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arXiv:cond-mat/0407685 · Physical Review Letters

Effect of Dephasing on the Current Statistics of Mesoscopic Devices

Marco G. Pala, Giuseppe Iannaccone

Published Dec 14, 2004• 21 citations
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Abstract

We investigate the effects of dephasing on the current statistics of mesoscopic conductors with a recently developed statistical model, focusing, in particular, on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we analyze the influence of an arbitrary degree of decoherence on the cumulants of the current. We recover known results for the limiting cases of fully coherent and totally incoherent transport and are able to obtain detailed information on the intermediate regime of partial coherence for a varying number of open channels. We show that dephasing affects the average current, shot noise, and higher order cumulants in a quantitatively and qualitatively similar way, and that consequently shot noise or higher order cumulants of the current do not provide information on decoherence additional or complementary to what can be already obtained from the average current.

DOI
10.1103/physrevlett.93.256803

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•Jan 1, 2009•1 citation
We investigate the effects of dephasing on the current statistics of mesoscopic conductors with a recently developed statistical model, focusing, in particular, on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we analyze the influence of an arbitrary degree of decoherence on the cumulants of the current. We recover known results for the limiting cases of fully coherent and totally incoherent transport and are able to obtain detailed information on the intermediate regime of partial coherence for a varying number of open channels. We show that dephasing affects the average current, shot noise, and higher order cumulants in a quantitatively and qualitatively similar way, and that consequently shot noise or higher order cumulants of the current do not provide information on decoherence additional or complementary to what can be already obtained from the average current.
We present simulations of the effects of dephasing on the shot noise properties of mesoscopic coherent devices, such as chaotic cavities and Aharonov-Bohm rings. We adopt a phenomenological model that exploits the statistical nature of the dephasing mechanism and is able to cover the intermediate regime between a fully coherent and completely incoherent (i.e., semiclassical) transport. By investigating conductance and noise properties as a function of the dephasing length, we conclude that decoherence has no specific effect on shot noise which can be distinguished from the one it has on conductance. In addition, when a large number of conducting channels is considered, semiclassical and quantum behavior must converge, yielding as a consequence the independence of DC and noise properties from dephasing.
We study the noise properties and efficiency of a mesoscopic resonant-level conductor which is used as a quantum detector, in the regime where transport through the level is only partially phase coherent. We contrast models in which detector incoherence arises from escape to a voltage probe, versus those in which it arises from a random time-dependent potential. Particular attention is paid to the back-action charge noise of the system. While the average detector current is similar in all models, we find that its noise properties and measurement efficiency are sensitive both to the degree of coherence and to the nature of the dephasing source. Detector incoherence prevents quantum limited detection, except in the nongeneric case where the source of dephasing is not associated with extra unobserved information. This latter case can be realized in a version of the voltage-probe model.
A three-site mesoscopic ring provides an ideal setting for an exact calculation of the bond current when the ring is threaded by an Aharonov-Bohm flux. The bond current is a measurable outcome of the coherent properties of the quantum phase. However the coherence is impeded by noise when the ring is put in contact with an environment. This coherence-to-incoherence transition is analyzed in detail here for both classical (Gaussian and telegraphic) and quantum noise and a comparative assessment is made when the quantum noise is governed by a spin-boson Hamiltonian of dissipative quantum mechanics.
We investigate the effect of dephasing (decoherence) on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, ${\ensuremath{\lambda}}_{F}∕L⪡1$. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from (i) an external closed quantum chaotic environment, (ii) a classical source of noise, and (iii) a voltage probe, i.e., an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak localization $\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}∕{\ensuremath{\tau}}_{\ensuremath{\phi}}]$, with the dephasing rate ${\ensuremath{\tau}}_{\ensuremath{\phi}}^{\ensuremath{-}1}$. The parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ depends strongly on the source of dephasing. For a voltage probe, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ is of order the Ehrenfest time $\ensuremath{\propto}\mathrm{ln}[L∕{\ensuremath{\lambda}}_{F}]$. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length $\ensuremath{\xi}$ of the coupling or noise potential replacing the Fermi wavelength ${\ensuremath{\lambda}}_{F}$. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions and numerically confirm our findings.
It is shown that the dephasing rate in Coulomb coupled mesoscopic structures is determined by charge relaxation resistances. The charge relaxation resistance together with the capacitance determines the RC-time of the mesoscopic structure and at small frequencies determines the voltage fluctuation spectrum. Self-consistent expressions are presented which give the charge relaxation resistance and consequently the dephasing rate in terms of the diagonal and off-diagonal elements of a generalized Wigner-Smith delay-time matrix. Dephasing rates are discussed both for the equilibrium state and in the transport state in which charge fluctuations are generated by shot noise. A number of different geometries are discussed. This article is to appear in {\it Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and R. Ellialtioglu, (Kluwer, unpublished).
Traditionally, (charge) transport phenomena describe the average current flow in response to a constant applied driving force. Additional information is provided by current-current correlations or noise, telling about the granularity, the statistical properties, and the interactions between the particles. The complete characterization of transport is given by the full counting statistics, quantifying the probability that n particles pass the device during a time window t. The desire for a complete characterization of transport in a mesoscopic device goes together with the development of new single-particle sources and the availability of quantum bits as measurement devices. In this thesis, we will describe how to combine these three elements, full counting statistics, single-particle sources, and qubit measurement devices and how these concepts relate to the description of charge transport of noninteracting electrons in a mesoscopic device. In the work on full counting statistics, we develop a new wave-packet formalism that provides access to an entire class of interesting results. The wavepacket formalism is derived from an insight regarding the equivalence between the fidelity of a quantum system and the generating function of full counting statistics; furthermore, we show how qubits can be used to measure both quantities, fidelity and full counting statistics, exploiting the induced ‘decoherence’ as a signal; thereby, we transfer the measurement of the fidelity and of the full counting statistics from the realm of a ‘Gedanken’ experiment to a practical proposal realizable with today’s qubit technology. Subsequently, we study the full counting statistics for the transmission of two identical particles with positive or negative symmetry under exchange, for the situation where the scattering depends on energy. We make use of our firstquantized wave-packet formalism and find interesting results. While it is expected that the noise as well as higher-order correlators will be sensitive to the exchange symmetry, we find the astounding result that exchange can hugely enhance (or suppress) the average charge already. The effect is a consequence of the symmetry-induced reshuffling of weight in the momentum distribution of the