Persistence of Coherent Quantum Dynamics at Strong Dissipation

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.

Figure 1

Domains of coherent (white) and incoherent (shaded) dynamics of the SB model for a sub-Ohmic environment (4) at zero temperature. Above (below) the solid line ${\alpha }_c(s)$ the system asymptotically reaches a thermal equilibrium that is localized (delocalized) [27]. A coherent-incoherent changeover only occurs along the dashed line ${\alpha }_{\mathrm{CI}}(s)$ (2). Dotted lines refer to results in Fig. 2 (left) and Fig. 3 (right), respectively.

Figure 2

Dynamics of $P_z(t)$ at $T=0$ and $\Delta /{\omega }_c=0.1$ according to PIMC calculations for $s=0.75$ and couplings $\alpha$ with ${\alpha }_c\approx 0.3>{\alpha }_{\mathrm{CI}}\approx 0.22$ (purple line). Blue (red) lines refer to coherent $\alpha <{\alpha }_{\mathrm{CI}}$ (incoherent $\alpha >{\alpha }_{\mathrm{CI}}$) dynamics (cf. Fig. 1). Statistical errors are of the size of the symbols.

Figure 3

Same as in Fig. 2 but for $s=0.25$ and values $\alpha >{\alpha }_c\approx 0.022$. The inset shows a blowup for very large couplings.

Figure 4

Coherences $P_x(t)$ (left axis) and entropy $S(t)$ (right axis) for $s=0.25$ (${\alpha }_c\approx 0.022$) at $T=0$ according to PIMC calculations.

Figure 5

$P_z(t)$ at $s=0.25$, $\alpha =0.1$ for various initial preparations of the reservoir with ${\omega }_c/\Delta =10$. See text for details.