We study the role of zero point fluctuations (ZPF) in dephasing at low temperatures. Unlike the Caldeira--Leggett model, wherein the interaction is with a homogeneous fluctuating field of force, here we consider the effect of short range scattering by localized bath modes. We find that in the presence of ZPF, the inelastic cross section gets renormalized. Thus, ZPF might indirectly contribute to the dephasing at low temperatures.
We study the role of zero point fluctuations (ZPF) in dephasing at low temperatures. Unlike the Caldeira--Leggett model, wherein the interaction is with a homogeneous fluctuating field of force, here we consider the effect of short range scattering by localized bath modes. We find that in the presence of ZPF, the inelastic cross section gets renormalized. Thus, ZPF might indirectly contribute to the dephasing at low temperatures.
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 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.
We discuss the detection of quantum fluctuations in the light of the relationship between time-dependent correlators and measurable properties [L. Van Hove, Phys. Rev 95, 249 (1954)]. Considering the interaction between the fluctuating electron system and a resonant circuit or a photon mode, we prove that zero-point fluctuations (ZPF) are not observable by a passive detector, corroborating the results of Lesovik and Loosen (Pis'ma Zh. \'Eksp. Teor. Fiz. [JETP Lett. 65, 269 (1997)]). By a passive detector we mean one which is itself effectively in the ground state, and cannot transfer energy to the ZPF whose detection is attempted. We find that the ZPF can, on the other hand, be observed from deexcitation of an active detector. We also make the connection between these statements and the recent discussion of whether decoherence can be caused by the ZPF. The distinction is made between decoherence via making a real excitation in the environment and effects due to its polarization by virtual excitations.
The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance ℓ<<L. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit (ℓ>>L). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.
We discuss some recent work on the dephasing of Bose-Einstein condensates of interacting atoms due to fluctuations in the chemical potential μ. At vanishing temperature such fluctuations are due to the uncertainty of the number of particles in the condensate caused by the depletion effect. The dephasing is in this case a non-diffusive (and in principle reversible) effect called ‘collapse’ (and ‘revival’). Above a certain cross-over temperature the dephasing proceeds mainly via a diffusive process which follows in time a short and ineffective phase collapse. The phase-diffusion constant is dominated by the temperature dependent condensate-number fluctuations caused by the scattering of low-energy excitations off the condensate. We also discuss the (in general subdominant) contribution of the occupation-number fluctuations in quasi-particle states in the thermal cloud. For simplicity we discuss here results for a box-like trapping potential.
As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. The ergodic phase can be defined by the nonzero dephasing rate, which makes transport incoherent and classical on long length scales. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling, obtaining a short-time expansion. However, no well-defined dephasing rate can be identified, and the expansion breaks down at long times. This perturbative expansion is not stabilized by including a mean-field cooperon ``mass'' (decay rate), signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order, we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations commonly employed in higher dimensions. Our results are relevant in two different contexts: first, in the search for precursors to many-body localization in the ergodic phase of an isolated many-fermion system. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength and provides an additional physical mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.