction of a function ${\ensuremath{\xi}}_{k}$ which depends on the boson frequency and renormalized tunneling. The results are as follows: (i) the nonequilibrium correlation function P(t)P(t)P(t), the dynamical susceptibility ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$, and the equilibrium correlation function C(t)C(t)C(t) are analytically obtained for $s\ensuremath{\leqslant}1$; (ii) the phase diagram of thermodynamic transition shows the delocalized-localized transition point ${\ensuremath{\alpha}}_{l}$ which agrees with exact results and numerical data from the numerical renormalization group; (iii) the dynamical transition point ${\ensuremath{\alpha}}_{c}$ between coherent and incoherent phase is explicitly given. A crossover from the coherent oscillation to incoherent relaxation appears with increasing coupling (for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, the coherent dynamics disappear); (iv) the Shiba's relation and sum rule are exactly satisfied when $\ensuremath{\alpha}\ensuremath{\leqslant}{\ensuremath{\alpha}}_{c}$; (v) an underdamping-overdamping transition point ${\ensuremath{\alpha}}_{c}^{*}$ exists in the function $S(\ensuremath{\omega})$. Consequently, the dynamical phase diagrams in both ohmic and sub-Ohmic case are mapped out. For $\ensuremath{\Delta}⪡{\ensuremath{\omega}}_{c}$, the critical couplings (${\ensuremath{\alpha}}_{l},{\ensuremath{\alpha}}_{c}$, and ${\ensuremath{\alpha}}_{c}^{*}$) are proportional to ${\ensuremath{\Delta}}^{1\ensuremath{-}s}$.
We study the dissipative quantum dynamics and the asymptotic behavior of a particle in a bistable potential interacting with a sub-Ohmic broadband environment. The reduced dynamics, in the intermediate to strong dissipation regime, is obtained beyond the two-level system approximation by using a real-time path integral approach. We find a crossover dynamic regime with damped intra-well oscillations and incoherent tunneling and a completely incoherent regime at strong damping. Moreover, a nonmonotonic behavior of the left/right well population difference is found as a function of the damping strength.
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.