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Canadian Journal of Physics

Reduced-density-matrix description of decoherence and relaxation processes for electron-spin systems: Applications to trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids

V. L. Jacobs

Published Dec 15, 2017• 0 citations
Publisher

Abstract

The quantum dynamics of many-electron spin systems is investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, together with spectral-line broadening phenomena, that are induced by interactions of many-electron spin systems with photons, phonons, nuclear spins, external electric, magnetic, and electromagnetic fields. Within the framework of a quantum-open-systems (reduced-density-operator) approach, these processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions that are derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations.

DOI
10.1139/cjp-2017-0594

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The quantum dynamics of many-electron spin systems is investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, together with spectral-line broadening phenomena, that are induced by interactions of many-electron spin systems with photons, phonons, nuclear spins, external electric, magnetic, and electromagnetic fields. Within the framework of a quantum-open-systems (reduced-density-operator) approach, these processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions that are derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations.
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Reduced density matrix descriptions are developed for linear and non-linear electromagnetic interactions of moving atomic systems, taking into account applied magnetic fields as well as atomic collisions together with other environmental decoherence and relaxation processes. Applications of interest include electromagnetically induced transparency and related pump-probe optical phenomena in warm atomic vapors. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowestorder perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical treatment of the electromagnetic interaction is adopted. However, the need for a fully quantum mechanical approach is emphasized. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear macroscopic electromagnetic-response tensors occurring in a perturbation-theory treatment of the semiclassical electromagnetic interaction. These expressions can be evaluated for coherent initial atomic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Collisional interactions between atoms can be treated in various approximations for the selfenergy operator, and the influence of Zeeman coherences on the macroscopic electromagnetic response can be investigated.
Reduced density matrix descriptions are developed for linear and non-linear interactions in electromagnetically induced transparency and related pump-probe optical phenomena involving moving atomic systems. Applied magnetic fields as well as atomic collisions, together with other environmental decoherence and relaxation processes, are taken into account. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowest-order perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical treatment of the electromagnetic interaction is adopted. However, the need for a fully quantum mechanical approach is emphasized. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear macroscopic electromagnetic-response tensors within the framework of a perturbation-theory treatment of the semiclassical electromagnetic interaction. These expressions can be evaluated for coherent initial atomic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Collisional interactions between atoms can be treated in various approximations for the self-energy operator, and the influence of Zeeman coherences on the electromagnetic-pulse propagation can be investigated.
Qubit coherence is an essential figure of merit for quantum information processing applications such as quantum computing, or quantum repeaters. Understanding the coherence properties of the underlying physical qubits that facilitate such applications is therefore are often limited by coupling to lattice phonons, which in turn constrains operation temperature. Here we study phonon induced electronic spin decoherence in group-IV vacancy centers in diamond. We begin by modeling the spin-phonon interaction and then employ the widely used Born-Markov approximation, highlighting its inconsistencies in this setting and its deviations from experimental observations. To close the gap between theoretical predictions and experimental results, we relax certain approximations, investigate their contributions to the predicted coherence times, and identify the dominant sources of discrepancy. We further demonstrate that experimentally measured electronic spin coherence dynamics are consistently captured within a non-Markovian framework, and we show how the magnetic field orientation influences the qubit coherence time.
Linear and non-linear interactions in electromagnetically induced transparency and related pump-probe optical phenomena involving moving many-electron atomic systems are investigated using a reduced-density-matrix approach. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowest-order perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical perturbation-theory treatment of the electromagnetic interaction is adopted. However, it is emphasized that a quantized-electromagnetic-field approach is essential for a self-consistent quantum-mechanical formulation. Our primary result is the derivation of compact Liouville-space operator expressions for the linear and the general (n'th order) non-linear macroscopic electromagnetic-response tensors. These expressions can be evaluated for coherent initial atomic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Collisional interactions between atoms can be treated in various approximations for the self-energy operator, and the influence of Zeeman coherences on the electromagnetic-pulse propagation can be investigated by including an applied magnetic field on an equal footing with the electromagnetic fields.
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