The Journal of Chemical Physics

Low temperature tunneling dynamics in condensed media

P. E. Parris, R. Silbey

Published Dec 1, 1985• 82 citations

Abstract

There has been considerable interest recently in the low temperature dynamics of condensed phase tunneling phenomena. In this paper we consider the interplay between quasiparticle transport and vibrational relaxation; the former taking place via tunneling in a double well potential, and the latter occurring due to interactions of the tunneling system with a harmonic bath. Taking the system–bath interactions to be linear in the bath coordinates, and explicitly allowing for a vibrationally excited well, we present a unified treatment of the weak and strong coupling regimes and obtain reduced equations of motion for the tunneling particle position operator. Solutions are obtained for several important limiting cases. In particular, we find that at sufficiently low temperatures, the dynamical behavior strongly resembles that of multisite spin jump model.

DOI: 10.1063/1.449686

Related papers

Multilevel tunneling and coherence: Dissipative spin-hopping dynamics at finite temperatures

H. Dekker

The real-time dynamics of a quantum-mechanical particle in a dissipative double-well potential at finite temperatures is solved ab initio by means of a multisite spin-hopping analysis. Both the macroscopic-quantum-coherence and macroscopic-quantum-tunneling regimes are covered. The theory gives a unified picture of tunneling transport and vibrational relaxation. The analysis is based on the Ohmic-model Hamiltonian [A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983); R. Zwanzig, J. Stat. Phys. 9, 215 (1973)] or the equivalent ``particle-on-a-string'' model [H. Dekker, Phys. Rev. A 31, 1067 (1985)]. The reduced quantum Liouville equation for the particle is derived and written in the energy representation. The usual truncation to the ground-state doublet of the vibrational ladder is not made. The interdoublet vibrational dynamics considerably simplifies upon coarse-graining and in the harmonic-well approximation. The intradoublet pseudospin dynamics is treated in the ``noninteracting-blip approximation'' [A. J. Leggett et al., Rev. Mod. Phys. 59, 1 (1987)]. The coarse-grained vibrational processes give rise to a Markovian one-step spin hopping between adjacent doublets (or sites). Inter alia ``inhomogeneous broadening'' and ``motional narrowing'' [P. E. Parris and R. Silbey, J. Chem. Phys. 83, 5619 (1985)] are discussed as special cases.

Physical Review AAug 1, 199119 citations

Strong Coupling Theory for Driven Tunneling and Vibrational Relaxation

Michael Thorwart, Milena Grifoni, Peter Hänggi A

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled non-Markovian master equations. We present analytical treatments that describe the dynamics in the regime of strong system-bath coupling. Our findings are corroborated by "ab initio" real-time path integral calculations.

arXiv:quant-ph/9912024Physical Review LettersJul 24, 200054 citations

Tunneling of heavy particles in condensed media. Fluctuation effects in barrier preparation, and the role of excited vibrational states of the tunneling species

Alexey Kuznetsov

The nonadiabatic-tunneling probability of heavy particles is calculated while allowing for a dependence of the resonance integral on the vibrational coordinates. It is shown that quantum fluctuations of the tunneling species in a transverse direction can be of distinct importance in preparing the barrier for tunneling. In the model of harmonic vibrations, expressions are obtained for the transition probability which include the contribution from excited vibrational states of the tunneling particle as well as the changes in their vibrational frequency and equilibrium coordinates which occur as the system moves toward the transition configuration.

Aug 1, 19860 citations

Forward–backward semiclassical dynamics in the interaction representation

Jiushu Shao, Nancy Makri

The forward–backward semiclassical dynamics methodology [J. Phys. Chem. 103, 7753, 9479 (1999)] is reformulated in the interaction representation. The new version of the method allows for a fully quantum mechanical description of a low-dimensional subsystem of interest, along with a semiclassical forward–backward treatment of the solvent coordinates and their coupling to the reference subsystem. Application to the long-time tunneling dynamics in a symmetric double-well system coupled to a harmonic bath shows that the interaction FBSD is capable of capturing quantitatively the tunneling and decoherence effects induced by weakly dissipative environments.

The Journal of Chemical PhysicsSep 1, 200036 citations

Controlling low-temperature tunneling dynamics with external fields

Manuel Morillo, Robert I. Cukier

The tunneling of a particle between two states, as influenced by coupling the particle to an external field, is investigated. A spin-boson Hamiltonian is used to describe the tunnel system and its interaction with a medium and is augmented by a term coupling the dipole moment of the particle to the external field. A projection operator method is introduced that provides equations of motion for the particle's density matrix and permits discussion of external field effects on tunneling even at very low temperatures. These equations of motion can exhibit solutions characterized by population relaxation with a rate constant that is an average over the period of the external field. As an application of this theory, the modification by an external field of the tunneling rate of a defect in a metal, where the system-medium interaction is characterized by an Ohmic spectrum, is evaluated. At sufficiently low temperatures, for experimentally relevant parameter values, suitably chosen (constant and/or sinusoidal), external fields can greatly suppress or enhance the tunneling rate relative to the field-independent value. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterNov 15, 199634 citations

Interaction-modulated tunneling dynamics of a mixture of Bose-Fermi superfluid

Hong-Ping Xu, Zhen-Zhen He, Zi-Fa Yu +1 more

In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a Bose-Einstein condensate (BEC) with weak repulsive interaction is confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically is positioned in the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theory to describe the evolution of the BEC in the double-well potential through the time-dependent Gross-Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, and hence can be simulated as well by a Gross-Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which results in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction among fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be expressed in three forms: the phase tends to be negative and monotonically decreases with time, the phase evolves with time, and the phase tends to be positive and increases monotonically with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in a Bose-Fermi superfluid mixture by varying different interaction parameters via Feshbach resonance and confinement-induced resonance.

Acta Physica SinicaJan 1, 20221 citation