We investigate the manner in which quantum interference is suppressed when a particle interacts with a spatially localized, dynamical environment. To do so we examine a model with two classical paths along which an electron can travel and allow it to interact with a bath of harmonic oscillators on one path and travel freely on the other. In particular, we show that the quantum fluctuations of the path of the particle can couple to the environment and thus lead to dephasing and calculate the dephasing time in the high-temperature limit. We compare this result to other views of how propagating electrons lose phase coherence.
We investigate the manner in which quantum interference is suppressed when a particle interacts with a spatially localized, dynamical environment. To do so we examine a model with two classical paths along which an electron can travel and allow it to interact with a bath of harmonic oscillators on one path and travel freely on the other. In particular, we show that the quantum fluctuations of the path of the particle can couple to the environment and thus lead to dephasing and calculate the dephasing time in the high-temperature limit. We compare this result to other views of how propagating electrons lose phase coherence.
I compare the quantum and classical dynamics of a particle moving in a cosine potential while subject to a time-dependent force. I concentrate here on the behavior of an initially well-localized wave packet at times before the classically chaotic motion is fully developed. I find that the quantum and classical dynamics are indistinguishable well beyond the Ehrenfest time where the wave packet delocalizes. The quantum and classical descriptions first differ precisely when the classical probability density is folded in the vicinity of a hyperbolic fixed point. At this point, the wave function acquires a nodal structure which I show to be the result of a simple beating phenomenon between paths in the semiclassical propagator. When the interaction of the classical manifold with the hyperbolic fixed point leads to escape from the remnant separatrix, representing the onset of classical chaos, the interference associated with the tendril leads to a long-lived accumulation of quantum amplitude on top of the cosine barrier. This effect also has a semiclassical interpretation, meaning that it arises from the interference between classical paths, but one must expand to second order in Planck's constant to describe the behavior correctly. Both the nodal structure and this pinning of amplitude on the barrier are dynamic mechanisms for the quantum inhibition of mixing. I then couple the system to a bath of harmonic oscillators in order to study the effect of the environment on these mechanisms. Although an oscillator bath environment brings dissipation as well as noise to the problem, the noise effect dominates for the high temperature, weak coupling regime I study. When there is sufficient noise to render the interfering classical paths indistinguishable, I find that the quantum interference gets erased. This dephasing occurs at very early times, long before there is appreciable dissipation of energy to the environment. Consequently, one can argue that the presence of an environment, even if its effect would be negligible in a nonchaotic setting, allows for the possibility of quantum mixing.
We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath.Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects.In particular in the latter case dephasing should be distinguished from renormalization effects.For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spinboson models.Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings.Then, we analyze the more general problem of a particle which interacts with a quantum field V (t, r(t)), the fluctuations of which are characterized by a dielectric function (ω, k).Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.
Dephasing in quantum systems is typically the result of their interaction with environmental degrees of freedom. We investigate within a spin-boson model the influence of a super-Ohmic environment on the dynamics of a quantum two-state system. A super-Ohmic environment thereby models typical bulk phonons which are a common disturbance for solid state quantum systems as, for example, nitrogen-vacancy centers. By applying the numerically exact quasiadiabatic path-integral approach we show that for strong system-bath coupling, pseudocoherent dynamics emerges, i.e., oscillatory dynamics at short times due to slaving of the quantum system to the bath dynamics. We extend the phase diagram known for sub-Ohmic and Ohmic environments into the super-Ohmic regime and observe a pronounced nonmonotonous behavior. Super-Ohmic purely dephasing fluctuations strongly suppress the amplitude of coherent dynamics at very short times with no subsequent further decay at later times. Nevertheless, they render the dynamics overdamped. The corresponding phase separation line shows also a nonmonotonous behavior, very similar to the pseudocoherent dynamics.
We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath. Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects. In particular in the latter case dephasing should be distinguished from renormalization effects. For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spin-boson models. Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings. Then, we analyze the more general problem of a particle which interacts with a quantum field V(t,r(t)), the fluctuations of which are characterized by a dielectric function epsilon(omega,k). Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.
We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization') quantum correction to the conductivity to saturate at T=0. Our calculation, which is intended to be illustrative rather than complete, uses a model in which an electron interacts with the fluctuations of the mean voltage in the sample. The average of the fluctuations produces the steady damping well known in Brownian motion, introduces a direction of time, ensures that arbitrarily long time-reversed electron paths lose phase coherence, and is consistent with the experimental observation of a finite low temperature phase-breaking lifetime.