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Physical Review A

Controlling quantum coherence by circularly polarized fields

Jiushu Shao, Peter Hänggi A

Published Dec 1, 1997• 37 citations
Publisher

Abstract

In terms of analytical results, we demonstrate that, within most parts in parameter space for a two-level magnetic system, suppression of quantum coherence can be induced by the circularly polarized fields. Low-frequency driving yields a dynamical localization opposite to the case of intermediate-to-high-frequency driving. The intrinsic relation between coherent suppression and the dressed-state level-crossing resonance is revealed.

DOI
10.1103/physreva.56.r4397

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In terms of analytical results, we demonstrate that, within most parts in parameter space for a two-level magnetic system, suppression of quantum coherence can be induced by the circularly polarized fields. Low-frequency driving yields a dynamical localization opposite to the case of intermediate-to-high-frequency driving. The intrinsic relation between coherent suppression and the dressed-state level-crossing resonance is revealed.
This paper reviews our work on dynamical localization of the two-level system (TLS). By mapping the quantum dynamics of a driven TLS to the classical one of a particle experiencing a two-dimensional harmonic force as well as a periodic magnetic field, deep insights into the mechanism of localization have been gained. Using this scheme we are able to obtain the condition for localization of a TLS subject to the linearly polarized field. The localization induced by delta-function pulses and circularly polarized fields has been analytically investigated. It is found that the circularly-polarized-field induced localization can be fully described by the geometry of an ellipse within a unit circle on a complex plane.
A two-level system subjected to a high-frequency driving field can exhibit an effect termed "coherent destruction of tunneling", in which the tunneling of the system is suppressed at certain values of the frequency and strength of the field. This suppression becomes less effective as the frequency of the driving field is reduced, and we show here how the detailed form of its fall-off depends on the phase of the driving, which for certain values can produce small local maxima (or revivals) in the overall decay. By considering a square-wave driving field, which has the advantage of being analytically tractable, we show how this surprising behavior can be interpreted geometrically in terms of orbits on the Bloch sphere. These results are of general applicability to more commonly used fields, such as sinusoidal driving, which display a similar phenomenology.
A two-level system subjected to a high-frequency driving field can exhibit an effect termed "coherent destruction of tunneling", in which the tunneling of the system is suppressed at certain values of the frequency and strength of the field. This suppression becomes less effective as the frequency of the driving field is reduced, and we show here how the detailed form of its fall-off depends on the phase of the driving, which for certain values can produce small local maxima (or revivals) in the overall decay. By considering a square-wave driving field, which has the advantage of being analytically tractable, we show how this surprising behavior can be interpreted geometrically in terms of orbits on the Bloch sphere. These results are of general applicability to more commonly used fields, such as sinusoidal driving, which display a similar phenomenology.
Coherent control of two-level quantum systems is typically achieved using resonant driving fields, forming the basis for qubit operations. Here, we report a mechanism for inducing complete Rabi oscillations in monochromatically driven two-level quantum systems, when the drive frequency is much larger than the Larmor frequency of the qubit. This effect$\unicode{x2015}$Rabi oscillations induced by nonresonant gyrating drive (RING)$\unicode{x2015}$requires a gyrating control field, i.e., an elliptic drive trajectory that encloses a nonzero area per cycle. We illustrate the effect with numerical simulations, and provide an analytical understanding via a simple effective Hamiltonian obtained from Floquet theory and perturbation theory. We show that RING enables coherent oscillations without relying on resonant energy exchange, allows for high-pass noise filtering, provides access to non-Abelian phases in finite magnetic fields. We detail a realization in electrically driven spin-orbit qubits and argue that the RING mechanism enables amplification of the Rabi frequency using the same gate voltage amplitudes at higher drive frequencies. Our results broaden the landscape of quantum control techniques, by highlighting a pathway to achieving coherent oscillations under off-resonant driving conditions.
Resonant radio frequency (rf) control fields have been employed to suppress decoherence in single quantum bits (qubits) encoded in the probability amplitudes of n p fine-structure states in Li Rydberg atoms. As described previously [1], static electric-field tuning of the spin and orbital angular momentum composition of the fine-structure eigenstates enables qubit storage in an approximate decoherence-free subspace in which phase errors due to small stray electric and magnetic fields are strongly suppressed. In addition, it was found that sequences of short electric field pulses could be utilized in a ‘bang-bang’ dynamic decoupling scheme to improve coherence times. We now show that a continuous resonant rf field can also suppress decoherence in this system. The rf-dressed fine-structure states form a more robust basis in which the energy splitting between the component qubit levels is locked to the drive frequency, and decoherence is essentially eliminated. Measurements of the operational range of rf frequency and field strength required to achieve decoherence suppression are in agreement with the predictions of a two-level model.
For a transition ${F}_{e}=0\ensuremath{\leftrightarrow}{F}_{g}=1$ driven by a linearly polarized light and probed by a transverse light, which has two equal circular components and is orthogonal to the linear polarization of the drive field and magnetic field, quantum coherence effects are investigated. Due to the coupling between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency, electromagnetically induced absorption, and the transition from positive to negative dispersion are obtained, as well as the populations coherently oscillating with a pump-probe detuning in the steady state. At the zero pump-probe detuning, the subluminal and superluminal light propagations are predicted. Finally, there exist the large population fluctuations when we vary the pump-probe detuning.