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Antiresonances as precursors of decoherence
| Content Provider | Semantic Scholar |
|---|---|
| Author | Torres, Luís Pastawski, Horacio Medina, Ernesto |
| Copyright Year | 2005 |
| Abstract | – We show that, in the presence of a complex spectrum, antiresonances act as a precursor for dephasing enabling the crossover to a fully decoherent transport even within a unitary Hamiltonian description. This general scenario is illustrated here by focusing on a quantum dot coupled to a chaotic cavity containing a finite, but large, number of states using a Hamiltonian formulation. For weak coupling to a chaotic cavity with a sufficiently dense spectrum, the ensuing complex structure of resonances and antiresonances leads to phase randomization under coarse graining in energy. Such phase instabilities and coarse graining are the ingredients for a mechanism producing decoherence and thus irreversibility. For the present simple model one finds a conductance that coincides with the one obtained by adding a ficticious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence. In the last decade the quantum-classical transition has been object of intense study leading to a substantial progress in its comprehension [1]. An essential ingredient is the fact that the properties of a given system, though simple, will be influenced by a hierarchy of interactions with the rest of the universe (the environment). However weak, such interactions lead to the degradation of the ubiquitous interference phenomena characteristic of a quantum system, i.e., decoherence. Current trends in technology focus on the tailoring of such interference phenomena to achieve different goals. These range from the control of electronic currents at the nanoscale in semiconductor and molecular devices [2,3] to the flow of quantum information [4] encoded in the phase of a quantum state. The crossover between the coherent and decoherent dynamics is manifest in the behavior of the quantum phase strikingly exhibited [5] by weak localization phenomena and the Aharanov-Bohm effect. Hence, the understanding and control of the effects of the coupling to the environment on the quantum phase constitute a central problem for both, fundamental physics and practical applications. (∗) Present address: DRFMC/SPSMS/GT, CEA-Grenoble 17 rue des Martyrs, 38054 Grenoble, France. L. E. F. Foa Torres et al.: Antiresonances as precursors of decoherence 165 Vkα,0 Vk'β,0 Vs E0 lead lead Cavity Fig. 1 – Schematic representation of the model system considered in the text: a quantum dot connected to left and right leads and to a chaotic cavity whose effect is the focus of this work. The most obvious source of decoherence is the creation of entangled system-environment states induced by complex many-body interactions. However, recent results on the Loschmidt Echo in chaotic systems [6] have suggested that complexity is a natural road to decoherence even in a one-body problem. Indeed, once the system is complex enough there is little chance to sustain a controllable interference experiment. In this paper, we will explore the notion that, in the presence of a complex spectrum, antiresonances are a precursor for dephasing and result in decoherent transport even within a fully unitary Hamiltonian description. This is illustrated by considering a toy model for a quantum dot tunneling device coupled to a chaotic cavity containing a large, but finite, number of states in the energy range of interest. A possible arrangement is depicted in fig. 1. The presence of the chaotic cavity induces definite phase changes (dephasing) in the resulting wave functions. Then, our main goal will be to gain insight into how this dephasing results in the emergence of decoherence. In what follows we will explore the effect of the coupled cavity on the phase and the transmission probability through the system. Furthermore, we will also address the consistency with Büttiker’s model of decoherence [7] where the sample is coupled via a fictitious voltage probe with a reservoir whose chemical potential is set to account for current conservation. The presence of such reservoir accounts for a decoherent [8] re-injection of particles. A Hamiltonian formulation for this picture was proposed by D’Amato and Pastawski [9]. In that work, the connection of the dot states to an infinite system with a continuous spectrum leads to a selfenergy with an imaginary part. This procedure is justified by considering decoherent electron reservoirs within the Keldysh formulation [10,11]. Here, we re-examine the latter path by exploring the consequences of the coupling with a system that contains a finite number of states. From this point of view, our main goal is to show how a “decoherent” behavior is an emergent phenomenon as the number of states in the chaotic cavity increases. While in our discussion we adopt a single-particle description, the conclusions will be of a general nature [12]. The total Hamiltonian is split into four terms: H = Hdot +Helectrodes +Hcavity +Hint. The device is represented by a Hamiltonian Hdot+Helectrodes consisting of a quantum dot that is coupled through potential barriers to the left and right electrodes. In addition, we introduce a chaotic cavity (represented by Hcavity) that serves as an “environment” that perturbs the system through the coupling term contained in Hint. 166 EUROPHYSICS LETTERS The dot sustains a set of states Ei whose corresponding creation and annihilation operators are di and di, respectively. This part of the Hamiltonian is written as Hdot = ∑ |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.foatorres.com/pubs/FoaTorres2006a.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/0511360v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Aharonov–Bohm effect Body cavities Coherence (physics) Conductance (graph) Dephasing Elegant degradation Hamiltonian (quantum mechanics) Interaction Interference (communication) Landauer's principle List comprehension Many-body problem Quantum decoherence Quantum dot Quantum entanglement Quantum information Quantum state Quantum system Semiconductor voltage |
| Content Type | Text |
| Resource Type | Article |
