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Results in Physics

Theory and computation of Markovian quantum antenna systems

Said M. Mikki

Published Apr 28, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2023.106453

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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.
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.
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
Stochastic unravelings provide a useful way to represent open quantum system dynamics in terms of pure state realizations, and have been widely studied both from a fundamental and from a computational point of view. They were initially formulated for Markovian dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation. However, due to recent technological and experimental development, most physical relevant dynamics present temporal correlations beyond the Markov approximation. Such correlations cause decay rates to turn temporarily negative, thus requiring the generalization of stochastic unravelings from Markovian to non-Markovian scenarios. Indeed, many unraveling techniques have been introduced in this regime, and a comprehensive review of the different jump methods is currently missing. In this work, we provide an overview of widely used quantum jump unraveling techniques for non-Markovian systems and also discuss them in terms of their numerical efficiency, divisibility requirements, Hilbert space extension, and measurement interpretation.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..