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International Journal of Circuit Theory and Applications

On small signal equivalent circuit models for quantum dots

Giovanni Miano, Carlo Forestiere, Amir Boag, Gregory Ya. Slepyan, Antonio Maffucci

Published Mar 22, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1002/cta.2330

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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.
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.
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.
Abstract A quantum system composed of a large number of non‐interacting spin ½ particles, biased by a large constant magnetic field along the z‐axis and excited by a small circularly polarized electromagnetic wave in the xy‐plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.
A quantum system composed of a large number of non-interacting spin ½ particles, biased by a large constant magnetic field along the z-axis and excited by a small circularly polarized electromagnetic wave in the xy-plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.
The role of local fields in quantum electrodynamics of isolated quantum dot (QD) has been analyzed. The system is modeled as a strongly confined in space two-level quantum oscillator illuminated by quantum light. Relation between local and acting fields in QD has been derived in the dipole approximation from the integral Maxwell equations for electromagnetic field operators. A formalism of the electromagnetic field quantization in electrically small scatterers has been developed. As a result, Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Schr\"odinger equation with that Hamiltonian has been solved in linear approximation. Interaction of QD with different quantum states of light, such as Fock states, coherent states, Fock qubits, entangled states, has been analyzed. It has been shown that the local-fields induce a fine structure of the QD absorption (emission) spectrum: instead of a single line with the frequency corresponding to the exciton transition, a doublet appears with one component shifted to the blue (red). The value of the shift depends only on the geometrical and electronic properties of QD while the intensities of components are completely determined by the quantum light statistics. It has been demonstrated that in the limiting cases of classical light and single-photon state the doublet is reduced to a singlet shifted in the former case and unshifted in the latter one. A physical interpretation of the predicted effect has been proposed. Possible ways of experimental observation of the effect has been discussed together with the potentiality of its utilization in the quantum information processing.
Abstract Recent progress in nano‐metre structure and measurements is capable of providing us with the freedom to harness fast and seemingly weak correlations between atoms in an ensemble, manifesting them at macroscopic level. So we have investigated a prospective model of solid state integrated circuits for quantum computation, based on our coherence retentive resonance dynamic dipole–dipole interaction (RDDDI) theory. In this model, each qubit is a block consisting of an ensemble of quantum dots, and the energetics of which suggests stability up to room temperature. Here, we propose a qubit swap (∏4) gate applying our RDDDI. Moreover, integration of the ∏4 gate is proposed to form quantum circuits that can transfer a qubit state to any position within them, realizing bit reversal permutation circuits with even and odd bits, and a shuffling circuit. Copyright © 2003 John Wiley & Sons, Ltd.