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arXiv:2206.11139

Bond current in a mesoscopic ring -- signature of decoherence due to classical and quantum noise

Sushanta Dattagupta, Tanmay Saha

Published Jun 22, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2206.11139

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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.
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Mesoscopic multiply connected samples such as conducting rings, cylinders or tori exhibit quantum size phenomena originating from the Aharonov–Bohm effects. One of the most spectacular phenomena is a persistent current [1] which is a direct manifestation of quantum phase coherence of the current carriers over a mesoscopic length scale. At a non-zero temperature, T > 0, the phase coherence of carriers is weakened and the samples exhibit the dissipative Ohmic contribution to the total current. There is a regime of temperatures in which both phase-coherent and dissipative Ohmic currents coexist. Such currents generate a magnetic flux. Its properties can be studied via modelling based on kinetic equations like Langevin equations [2]. The long-time, steady states of the magnetic flux are characterized by properties of the stationary probability density obtained from the corresponding Langevin equation. For instance, if the stationary probability density is bimodal, i.e., it has two maxima it reflects the possibility of occurrence of non-zero magnetic fluxes and in consequence the currents. One can notice an obvious analogy to the Josephson-based flux qubits [3]. There are serious advantages for using non-superconducting samples like rings as a building blocks for qubit storage because due to a small size they seem to be more stable with respect to decoherence and dephasing [4]. For higher temperatures, when __________
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It is suggested that the quantum uncertainty of cavity radiation is measurable via Aharonov-Bohm effects for electrons in a ring which is threaded by the magnetic cavity flux. When the electrons follow this oscillatory flux nearly adiabatically, and dissipation is negligible, the noise in the ring current should provide a quantum-nondemolition measure of the flux uncertainty. Unlike standard photodetection, such measurements should reveal the scaling of the flux uncertainty with the diamagnetic or dielectric index of the cavity medium, depending on the dimensions of the electron ring.
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.
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