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Physical Review A

Decoherence effects on quantum control by reverse optimized pulse sequences

C. A. Estrada Guerra, David Velasco Villamizar, Luís G. C. Rego

Published Aug 17, 2012• 7 citations
Publisher

Abstract

The external coherent control over the dynamics of quantum systems has been the aim of many studies in recent years, and several theoretical frameworks have been devised for that purpose. However, several of the proposed methods have been developed to control isolated quantum systems, disregarding the decoherence effects that impinge on the ubiquitous open quantum systems that exhibit a more complex dynamics than their isolated counterparts. In this paper, we investigate the effects of dissipation and decoherence for a quantum-control procedure based on sequences of reverse optimized electromagnetic pulses. Although the method performs well for pure quantum systems, moderate decoherence and dissipation hinders its accomplishment for ordinary conditions, irrespective of the pulse sequence rate. The method can be appropriate, nonetheless, for dynamical decoupling of the quantum subsystem from the environment.

DOI
10.1103/physreva.86.023411

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The external coherent control over the dynamics of quantum systems has been the aim of many studies in recent years, and several theoretical frameworks have been devised for that purpose. However, several of the proposed methods have been developed to control isolated quantum systems, disregarding the decoherence effects that impinge on the ubiquitous open quantum systems that exhibit a more complex dynamics than their isolated counterparts. In this paper, we investigate the effects of dissipation and decoherence for a quantum-control procedure based on sequences of reverse optimized electromagnetic pulses. Although the method performs well for pure quantum systems, moderate decoherence and dissipation hinders its accomplishment for ordinary conditions, irrespective of the pulse sequence rate. The method can be appropriate, nonetheless, for dynamical decoupling of the quantum subsystem from the environment.
Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems. These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise. We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems. We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition. A detailed mathematical description of how dephasing and the suppression of dephasing can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences. Our work then takes this practical perspective in addressing both "standard" sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information. Additionally, we review new techniques for the numerical construction of optimized pulse sequences using the filter-design perspective. We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality. The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrating that dynamics analogous to evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.
Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems.These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise.We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems.We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition.A detailed mathematical description of how dephasing and the suppression of dephasing can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences.Our work then takes this practical perspective in addressing both "standard" sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information.Additionally, we review new techniques for the numerical construction of optimized pulse sequences using the filter-design perspective.We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality.The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.
A general coherent control scenario to suppress or accelerate tunneling of quantum states decaying into a continuum is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling protocols and to sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrates that dynamics analogous to the evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.
Coherent-optical-control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways and manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of quantum information. Inspired by nuclear magnetic resonance spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent-control techniques. This article reviews related developments in the fields of coherent optical control and dynamical decoupling, emphasizing the control of tunneling and decoherence in general model systems. Considering recent experimental breakthroughs in the demonstration of active control of a variety of systems, we anticipate that the reviewed coherent-control scenarios and dynamical-decoupling methods should raise significant experimental interest.