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Journal of Physics A Mathematical and General

Dynamical localization for two-level systems periodically driven

Daniele Lodi, Marco Maioli, Andrea Sacchetti

Published Dec 16, 2004• 2 citations
Publisher

Abstract

Here, we consider a two-level system driven by an external periodic field. We show that the coherent destruction of tunnelling, as proved by Grossmann and co-workers (1991 Phys. Rev. Lett. 67 516; 1992 Europhys. Lett. 18 571) in the case of a monochromatic field, also appears for any periodic driving field given by an even regular function with zero mean value and satisfying a technical condition on the zeros of this function.

DOI
10.1088/0305-4470/38/2/l01

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Here, we consider a two-level system driven by an external periodic field. We show that the coherent destruction of tunnelling, as proved by Grossmann and co-workers (1991 Phys. Rev. Lett. 67 516; 1992 Europhys. Lett. 18 571) in the case of a monochromatic field, also appears for any periodic driving field given by an even regular function with zero mean value and satisfying a technical condition on the zeros of this function.
Some aspects of quantum tunneling of a particle in a double-well potential periodically driven by an external force are studied within the two-level approximation. A closed expression for the temporal evolution of the occupation probability is obtained in the limit of large-amplitude oscillation by the transfer-matrix formalism. The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is made clear from a viewpoint of interference at periodic level crossings.
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.
Some aspects of quantum tunneling of a particle in a double-well driven by an external field are studied within the two level approximations. The localization problems of particles are studied when the system are driven by far off-resonance and/or strong laser fields. A nonperturbative expression of the time evolution of system regardless of the coupling strength value is obtained, in the strong field regime, because of the asymptotic behavior of the Bessel function, the conclusion remain valid even when the far off-resonance condition is not fulfilled. That, when the zeros Bessel function vanishes, coherent destruction of tunneling will occur.Instead of discuss the two limitations one by one, simple expression with profound meaning is given.
Coherent Control of Two-level Systems with Periodic NNN-Steps Driving Fields
In this work, we derive the exact solutions of the dynamical equation, which can describe all two-level Hermitian systems driven by periodic NNN-steps driving fields. The solutions are a set of quasi-periodic functions, and the expressions of the amplitudes and phases are obtained in the frequency-domain. Particularly, we develop a general formalism for the effective Hamiltonian without any approximations, and give the validity range according to the transition probability of the micromotion operator. With the guidance of the exact solutions and the effective Hamiltonian, we find that the coherent destruction of tunneling phenomenon, the resonance phenomenon, and the beat-frequency phenomenon can emerge in this system. Finally, some applications are demonstrated in quantum information processing by periodic NNN-steps driving fields.