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.
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.
We investigate the quantum dynamics of two interacting bosonic atoms confined in a one-dimensional anharmonic trap. The tunneling rate, an experimentally measurable parameter of the system, is calculated as a function of the effective coupling interatomic constant
g from the ground (
n=N=0) and first excited atomic states in the trap with respect to relative (
n=2,N=0) and center-of-mass (
n=0,N=2) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant
g, of the system by comparing the calculated tunneling rate with the experimental one. We observe that the only possible tunneling scenario is a sequential particle tunneling in the cases we consider. We also analyze a rearrangement $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.
This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For
s<1 the system is localized at zero temperature, and at finite
T relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For
s>2 it undergoes underdamped coherent oscillations for all relevant temperatures, while for
1<s<2 there is a crossover from coherent oscillation to overdamped relaxation as
T increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case,
s=1, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature
T: over most of the ($\ensuremath{\alpha}$,
T) plane (including the whole region $\ensuremath{\alpha}>1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low
T and $0<\ensuremath{\alpha}<\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.
The aim to control the internal and external degrees of freedom of quantum systems is of great interest for many fields of physics and chemistry. One opportunity to realize such a coherent control is provided by strong, time depended, external fields. In this work the experimental realization of a model-system is presented. The coherent control of the tunneling dynamics of single atoms by means of a time-periodic, external field is demonstrated. Depending on the parameters of the driving force the tunneling rate can be varied up to a total suppression of the tunneling process in the extreme. This type of dynamical localization is known as "coherent destruction of tunneling". The experimental setup allows a direct access to the tunneling dynamics of single atoms in a double well structure and enables great freedom concerning the parameters. Not only the double well potential, the driving frequency and the driving amplitude can be varied, but also the temporal and spatial symmetry of the driving. A coherent beam of slow, metastable argon atoms serves as source of particles, which can be detected spatially resolved enabling the direct observation of the tunneling dynamics in momentum space.
A real-time functional-integral method is used to derive an effective action that gives the transmission spectrum of a tunneling particle interacting with a bath of harmonic oscillators. The transmission spectum is expressed in terms of double functional integrals with respect to the coordinate of the particle which are evaluated by means of the stationary-phase approximation. The equations of motion for the stationary-phase trajectories are solved exactly for an arbitrary spectral density function of the bath, and the obtained solutions are used to find the transmission spectra for specific examples. For a bath with single frequency \ensuremath{\omega}, an analytic expression of the transmission spectrum is obtained which covers from the sudden tunneling (\ensuremath{\omega}
T0\ensuremath{\ll}1) to the adiabatic one (\ensuremath{\omega}
T0\ensuremath{\gg}1), where
T0 is the time it would take a classical particle to traverse the inverted bare potential barrier. For a bath with an Ohmic spectrum, the differential tunneling conductance at low bias voltage V and for \ensuremath{\eta}
T0\ensuremath{\ll}1 is found to obey a power law \ensuremath{\sim}(
eVT0/\ensuremath{\Elzxh}${)}^{\mathrm{\ensuremath{\eta}}{\mathit{T}}_{0}{\mathit{S}}_{0}/2\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\Elzxh}}}$, where \ensuremath{\eta} is the friction coefficient and
S0 is the tunneling exponent in the absence of interaction. \textcopyright{} 1996 The American Physical Society.
A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum
Z gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.