Some recent works on the tunneling of light interstitial particles (protons and positive muons) in metals are reviewed. They provide examples of simple quantum systems coupled to “baths” consisting of phonons and conduction electrons. In the limit of strong coupling to such an environment the positive muons move by quantum diffusion, where coherence is lost between each tunneling event, whereas in the weak coupling limit coherence can be maintained and allow a quantum propagation, i.e. a band-like motion. These phenomena can also be seen as examples of wave-function reduction in the presence of dissipative environments and may help to understand the details of such processes.
Some recent works on the tunneling of light interstitial particles (protons and positive muons) in metals are reviewed. They provide examples of simple quantum systems coupled to “baths” consisting of phonons and conduction electrons. In the limit of strong coupling to such an environment the positive muons move by quantum diffusion, where coherence is lost between each tunneling event, whereas in the weak coupling limit coherence can be maintained and allow a quantum propagation, i.e. a band-like motion. These phenomena can also be seen as examples of wave-function reduction in the presence of dissipative environments and may help to understand the details of such processes.
Theoretical models of quantum systems in the presence of their environment find many applications, ranging from condensed matter physics to quantum information science and quantum thermodynamics. In the field of macroscopic quantum systems, the Caldeira-Leggett model has been employed to study the effects of thermal baths on the coherence properties of superconducting qubits. However, if the quantum system of interest consists of many electrons in a solid, the role of the environment can be played by a quantum field of lattice vibrations, i.e. phonons, modeled by means of noninteracting bosons .
In this work, we studied widely known models of quantum systems linearly coupled to their bosonic environment, ranging from simple driven two-level systems, i.e. qubits, to many electrons systems.
Our approach has been focused on interesting model parameter ranges where well-established weak-coupling approximations fail in describing the physics involved. Indeed, these regimes are interesting and accessible to experiments. In the case of a driven qubit in contact with its environment, strong coupling effects in system-bath interactions, decoherence and crossover to totally incoherent tunneling dynamics have been studied. In addition, by considering prototypical models of fermionic systems strongly coupled to phonons on a lattice, we studied how topological features can be dramatically modified in the presence of electron-phonon interaction.
Decoherence is a relatively recent concept in the field of quantum mechanics. Although the pioneers of the field must have understood that loss of phase coherence in quantum superpositions is the reason underlying the appearance of definite outcomes in the quantum measurement problem, the latter was not treated in terms of decoherence until sixty years after the formulation of quantum mechanics as described in a report by Joos and Zeh in 1983 [1]. However, soon after, the theory was developed in further detail, and experiments to measure the actual decoherence rates in various systems commenced. Today, decoherence is the main concern for another reason, i.e., the fact that superposition states must be maintained undisturbed in the quantum communication systems and decoherence presents a strong limitation for their practical application. Decoherence appears in open quantum systems, where the basic system under consideration interacts relatively strongly with an environment. Decoherence times may be as long as seconds for small atomic systems in extreme vacua, although below what is presently measurable (i.e., less than a fraction of a femtosecond) in most liquids and solids, where coupling to the surrounding molecules or atomic arrangements is strong. The relatively slow decoherence in well-isolated particle systems has been described in several recent articles on quantum optics, while the rapid decoherence in liquids and solids has not received this kind of attention. It is the purpose of the present review to fill this gap.
A wave equation formulation of the problem of quantum tunneling in a dissipative medium is developed by considering a many-body system in which the central particle is subject to an arbitrary force law, and at the same time is coupled to a bath of noninteracting harmonic oscillators. For the motion of the central particle it is possible to obtain an effective Lagrangian and Hamiltonian by eliminating the degrees of freedom of the oscillators. However both of these operators are nonlocal, and it is difficult to derive a wave equation for this motion. As an alternative method one can write a many-body Schrödinger equation for the whole system, and then eliminate the wave functions of all of the oscillators. This result is a many-channel Schrödinger equation for the motion of the central particle. By truncating this set of coupled equations, one can solve the problem for different force laws. In particular, in this work, the cases of dissipative tunneling, hopping, and quantum coherence are studied in detail. It is also shown how this approach can be generalized to multidimensional dissipative systems.
Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green’s function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent. The double-well potential is one of the simplest and best understood problems in modern quantum mechanics. Its utility is likewise unparalleled. Potential applications of double-well devices have been noted in Refs. [1-5]. For such devices to be useful, an understanding of the processes which couple the microscopic device to the macroscopic environment is paramount. That is to say, the decoherence processes of such systems must be well understood. To this end, we consider a simple exactly solvable model of two coupled quantum dots. An excellent review of related systems and some approximate solutions are given in Ref. [6]. Each dot is coupled to an environment (a triple-barrier system) as in Fig. 1. The environment consists of a continuum of states, as would be appropriate for a macroscopic lead. Only one state in each quantum dot is considered, which amounts to the assumption that the tunneling parameters connecting our two states to any neglected state are much less than the energy differences with that state. The Hamiltonian of the system can be written as the sum of two terms, H = H0 + Hc. The first term, H0, represents the dynamics of the simple two-state system, H0 = ε1d † 1d1 + ε2d † 2 d2 + V (d† 1d2 + d†
We review our recent contributions to two topics that have become of interest in the field of open, dissipative quantum systems: non-Gaussian noise and decoherence in fermionic systems. Decoherence by non-Gaussian noise, i.e. by an environment that cannot be approximated as a bath of harmonic oscillators, is important in nanostructures (e.g. qubits) where there might be strong coupling to a small number of fluctuators. We first revisit the pedagogical example of dephasing by classical telegraph noise. Then we address two models where the quantum nature of the noise becomes essential: "quantum telegraph noise" and dephasing by electronic shot noise. In fermionic systems, many-body aspects and the Pauli principle have to be taken care of when describing the loss of phase coherence. This is relevant in electronic quantum transport through metallic and semiconducting structures. Specifically, we recount our recent results regarding dephasing in a chiral interacting electron liquid, as it is realized in the electronic Mach-Zehnder interferometer. This model can be solved employing the technique of bosortization as well as a physically transparent semiclassical method. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim