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arXiv:2102.11851 · New Journal of Physics

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

Marjan Mirahmadi, Burkhard Schmidt, Břetislav Friedrich

Published May 13, 2021• 9 citations
arXivHTMLPDF

Abstract

Abstract We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work (2014 Front. Phys. 2 37, 2017 Eur. Phys. J. D 71 149). This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.

DOI
10.1088/1367-2630/ac00d6

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Abstract We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work (2014 Front. Phys. 2 37, 2017 Eur. Phys. J. D 71 149). This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.
We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, Δτ, with respect to the rotational period of the rotor, τr. In the sudden, non-adiabatic limit, Δτ ≪ τr, we derive analytic expressions for the rotor’s wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding time-dependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, Δτ > τr, where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of population quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration.
Abstract We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. The possibility of introducing an adiabatic modulation of the driving protocol is investigated by considering a slow evolution of the instants when the sequence of potentials is switched on/off. By assuming that the slow and fast timescales in the problem can be decoupled, we derive the stroboscopic (effective) Hamiltonian for a four-step driving sequence up to the first order in perturbation theory and apply this approach to a rigid rotor, where the adiabatic modulation of the driving protocol is chosen to produce an evolving emergent magnetic field that interacts with the rotor's spin. The emergence of diabolical points and diabolical loci in the parameter space of the effective Hamiltonian is examined. Further, we study the topological properties of the maps of the adiabatic paths in the parameter space to the eigenspace of the effective Hamoiltonian. In effect, we obtain a technique to tune the topological properties of the eigenstates by selecting various adiabatic evolutions of the driving protocol characterized by different paths in the parameter space.
Optimal control simulations are performed for orientation and entanglement of two dipole-dipole coupled identical quantum rotors. The rotors at various fixed separations lie on a model non-interacting plane with an applied control field. It is shown that optimal control of orientation or entanglement represents two contrasting control scenarios. In particular, the maximally oriented state (MOS) of the two rotors has a zero entanglement entropy and is readily attainable at all rotor separations. Whereas, the contrasting maximally entangled state (MES) has a zero orientation expectation value and is most conveniently attainable at small separations where the dipole-dipole coupling is strong. It is demonstrated that the peak orientation expectation value attained by the MOS at large separations exhibits a long time revival pattern due to the small energy splittings arising form the extremely weak dipole-dipole coupling between the degenerate product states of the two free rotors. Moreover, it is found that the peak entanglement entropy value attained by the MES remains largely unchanged as the two rotors are transported to large separations after turning off the control field. Finally, optimal control simulations of transition dynamics between the MOS and the MES reveal the intricate interplay between orientation and entanglement.
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.
We investigate the dynamics of interacting quantum planar rotors as the building blocks of gear trains and nanomachinery operating in the quantum regime. Contrary to a classical hard-gear scenario of rigidly interlocked teeth, we consider the coherent contactless coupling through a finite interlocking potential, and we study the transmission of motion from one externally driven gear to the next as a function of the coupling parameters and gear profile. The transmission is assessed in terms of transferred angular momentum and transferred mechanical work. We highlight the quantum features of the model such as quantum state revivals in the interlocked rotation and interference-enhanced transmission, which could be observed in prospective rotational optomechanics experiments.
We report a theoretical study of the optical centrifuge acceleration of an asymmetric top molecule interacting with an electric static field by solving the time-dependent Schr\"odinger equation in the rigid rotor approximation. A detailed analysis of the mixing of the angular momentum in both the molecular and the laboratory fixed frames allows us to deepen the understanding of the main features of the acceleration process, for instance, the effective angular frequency of the molecule at the end of the pulse. For the case of the SO2{\mathrm{SO}}_{2}SO2​ molecular super-rotor, we show numerically that it rotates around one internal axis and that its dynamics is confined to the plane defined by the polarization axis of the laser, in agreement with experimental findings. Furthermore, we consider the orientation patterns induced by the dc field, showing the characteristics of their structure as a function of the strength of the static field and the initial configuration of the fields.