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Journal of Optics B Quantum and Semiclassical Optics

Universal dynamical control of decay and decoherence in multilevel systems

Goren Gordon, Gershon Kurizki, Abraham G. Kofman

Published Sep 15, 2005• 12 citations
Publisher

Abstract

A unified theory is presented of dynamically modified decay and decoherence in driven multilevel quantum systems that are weakly coupled to arbitrary zero-temperature reservoirs. Examples of different phase and amplitude modulations are given for two-level systems (qubits). Analysis of modulations on multilevel systems is detailed with a numerical example using quasiperiodic impulsive phase jumps. The merits and disadvantages of the different modulation types are discussed.

DOI
10.1088/1464-4266/7/10/012

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A unified theory is presented of dynamically modified decay and decoherence in driven multilevel quantum systems that are weakly coupled to arbitrary zero-temperature reservoirs. Examples of different phase and amplitude modulations are given for two-level systems (qubits). Analysis of modulations on multilevel systems is detailed with a numerical example using quasiperiodic impulsive phase jumps. The merits and disadvantages of the different modulation types are discussed.
A unified theory is given of dynamically modified decay and decoherence in driven two-level and multilevel quantum systems that are weakly coupled to arbitrary finite-temperature reservoirs and undergo random phase fluctuations. Criteria for the optimization of decoherence suppression and the limitations of this approach are obtained. For a driven qubit that is strongly coupled to the continuum edge of reservoir's spectrum, we demonstrate that only an appropriately ordered sequence of abrupt changes of the resonance frequency, near the continuum edge, can effectively protect the qubit state from decoherence.
A unified theory is given of dynamically modified decay and decoherence in driven quantum systems that are coupled to arbitrary finite-temperature reservoirs and undergo random phase fluctuations. Criteria for the optimization of the suppression and the limitations of this approach are obtained. Decay acceleration by frequent measurements (interruptions of the coupling), known as the anti-Zeno effect (AZE) is argued to be much more ubiquitous than its inhibition in one- or two-level systems coupled to reservoirs (continua). In multilevel systems, frequent measurements cause accelerated decay by destroying the multilevel interference, which tends to inhibit decay in the absence of measurements.
A unified theory is given of dynamically modified decay and decoherence of field-driven multipartite systems. When this universal framework is applied to two-level systems or qubits experiencing either amplitude or phase noise due to their coupling to a thermal bath, it results in completely analogous formulae for the modified decoherence rates in both cases. The spectral representation of the modified decoherence rates underscores the main insight derived from this approach, namely, that the decoherence rate is the spectral overlap of the noise and modulation spectra. This allows us to come up with general recipes for modulation schemes for the optimal reduction of decoherence under realistic constraints. An extension of the treatment to multilevel and multipartite systems exploits intra-system symmetries to dynamically protect multipartite entangled states. Another corollary of this treatment is that entanglement, which is very susceptible to noise and can die, i.e., vanish at finite times, can be resuscitated by appropriate modulations prescribed by our universal formalism. This dynamical decoherence control is also shown to be advantageous in quantum computation setups, where control fields are applied concurrently with the gate operations to increase the gate fidelity.
In this paper, we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude or phase noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.