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IEEE International Conference on Nanotechnology (IEEE-NANO)

Equivalent electrical multiport for quantum systems in entangled states

Gregory Ya. Slepyan, Amir Boag, Vladimir I. Mordachev, E. Sinkevich, С. А. Максименко, P. Kuzhir, Giovanni Miano, Mikhail E. Portnoi, Antonio Maffucci

Published Jul 1, 2015• 2 citations
Publisher

Abstract

This paper introduces the concept of equivalent electrical multiport for a quantum device made of a pair of two-level objects, coupled via entanglement. The coupled pair is described in terms of an equivalent 2×2 admittance matrix, derived from the theory of the generalized susceptibility. This result provides a valuable tool to analyze quantum circuits in the frame of the classical circuit theory. The study of the properties of the admittance matrix highlights the effect of a new coupling mechanism, due to entanglement, which adds to the classical electromagnetic coupling.

DOI
10.1109/nano.2015.7388952

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This paper introduces the concept of equivalent electrical multiport for a quantum device made of a pair of two-level objects, coupled via entanglement. The coupled pair is described in terms of an equivalent 2×2 admittance matrix, derived from the theory of the generalized susceptibility. This result provides a valuable tool to analyze quantum circuits in the frame of the classical circuit theory. The study of the properties of the admittance matrix highlights the effect of a new coupling mechanism, due to entanglement, which adds to the classical electromagnetic coupling.
Abstract Physics is not scale invariant, and today the scale of atoms and molecules challenges designers of machines in which quantum effects have dominant sway. What role could circuit theory play in designing machines described by quantum‐classical models? Classical equivalent circuits do exist for systems composed of metal contacted and wired devices, such as resonant tunneling diodes, single electron transistors, metal–insulator–metal diodes, etc. circuits, but not for quantum‐entangled networks, such as multi‐quantum‐state atoms. If devices were not contacted and wired by macroscopic metals, i.e. devices were classically field coupled, then generalized circuit models can be introduced. Case studies have been presented on the role of circuit models in quantum‐classical systems. However, there are no ideal circuit elements capable of capturing the port properties of quantum‐mechanical and/or quantum‐optical subsystems and their coupling to classical waveguides or cavities. Copyright © 2007 John Wiley & Sons, Ltd.
A mesoscopic circuit, where field quantization (e.g., coherent states and squeezed states) can be exhibited, is one of the ideal quantum systems for manifesting diverse quantum field theoretical phenomena and thermally statistical characteristics. Because of inevitable electromagnetic coupling (e.g., mutual capacitor coupling and mutual inductor coupling) in two neighboring mesoscopic electric circuits, quantum effects relevant to mesoscopic circuit coupling may play a key role in some devices of quantum information processing. Such a circuit coupling can lead to circuit entangled states, where the Fock number states of energy quanta in different circuits are entangled with each other. Since the time dependence in parameters of coupled-circuit Hamiltonian would result from environmental perturbations (e.g., temperature fluctuations in devices) or from some controllable manipulation (e.g., an incident ultrasonic wave), the circuit entangled states would evolve due to these external conditions. Time evolution of entangled states in coupled mesoscopic circuits is considered within a framework of time-dependent quantum theoretical formalism. Note that an applied photon field can also be coupled to such quantum entangled circuits. Then it is possible that an effect of entanglement transfer (i.e., transportation of superposition coefficients in the entangled state) from the quantum mesoscopic coupled LC circuits to the applied external photon field would also occur under some proper parameter conditions. The present characteristics of both quantized coupled mesoscopic circuits and entanglement transfer can also be found in some alternative microscopic- and mesoscopic-scale devices such as the systems in cavity quantum electrodynamics (QED).
Summary In this paper, we introduce small signal equivalent circuit models for quantum dots at equilibrium driven by classical electromagnetic fields. We investigate both an isolated quantum dot and a pair of interacting quantum dots coupled by the electric dipole–dipole interaction. In particular, we derive the impulse responses of the equivalent circuit elements from the density operator of the quantum dots. The use of equivalent circuit elements for complex systems of quantum dots may greatly simplify the analysis and the design of light‐matter interaction processes at the nanoscale. Copyright © 2017 John Wiley & Sons, Ltd.
The Uhlmann phase extends the concept of geometric phases to mixed quantum states through a parallel-transport condition on purification amplitudes, but its experimental realization has so far required sophisticated quantum platforms with carefully engineered auxiliary degrees of freedom. In this work, we reformulate the Uhlmann parallel-transport condition as a linear matrix differential equation and vectorize it to obtain an effective dynamical generator. This generator can be directly mapped onto the admittance matrix of a classical RC circuit, thereby translating the Uhlmann dynamics into the evolution of circuit node voltages. We illustrate the mapping using the equatorial-loop model and, via a rotating-frame transformation followed by a real decomposition, derive a time-independent, real-valued dynamical system suitable for analog implementation. LTspice simulations of the resulting active RC network faithfully reproduce the Uhlmann geometric phase and its topological transition at the critical purity, demonstrating that classical electrical circuits offer a simple and accessible platform for probing mixed-state geometric phases.
Abstract The development of nanocircuits designed to ultimately interact with classical electromagnetic environments demands a description of their performance in circuit terms, i.e. in terms of voltages and currents for incident, reflected and transmitted waves. A class of quantum systems which are particularly promising for applications (e.g. in spintronics) and at the same time easy to analyse and to understand physically are the two‐state systems. Here, we present equivalent circuits for a generic two‐state quantum system imbedded in a one‐port or two‐port structure guiding a linearly polarized electromagnetic wave. For the sake of concreteness we explicitly refer to a system of spin ½ particles whose magnetic moments are aligned with the axis of the guiding structure by a strong constant magnetic field; but the formalism can be easily extended to particles endowed with electric dipole moments or any other system with two degrees of freedom. Copyright © 2007 John Wiley & Sons, Ltd.