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arXiv:1305.1197 · New Journal of Physics

Coherent destruction of tunneling and dark Floquet state

Xiaobing Luo, Liping Li, Li You, Biao Wu

Published Jan 9, 2014• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/16/1/013007

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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.
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.
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.
We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using the spectrum of the nonmodulated Hamiltonian. Furthermore, we use Floquet analysis to explain the coherent destruction of tunneling (CDT) occurring in a large-amplitude modulated system. Finally, we present two ways to create a NOON state (a superposition of NNN particles in mode 1 with zero particles in mode 2 and vice versa). One is based on a coherent oscillation caused by detuning from a partial CDT. The other makes use of an adiabatic variation of the modulation frequency. This results in a Landau-Zener type of transition between the ground state and a NOON-like state.
We investigate the quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasienergies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasienergy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second-quantized model, we find also a triangular structure in the quantum quasienergy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasienergies is further explored by a semiclassical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasienergies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.