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arXiv:1406.3755 · Physical Review A

Maximum population transfer in a periodically driven quantum system

Pablo M. Poggi, F. J. Arranz, R. M. Benito, F. Borondo, Diego A. Wisniacki

Published Dec 3, 2014• 12 citations
arXivHTMLPDF

Abstract

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate-frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well-defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multilevel systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model.

DOI
10.1103/physreva.90.062108

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We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate-frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well-defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multilevel systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model.
We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.
We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap. The interaction between the atoms is changed by varying the s-wave scattering length in two ways, the cosine and the square-wave modulations. It is found that as the driving frequency increases, the Floquet spectrum exhibits two main features for both modulations, the accumulating and the spreading of the quasienergy levels, which further lead to different dynamical behaviors. The accumulation is associated with collective excitations and the persistent growth of the energy, while the spread indicates that the energy is bounded at all times. The initial scattering length, the driving frequency and amplitude can all significantly change the Floquet spectrum as well as the dynamics. However, the corresponding relation between them is valid universally. Finally, we propose a mechanism for selectively exciting the system to one specific state by using the avoided crossing of two quasienergy levels, which could guide preparation of a desired state in experiments.
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In this paper, this second (and final) step towards the controlled population transfer using modified (i.e. many level system) Rabi oscillations is discussed. The results presented herein can be regarded as an extension of the standard πππ-pulse theory - also strictly valid only in the two level systems - to the coherently driven population oscillations in general many level systems.
Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel quantum states, though their preparation and measurement remains challenging. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured and their behavior as a function of the interaction strength is analyzed in the high- and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time scales that adiabatically connect the initial ground state to different targeted Floquet states. The micromotion that exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations.
The dynamic effect of particles in a periodically driven two-level system is studied with the help of SU(2) symmetry. General closed-form solutions for the quasienergy and the Floquet states are obtained, from which it is found that the avoided quasienergy crossing is confined in the range (−ω/2, ω/2), where ω is the frequency of the driving fields. Of particular interest are high-frequency driving fields, of which it is demonstrated that the exact quasienergy crossings occur at certain values of amplitude and frequency of driving fields, and this phenomenon of dynamic localization should be determined by experiments.
Coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding approximation. In the high-frequency regime within or without multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the special Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. Applying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.