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arXiv:quant-ph/0605254

Quantum state stability against decoherence

A. Krügel, Luis Roa, C. Saavedra

Published May 31, 2006• 0 citations
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Abstract

We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson bath temperature, changes depending on the intensity of the classical field.

DOI
10.48550/arxiv.quant-ph/0605254

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We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson bath temperature, changes depending on the intensity of the classical field.
We have found, for a specific model of interaction, an expression which allows us to estimate the time scale order of magnitude for which the decoherence instability of a quantum state is onset. We study the stability of the coherence of a pure state for a three level quantum system under the effect of an interaction with a set of boson systems and driven by two Raman classical fields. Evaluating the order of magnitude of the decoherence time scale and assuming the boson systems to be in thermal states, we find for a symmetric V -system a set of three states stable against decoherence and, for a symmetric cascade-system we find a bidimensional subspace whose states are stable against the considered decoherence mechanism.
A short-time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator $\ensuremath{\Lambda}$ and its conjugate ${\ensuremath{\Lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}$ in order to evaluate the onset of decoherence at low temperatures in quantum systems interacting with the environment. The developed approach is complementary to Markovian approximations and appropriate for the evaluation of quantum computing schemes. An example of a spin system coupled to a bosonic heat bath via $\ensuremath{\Lambda}\ensuremath{\propto}{\ensuremath{\sigma}}_{\ensuremath{-}}$ is worked out in detail.
We analyze the onset of classical behaviour after a second-order phase transition in quantum field theory. We consider a scalar theory in which the system-field interacts with its environment, represented both by further scalar fields and by its own short-wavelength modes. We compute the decoherence time for the system-field modes and compare it with the other time scales of the model. Within our approximations we see that the long-wavelength modes have decohered by the time that the transition has been first implemented (the spinodal time)
We compare quantum decoherence in generic regular and chaotic systems that interact with a thermal reservoir via a dipole coupling. Using a time-dependent, self-consistent approximation in the spirit of Hartree, we derive in the high temperature limit an expression for the off-diagonal elements of the system density operator that initially corresponds to a coherent superposition of two adjacent wave packets. We relate the decoherence rate to the Lyapunov exponent in the Ehrenfest regime. In this regime, the greater the instability of the system the faster the loss of coherence occurs.