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IEEE Conference on Decision and Control (CDC)

Constructive control of a spin system via periodic control

Viswanath Ramakrishna, Raimund J. Ober, Kathryn L. Flores, HERSCHEL A. RABITZ

Published Jul 10, 2003• 2 citations
Publisher

Abstract

Constructive procedures for the control of a class of coupled spin systems with bounded amplitude sinusoidal pulses are described. Full details are first illustrated for a single spin 1/2 particle. The key steps for a pair of such particles are then sketched. The fact that the amplitudes can be arbitrarily bounded implies that the separation between the Larmor frequencies of the individual spin 1/2 particles can be quite small and yet the system can be controlled by addressing each spin individually.

DOI
10.1109/cdc.2001.980115

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Constructive procedures for the control of a class of coupled spin systems with bounded amplitude sinusoidal pulses are described. Full details are first illustrated for a single spin 1/2 particle. The key steps for a pair of such particles are then sketched. The fact that the amplitudes can be arbitrarily bounded implies that the separation between the Larmor frequencies of the individual spin 1/2 particles can be quite small and yet the system can be controlled by addressing each spin individually.
Constructive procedures for the control of a class of coupled spin systems with bounded amplitude sinusoidal pulses are described. Full details are first illustrated for a single spin 1/2 particle. The key steps for a pair of such particles are then sketched. The fact that the amplitudes can be arbitrarily bounded implies that the separation between the Larmor frequencies of the individual spin 1/2 particles can be quite small and yet the system can be controlled by addressing each spin individually.
Constructive techniques for preparing a specific unitary generator from a coupled two-spin system, via bounded amplitude radio frequency selective single spin pulses, are presented. The frequency of any pulse in the sequence is one of the two Larmor frequencies, while the phase takes one of two values. The fact that the amplitude is bounded implies that the Larmor frequency separation between the two spins need not be large to maintain selectivity. In addition, the contribution of the J coupling term to single spin evolution is not neglected, but instead plays a crucial role. The procedure is based on a certain decomposition of SU(4) available in the literature. A method for determining the parameters entering this factorization, in terms of the entries of the target unitary generator, is also provided.
In this paper we develop a method for exact constructive controllability of quantum mechanical systems. The method has three steps, first a path from the initial state to the final state is determined and intermediate points chosen such that any two consecutive points are close, next small sinusoidal control signals are used to drive the system between the points, and finally quantum measurement technique is used to exactly achieve the desired state. The methodology is demonstrated for the control of spin-half particles in a Stern-Gerlach setting.
In this paper we develop a method for exact constructive controllability of quantum mechanical systems. The method has three steps, first a path from the initial state to the final state is determined and intermediate points chosen such that any two consecutive points are close, next small sinusoidal control signals are used to drive the system between the points, and finally quantum measurement technique is used to exactly achieve the desired state. The methodology is demonstrated for the control of spin-half particles in a Stern-Gerlach setting.
The purpose of this paper is four fold: 1) a brief description of how finite dimensional models arise in quantum control is given; 2) many notions in quantum engineering such as universality of logic gates, hard pulse approximation in NMR spectroscopy, etc., are related to controllability of systems on the unitary groups; 3) recent results of the authors, on constructive controllability, in the class of piecewise constant controls with constraints placed on them, for systems with drift on the unitary groups are sketched; and 4) a new decomposition of SU(2) matrices is provided and used to illustrate how problems caused by periodicity arguments, to address the presence of drift, may be circumvented.
Controlling the decoherence induced by the interaction of quantum system with its environment is a fundamental challenge in quantum technology. Utilizing Floquet theory, we explore the constructive role of temporal periodic driving in suppressing decoherence of a spin-1/2 particle coupled to a spin bath. It is revealed that, accompanying the formation of a Floquet bound state in the quasienergy spectrum of the whole system including the system and its environment, the dissipation of the spin system can be inhibited and the system tends to coherently synchronize with the driving. It can be seen as an analog to the decoherence suppression induced by the structured environment in spatially periodic photonic crystal setting. Comparing with other decoherence control schemes, our protocol is robust against the fluctuation of control parameters and easy to realize in practice. It suggests a promising perspective of periodic driving in decoherence control.