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Physical Review A

Role of a nontrivial quantum phase in the dynamical band gap collapse

Y. Mizumoto, Yōsuke Kayanuma

Published Sep 6, 2012• 2 citations
Publisher

Abstract

In the quasi-one-dimensional lattice system with a band gap, the effective magnitude of the gap may be reduced, and even collapsed, by applying a monochromatic oscillating external field. The internal relationship between this dynamical band gap collapse (BGC) and the well-known coherent destruction of tunneling (CDT) in the periodically driven two-state model is clarified from a unified point of view. The destructive interference between the resonant scattering paths plays an essential role in both the dynamical BGC and the CDT. This leads to the suppression of the Bragg reflection in the momentum space for the dynamical BGC, and to the suppression of tunneling in the coordinate space for the CDT.

DOI
10.1103/physreva.86.035601

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In the quasi-one-dimensional lattice system with a band gap, the effective magnitude of the gap may be reduced, and even collapsed, by applying a monochromatic oscillating external field. The internal relationship between this dynamical band gap collapse (BGC) and the well-known coherent destruction of tunneling (CDT) in the periodically driven two-state model is clarified from a unified point of view. The destructive interference between the resonant scattering paths plays an essential role in both the dynamical BGC and the CDT. This leads to the suppression of the Bragg reflection in the momentum space for the dynamical BGC, and to the suppression of tunneling in the coordinate space for the CDT.
This paper investigates the manipulation of coherent quantum tunneling by controlling second-order coupling in zigzag-shaped lattice arrays with only one site periodically driven against the others. Different from normal coherent destruction of tunneling (CDT), we propose a surprisingly large and nontrivial effect of second-order coupling on broadened CDT essentially attributed to avoided level crossings and localized Floquet states. Moreover, our results at high-frequency approximation supported by exact numerical ones demonstrate that the extent to which the normal CDT is broadened depends on the separation of quasienergy levels in the vicinity of zeros of ${J}_{0}(A/\ensuremath{\omega})$. Remarkably, beyond the intensity of second-order coupling, the lattice size and its parity also significantly influence Floquet dynamics by either facilitating or suppressing tunneling probabilities, which in essence are also determined by noncrossing quasienergies and localized Floquet states. These findings substantially extend the theory of normal CDT, unveil the intrinsic physics behind broadened CDT, and open up an exciting possibility for quantum state control.
We study a system of three coherently coupled states, where one state is shifted periodically against the other two. We discover that this system possesses a dark Floquet state that has zero quasi-energy and negligible population at the intermediate state. This dark Floquet state manifests itself dynamically in terms of the suppression of inter-state tunneling, a phenomenon known as coherent destruction of tunneling (CDT). Owing to its different origin from the CDT found in a two-state-driven system, we call it dark CDT. At a high-frequency limit for the periodic driving, this Floquet state reduces to the well-known dark state. Our results can be generalized to systems with more states and be verified with easily implemented experiments within the current technologies.
We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of SU(2) operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the SU(2) operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level crossings.
The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically.In our findings,when the system is with only repulsive twobody interactions or only three-body interactions,the tunneling will be suppressed;while in the case of the coupling between two- and three-body interactions,the tunneling can be either suppressed or enhanced.Particularly,when attractive three-body interactions are twice large as repulsive two-body interactions,CDT occurs at isolated points of driving force,which is similar to the linear case.Considering different interaction,the system can experience different transformation from coherent tunneling to coherent destruction of tunneling(CDT).The quasi-energy of the system as the function of the periodically driving force shows a triangular structure,which provides a deep insight into the tunneling dynamics of the system.
Abstract The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system.
The tunneling dynamics of a dipolar bosonic gas with repulsive interactions in a periodically driven triple-well are investigated. Because of the coupled effect of long-range dipole-dipole interaction and the short-range of on-site interaction, the increase of the repulsive atomic interactions can either suppress tunneling or enhance tunneling and, thus, the system experiences rich coherent tunneling(CT)-coherent destruction of tunneling (CDT) transitions. In particular, as the repulsive atomic interactions increase, the system can undergo CT-CDT-CT-CDT or CDT-CT-CDT-CT-CDT transitions. This cannot occur in non-dipolar gas, where the increase of the repulsive atomic interaction only suppress tunneling and the system can only undergo CT-CDT transition. We further present a good understanding of the results with the help of the quasi-energy spectrum of the system.