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Modern Physics Letters B

CONTROLLING THE QUANTUM ROTOR WITH A TIME-DEPENDENT MAGNETIC FLUX

Alexandre G. M. Schmidt, Bruno N. Martins

Published Jun 10, 2009• 1 citation
Publisher

Abstract

We study the possibility of controlling a quantum rotor interacting with a time-dependent external field, namely, using a continuous or a piecewise continuous (bang-bang control) magnetic flux. Using the exact eigenfunctions we show how to steer a wave-packet constructed as a superposition of these eigenstates. In the first case we show how to steer a Gaussian wave-packet (GWP) to two other positions: one of them which would not be realized if the evolution were free, and the second is the one where wave-packet revival takes place. In the piecewise approach we implement a kind of tracking control, i.e. before steering it to the final target we achieve another given GWP.

DOI
10.1142/s0217984909019892

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We study the possibility of controlling a quantum rotor interacting with a time-dependent external field, namely, using a continuous or a piecewise continuous (bang-bang control) magnetic flux. Using the exact eigenfunctions we show how to steer a wave-packet constructed as a superposition of these eigenstates. In the first case we show how to steer a Gaussian wave-packet (GWP) to two other positions: one of them which would not be realized if the evolution were free, and the second is the one where wave-packet revival takes place. In the piecewise approach we implement a kind of tracking control, i.e. before steering it to the final target we achieve another given GWP.
The time evolution of a Gaussian wave packet of an electron, which is confined in a quantum dot subjected to uniform magnetic fields, is analytically studied in terms of the exact Feynman kernel. The central position of the wave packet follows the classical trajectory. Although the motion of the central position is aperiodic due to its dual period, the variance of the probability density changes periodically. If the shape of the initial wave packet is the same as that of the wave function of the ground state, its shape never alters. For more general systems in which the periodic full revival of electron wave packets is realized, the characteristic of energy eigenvalues is discussed.
The techniques of controlling the free evolution of a nonrelativistic charged particle by time-dependent magnetic fields are proposed and the possibility of more general operations upon the Schrödinger wave packet is discussed. It is found that a properly programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to ‘‘go back in time’’ to recover its past shape. Our manipulation prescriptions hold also for nonrelativistic particles of arbitrary spin.
We study control of wave packets with a finite accuracy, approaching it as quantum information processing. For a given control resolution, we define the analogs of several quantum bits within the shape of a single wave packet. These bits are based on wave packet symmetries. Analogs of one- and two-bit gates can be implemented using only free wave packet evolution and coordinate-dependent ac Stark shifts applied at the moments of fractional revivals. As in quantum computation, the gates form a logarithmically small set of basis operations which can be used to approximate any unitary transformation desired for quantum control of the wave packet dynamics. Numerical examples show the application of this approach to control vibrational wave packet revivals.
Abstract The tracking control of quantum correlations between two coupled qubits is analyzed, where only one of the qubits is coupled to a Markovian environment. Such a system is a generalized model that can be used, for example, to study the problem of a nuclear spin coupled to the electron spin exposed to the environment. Using an external control field, we increase the time for which the system remains coherent and entangled. The control field is an external potential applied to the system, which contains two adjustable parameters, the intensity and the phase of the field. Furthermore, we present quantum control protocols with different targets. First, for population control of both qubits, second for the coherence control of both two-level systems, and finally for the control of entanglement. Due to analytical for X states the target function can directly be identified with the entanglement. Furthermore, we have shown that when smaller dissipation rates are considered, the control method generates larger stable entanglement between the qubits.
Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations for the observables. However, fields found in this manner are often plagued by undesirable singularities. In this paper we consider a planar molecular rotor and derive singularity-free tracking expressions for the fields that steer the expectation of the orientation of the rotor along the desired trajectories in time. Simulations are presented that utilize two orthogonal control electric fields to drive the orientation of the rotor along a series of designated tracks.