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Journal of Physics A Mathematical and Theoretical

Multi-polarization quantum control of rotational motion through dipole coupling

Gabriel Turinici, HERSCHEL A. RABITZ

Published Feb 18, 2010• 9 citations
Publisher

Abstract

Abstract. In this work we analyze the quantum controllability of rotational motion under the influence of an external laser field coupled through a permanent dipole moment. The analysis takes into consideration up to three polarization fields, but we also discuss the consequences for working with fewer polarized fields. Multi-polarization quantum control of rotational motion through dipole coupling 2

DOI
10.1088/1751-8113/43/10/105303

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Abstract. In this work we analyze the quantum controllability of rotational motion under the influence of an external laser field coupled through a permanent dipole moment. The analysis takes into consideration up to three polarization fields, but we also discuss the consequences for working with fewer polarized fields. Multi-polarization quantum control of rotational motion through dipole coupling 2
This chapter describes a versatile technique to control molecular rotation and translation. The technique is based on the combined effect of external electric fields that act concurrently on the molecular permanent and induced dipole moments. This synergistic effect arises for any polar molecule, as only an anisotropic polarizability, along with a permanent dipole moment, is required. This is always available in polar molecules. The effect of the combined fields can be achieved either by superimposing an electrostatic and a far-off resonant optical field (i.e., one that supplies electric field strength but does not cause transitions) that act, respectively, on the molecule's permanent and induced electric dipole, or by making use of a unipolar electromagnetic pulse that seizes the permanent and induced dipole moments simultaneously. If the combined electric fields are homogeneous, only molecular rotation is affected, whereas inhomogeneous fields affect both molecular rotation and translation. As noted in the chapter, the ability to manipulate molecular rotation and translation has wide-ranging applications – in research areas as diverse as reaction dynamics, spectroscopy, higher harmonic generation and molecular orbital imaging, the focusing and trapping of molecules, as well as quantum simulation and computing.
In a typical experiment aiming to control quantum dynamics phenomena, each molecule experiences the same temporal laser field, but with an amplitude that depends on the spatial location and orientation of the molecule in the laser beam. It is proved under commonly arising conditions that at least one optimal laser field exists which will control all molecules in the sample, regardless of their orientation or spatial location. The optimal laser field may consist of a multipolarization control containing up to three orthogonal, independently shaped components. The analysis also includes the prospect of multipartite control where the field couples distinct groupings of states (e.g., multiple vibronic states), but without direct coupling within a group of states. This conclusion shows that achieving quantum control is not a matter of striking a compromise over the sample diversity, but rather a task subject to optimization to reach the highest possible level of control for all molecules in the sample.
The main goal of this paper is to analyze a two-photon degenerate four-wave-mixing process that occurs in an isotropic media modeled by homogeneously broadened two-level systems having unequal permanent dipole moments and subject to rotational diffusion. Our theoretical treatment is based upon a third-order perturbative solution of the density-matrix equations and does not require the rotating-wave approximation. The medium being excited by three stationary fields, we give an analytical expression of the macroscopic polarization up to the third order, including permanent dipole moments, orientational diffusion, and field polarizations. We apply these general results to the description of a degenerate four-wave-mixing process by selecting, in the expressions, the contributions in the direction ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$-${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$+${\mathbf{k}}_{\ensuremath{\gamma}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\alpha}}}$, ${\mathbf{k}}_{\mathrm{\ensuremath{\beta}}}$, and ${\mathbf{k}}_{\ensuremath{\gamma}}$ being, respectively, the wave vectors of the exciting fields. We show that the two-photon degenerate four-wave mixing is dependent on the permanent dipole moments and is not present if these dipole moments are equal or zero. We analyze the influence of rotational diffusion. Different cases of field polarizations are also considered, and we discuss a comparison of the well-known one-photon degenerate four-wave-mixing process and this two-photon process. This process is also discussed in the particular case of phase conjugation.
Rotation is a fundamental degree of freedom of isolated molecules and a property that affects their interaction with other physical systems. This article reviews theory and a multitude of experimental methods aiming to control molecular rotation. Applications include studies of a variety of single particle quantum phenomena, controlled molecular collisions, and rotational dynamics in solvents, as well as the perspective use of long distance dipolar interactions to simulate many-body Hamiltonians.
Abstract A novel design for an electromagnetic trap is proposed for confinement of neutral particles having a permanent electric dipole moment. The device uses a combination of a sextupole electric and quadrupole magnetic fields superimposed with a strong constant electric field perfectly aligned along the z-axis. We use the extended dipole model to study the dynamics of particle in this position dependent electromagnetic field. The motion of the centre of mass of the dipole is nonlinearly coupled with its rotation. We find three families of particular solutions for which the orbits are periodic or quasiperiodic. They correspond to the particular cases when the whole energy is accumulated in either translational or rotational degrees of freedom. Stability analysis of chosen particular solutions provides trapping conditions. We present several numerical simulations which illustrate trapping and confinement of an electric dipole in the proposed trap. These simulations were performed for three kinds of polar particles and various fields selections. We hope that the proposed model allows experimental physicists to apply a wide variety of non-destructive methods for manipulation, detection and analysis of trapped particles.
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical and the other where the center-of-mass motion is treated classically, while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion and that it departs from the Mathieu equation solution found for atomic ions. For the case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.