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Communications in Theoretical Physics

Dissipative Effects on Resonant Tunneling

Mingli Zhou, Yumei Zhang, Xiang Xia Wu

Published Sep 1, 1993• 0 citations
Publisher

Abstract

The resonant tunneling of a particle coupled with a set of local bosons can be mapped onto the single-site model in an appropriate time scale. In this paper we investigate the process of the particle through a barrier associated with the dissipative source. The frequency and temperature-dependent tunneling probability has been evaluated explicitly in the spirit of independent boson assumption by using golden rule for transition rate. The character of sideband structure is revealed and the tunneling current with dissipation is also given.

DOI
10.1088/0253-6102/20/2/135

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The resonant tunneling of a particle coupled with a set of local bosons can be mapped onto the single-site model in an appropriate time scale. In this paper we investigate the process of the particle through a barrier associated with the dissipative source. The frequency and temperature-dependent tunneling probability has been evaluated explicitly in the spirit of independent boson assumption by using golden rule for transition rate. The character of sideband structure is revealed and the tunneling current with dissipation is also given.
Resonant tunneling of electrons through a dissipative barrier is studied within a generalized spin–boson model. The model accounts for a nonlinear inelastic coupling between the electron and harmonic (bath) nuclear modes inside the barrier. In particular, we study the case in which the nuclear frequencies are similar to the decay rate of the electronic resonance states, as may appear in electron transport through narrow molecular barriers. Two cases are considered. In the case of a single responsive mode numerically exact wave-packet dynamics shows that the inelastic coupling increases the time delay of the tunneling electron in the barrier and the decay process out of the barrier is characterized by nonexponential steps. In the case of a multimode (Ohmic) bath an approximate treatment of the dynamics, based on temperature dependent nonlinear Langevin–Schrödinger equations, implies that the trapped electron wavepacket is fully solvated in the barrier due to irreversible dissipation at low temperatures. An interpretation of the solvation process in terms of the mean-field approximation is given and discussed.
The effect of a low-frequency dissipative medium on the tunneling rate of a particle trapped in a metastable potential is investigated with the aid of a frozen-bath sudden approximation. The sudden theory is formulated for arbitrary time-dependent friction and for all temperatures at which the escape process is dominated by tunneling. The validity criterion of the theory is only that the bath frequency spectrum be substantially lower than the system frequency. It is applicable both in the weak- and strong-damping limits. The sudden theory is applied to tunneling in a cubic potential and a piecewise harmonic potential where the barrier frequency differs from the well frequency. In contrast to the ImF method, the sudden theory, when valid, can provide estimates of tunneling rates from well-defined excited resonance states and is not limited to estimates of only thermal rates. We find that, if the barrier is thin relative to the well, dissipation can serve to enhance tunneling rates from excited states.
We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that Markovian semigroup which approximates the particles dynamics on the time scale τ=λ2t\tau=\lambda^2tτ=λ2t (λ\lambdaλ strength of the coupling) is determined by the resonances of the full energy operator. We also show that Markovian master equation technique leads to the right prediction for the life-time of resonances. We discuss the dissipation of the particle into its ground state both in the time mean and on the above time scale.
Results are here reported of a model calculation for the one-dimensional tunneling of a particle coupled to a quantum harmonic oscillator. Interaction is at the barrier, to mimick the influence on transmission of possible surface excitations. The tunneling process turns out to be fast with respect to low energy modes such as surface phonons. Total transmission is enhanced with respect to the case without coupling, while the elastic one shows a kind of dissipative behaviour. On the contrary, the time scale for resonant tunneling is ?, where ? is the halfwidth of the resonance. Virtual excitation of high energy modes (e.g., surface plasmons) acts as a van der Waals-type force which renormalizes the barrier and increases the elastic transmission.
We consider the Bose-Hubbard model with particle losses at one lattice site. For the noninteracting case, we find that half of the bosons of an initially homogeneous particle distribution are not affected by dissipation that only acts on one lattice site in the center of the lattice. A physical interpretation of this result is that the surviving particles interfere destructively when they tunnel to the location of the dissipative defect and therefore never reach it. Furthermore we find for a one-dimensional model that a fraction of the particles can propagate across the dissipative defect even if the rate of tunneling between adjacent lattice sites is much slower than the loss rate at the defect. We analyze the robustness of our findings with respect to small interactions and small deviations from the symmetric setting. A possible experimental realization of our setup is provided by ultracold bosonic atoms in an optical lattice, where an electron beam on a single lattice site ionizes atoms that are then extracted by an electrostatic field.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.