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IEEE Antennas and Wireless Propagation Letters

Quantum Radiating Arrays and Their Directivity: A Dynamical Open System Approach

Said M. Mikki

Published Nov 4, 2022• 6 citations
Publisher

Abstract

We investigate the directive properties of radiating quantum antennas comprised of coupled two-level (qubit) systems interacting with bosonic modes and excited by classical fields. A directivity formula inspired by classical antenna theory is proposed. The density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, is evolved in time using the Gorini–Kossakowski–Sudarshan–Lindblad master equation. We illustrate the method in a numerical example where it is shown that manipulating the phase excitations of individual quantum dots may significantly enhance the directive radiation properties of the quantum dot antenna system.

DOI
10.1109/lawp.2022.3217295

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We investigate the directive properties of radiating quantum antennas comprised of coupled two-level (qubit) systems interacting with bosonic modes and excited by classical fields. A directivity formula inspired by classical antenna theory is proposed. The density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, is evolved in time using the Gorini–Kossakowski–Sudarshan–Lindblad master equation. We illustrate the method in a numerical example where it is shown that manipulating the phase excitations of individual quantum dots may significantly enhance the directive radiation properties of the quantum dot antenna system.
We describe a general framework for the modeling and analysis of Markovian quantum antenna systems viewed as a special problem in quantum stochastic dynamics. The quantum radiator, which can be used to spatially direct radiated quantum states in future quantum communication systems, is modeled as an open quantum system capable of controlling the composition of its radiation modes through external source manipulations while in continuous interaction with the surrounding thermal and random environments. Our analysis and computational methods are based on deploying the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation to account for environment-induced jump processes such as quantum dissipation and decoherence. We construct a definition of the quantum antenna directivity inspired by the corresponding formulas in classical antenna theory and present several versions of the quantum directivity formula. As a computational example, we study the flow of the density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, which is evolved in time using the quantum master equation. It is shown that by manipulating the amplitude and phase excitations of individual quantum dots, one may significantly enhance the directive radiation properties of the Markovian quantum antenna system.
We describe a general framework for the modeling and analysis of Markovian quantum antenna systems viewed as a special problem in quantum stochastic dynamics. The quantum radiator, which can be used to spatially direct radiated quantum states in future quantum communication systems, is modeled as an open quantum system capable of controlling the composition of its radiation modes through external source manipulations while in continuous interaction with the surrounding thermal and random environment. Our analysis and computational method are based on deploying the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation to account for environment-induced jump processes such as quantum dissipation and decoherence. We construct a definition of the quantum antenna directivity inspired by the corresponding formulas in classical antenna theory and use the GKSL formalism to derive several versions of the quantum directivity formula. As a computational example, we study the flow of the density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, which is evolved in time using the quantum Liouville-type equation (the master equation). It is shown that by manipulating the amplitude and phase excitations of individual quantum dots, one may significantly enhance the directive radiation properties of the Markovian quantum antenna system.
We describe a general framework for the modeling and analysis of Markovian quantum antenna systems viewed as a special problem in quantum stochastic dynamics. The quantum radiator, which can be used to spatially direct radiated quantum states in future quantum communication systems, is modeled as an open quantum system capable of controlling the composition of its radiation modes through external source manipulations while in continuous interaction with the surrounding thermal and random environment. Our analysis and computational method are based on deploying the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation to account for environment-induced jump processes such as quantum dissipation and decoherence. We construct a definition of the quantum antenna directivity inspired by the corresponding formulas in classical antenna theory and use the GKSL formalism to derive several versions of the quantum directivity formula. As a computational example, we study the flow of the density operator of a coupled two-level quantum dot (qubit) array, excited by classical external signals with variable amplitude and phase, which is evolved in time using the quantum Liouville-type equation (the master equation). It is shown that by manipulating the amplitude and phase excitations of individual quantum dots, one may significantly enhance the directive radiation properties of the Markovian quantum antenna system.
An open quantum system can be described by a master equation, of which one of the most popular is the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We revisit description of driven-dissipative quantum systems focusing on the appropriate choice of the system's basis and the respective transformations. We consider the GKSL equation in different bases and calculate the dynamics for a qubit and for a qudit. An appropriate choice of the basis is a fundamental problem for theoretical consideration of open quantum systems and provides an opportunity to obtain the desired evolution in practice.
Abstract Chapter 22 investigates the dynamics of open quantum systems that interact with their environment. We discuss the time-evolution of the joint system in terms of a time-ordered exponential of an integral over the Hamiltonian and determine a similar formulation for a Liouvillian super-operator. Based on these ideas we develop the notion of dynamical maps and apply the Born-Markov approximation to arrive at a dynamical semi-group and general Markovian master equations. We then turn to a specific example of such an equation of motion for the density operator: the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation which captures both dissipative dynamics and decoherence using Lindblad operators. We employ the GKLS equation to model the absorption, and spontaneous as well as stimulated emission of radiation by a two-level atom. We then discuss the Jaynes-Cummings model that describes the interaction of such an atom with a single mode of the electromagnetic field in a cavity
Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension 2. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to 1, and find a moment of time starting from which the FGKLS equation can be used—the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system.