The interaction with an environment provokes decoherence in quantum systems, which gradually suppresses their capability to display interference traits. Hence carpet-type structures, which arise after the release of a localized state inside a quantum cavity, constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Such a released localized state may represent a radiation mode inserted into a multimode interference device or a cold-atom system released in an optical trap, for instance. Here, without losing any generality, for simplicity, the case of a particle with a mass
m is considered and described by a localized state corresponding to the ground state of a square box of width
w, which is released inside a wider cavity (with a width
L>w). The effects of decoherence are then numerically investigated by means of a simple dynamical model that captures the essential features of the phenomenon under Markovian conditions, leaving aside extra complications associated with a more detailed dynamical description of the system-environment interaction. As it is shown, this model takes into account and reproduces the fact that decoherence effects are stronger as energy levels become more separated (in energy), which translates into a progressive collapse of the energy density matrix to its main diagonal. However, because energy dissipation is not considered, an analogous behavior is not observed in the position representation, where a proper spatial localization of the probability density does not take place, but rather a delocalized distribution. This result emphasizes the fact that classicality is reached only if both decoherence and dissipation coexist; otherwise, nonclassical traits might still persist. Actually, as it is also shown, in the position representation some off-diagonal correlations indeed survive unless an additional spatial-type factor is included in the model. This makes evident the rather complex nature of the decoherence phenomenon and hence the importance to have a familiarity with how it manifests in different representations, particularly with the purpose to determine and design reliable control mechanisms.
We discuss how a background bath of gravitons can induce decoherence of quantum systems. The mechanism is dephasing, the loss of phase coherence due to quantum geometry fluctuations caused by the gravitons. This effect is illustrated in a simple analog model of quantum particles in a cavity whose walls undergo position fluctuations, and create the same effect expected from spacetime geometry fluctuations. We obtain an explicit result for the decoherence rate in the limit where the graviton wavelength is large compared to the size of the quantum system, and make some estimates for this rate.
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.
The properties of quantum vacuum are highly sensitive to the underlying spacetime geometry and boundary conditions. We investigate in this paper the decoherence dynamics of a two-level system (detector) coupled to a vacuum scalar field through the
σ^z-coupling scheme under various boundary environments. By rigorously evaluating the reduced density matrix of the detector, we derive an exact general expression for the detector's decoherence function,
γ(Δt), and use it to characterize the dynamical decoherence of a detector in three scenarios: free space, a perfectly reflecting boundary, and a cavity formed by two parallel reflecting boundaries. We find that in free space the detector's coherence decays monotonically with time, indicating that vacuum fluctuations alone inevitably lead to a complete loss of coherence. In the single-boundary case, by contrast, the detector's coherence displays non-monotonic time evolution:
γ(Δt) increases with time up to a maximum and then settles to a steady value, indicating that the initial coherence can be partially preserved due to the presence of the boundary. When the detector is placed inside a cavity, its coherence evolution exhibits oscillatory behavior, and a significant fraction of the initial coherence survives. Moreover, for the same detector-boundary distance, more coherence is preserved in the cavity case than in the single-boundary case. These results provide a viable route for engineering quantum coherence via boundary conditions.
We consider a simple one-dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent superposition of two spatially separated wave packets with opposite momentum and the light particle localized in the region between the two wave packets. We characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. We derive the corresponding reduced density matrix for the heavy particle and explicitly compute the (partial) decoherence effect for the heavy particle induced by the presence of the light one for a particular set up of the parameters.
Environment induced decoherence entails the absence of quantum interference phenomena from the macroscopic world. The loss of coherence between superposed wave packets is a dynamical process the speed of which depends on the packet separation: The farther the packets are apart, the faster they decohere. The precise temporal course depends on the relative size of the time scales of decoherence and other processes taking place in the open system and its environment. We use the exactly solvable model of a harmonic oscillator coupled to a bath of harmonic oscillators to illustrate various decoherence scenarios: These range from exponential golden-rule decay for microscopic superpositions, system-specific decay for larger separations in a crossover regime, and finally the universal interaction-dominated decoherence for ever more macroscopic superpositions investigated in great generality in the accompanying Paper I [W. T. Strunz, F. Haake, and D. Braun, Phys. Rev. A
67, 022101 (2003)].