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Lecture notes in physics. M, Monographs

Crossover-Time in Quantum Boson and Spin Systems

G. P. Berman, Evgeny N. Bulgakov, Darryl D. Holm

Published Jan 1, 1994• 29 citations
Publisher
DOI
10.1007/978-3-540-48415-8

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Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise noninteracting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, ${\ensuremath{\alpha}}_{c}$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between ${\ensuremath{\alpha}}_{c}=0.5$ and ${\ensuremath{\alpha}}_{c}=1$ depending upon the spin separation and the strength of the transverse tunneling field. This is in contrast to the analogous single-spin case, for which the crossover occurs (in the scaling limit) at fixed ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}1$. We also discuss links between the two-impurity spin-boson model and a dissipative two-spin transverse Ising model, showing that the latter possesses the same qualitative features as the Ising strength is varied. Finally, we show that signatures of the crossover may be observed in single impurity observables, as well as in the behavior of the system-environment entanglement.
We investigate the dynamical quantum Fisher information of a two-level system coupled to a bosonic environment, focusing on the estimation of the qubit gap. We combine analytical calculations with numerically controlled matrix-product-state simulations. In the exactly solvable pure-dephasing Ohmic regime at zero temperature, the long-time quantum Fisher information displays a coupling-dependent algebraic behavior, leading to a dynamical crossover: it grows without bound at weak coupling, approaches a finite asymptotic value at the crossover coupling, and vanishes at strong coupling. At finite temperature, thermal fluctuations suppress the long-time growth and generate a finite-time maximum, whose dependence on the dephasing coupling retains a clear signa- ture of the zero-temperature crossover. We show that this crossover is absent at zero temperature in non-Ohmic baths: the long-time quantum Fisher information vanishes in the sub-Ohmic and diverges in the super-Ohmic regimes. At non-zero temperature instead, the crossover appears for a super-Ohmic quadratic bath and the crossover coupling becomes temperature-dependent. Moreover, in the zero-temperature Ohmic regime, we introduce an additional amplitude-damping system-bath coupling that induces energy relaxation. This relaxation channel replaces the unbounded long-time growth with a finite asymptotic quantum Fisher information associated with the reduced interacting ground state, while a signature of the pure-dephasing crossover persists in the early-time dynamics. These results establish a direct connection between the low-frequency structure of the bath and the asymptotic metrological behavior of dynamical gap sensing, and show how thermal fluctuations and energy relaxation regularize the ideal pure-dephasing dynamical crossover of the quantum Fisher information.