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Physical Review Letters

Electromagnetic Realization of Orders-of-Magnitude Tunneling Enhancement in a Double Well System

I. Vorobeichik, Edvardas Narevicius, Gershon Rosenblum, Meir Orenstein, Nimrod Moiseyev

Published May 2, 2003• 43 citations
Publisher

Abstract

We report on tunneling enhancement in a periodically perturbed double well system. The double well system was realized by a structure of two optical waveguides. The transfer of light power from one waveguide to the another as induced by the periodic variations of the waveguide geometry was investigated. Our experimental measurements show that, in the presence of periodic perturbation, this transfer of light power can be enhanced by more than 500 times. We use an analogy between electromagnetic wave optics and the quantum wave phenomena to provide an experimental support to the theoretical model of tunneling enhancement of a quantum particle, facilitated by its interaction with auxiliary quantum states.

DOI
10.1103/physrevlett.90.176806

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We report on tunneling enhancement in a periodically perturbed double well system. The double well system was realized by a structure of two optical waveguides. The transfer of light power from one waveguide to the another as induced by the periodic variations of the waveguide geometry was investigated. Our experimental measurements show that, in the presence of periodic perturbation, this transfer of light power can be enhanced by more than 500 times. We use an analogy between electromagnetic wave optics and the quantum wave phenomena to provide an experimental support to the theoretical model of tunneling enhancement of a quantum particle, facilitated by its interaction with auxiliary quantum states.
Fractional-photon-assisted tunneling is investigated both analytically and numerically for few interacting ultracold atoms in the double wells of an optical superlattice. This can be realized experimentally by adding periodic shaking to an existing experimental setup [Cheinet et al., Phys. Rev. Lett. 101, 090404 (2008)]. Photon-assisted tunneling is visible in the particle transfer between the wells of the individual double wells. In order to understand the physics of the photon-assisted tunneling, an effective model based on the rotating-wave approximation is introduced. The validity of this effective approach is tested for wide parameter ranges that are accessible to experiments in double-well lattices. The effective model goes well beyond previous perturbation theory approaches and is useful for investigating in particular the fractional-photon-assisted tunneling resonances. Analytic results on the level of the experimentally realizable two-particle quantum dynamics show very good agreement with the numerical solution of the time-dependent Schr\"odinger equation. Far from being a small effect, both the one-half-photon and the one-third-photon resonances are shown to have large effects on the particle transfer.
We report on an experimental demonstration of light transfer in an engineered triple-well optical waveguide structure which provides a classic analog of coherent tunneling by adiabatic passage (CTAP) recently proposed for coherent transport in space of neutral atoms or electrons among tunneling-coupled optical traps or quantum wells [A. D. Greentree et al., Phys. Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)]. The direct visualization of CTAP wave-packet dynamics enabled by our simple optical system clearly shows that in the counterintuitive passage scheme light waves tunnel between the two outer wells without appreciable excitation of the middle well.
We identify a non-Hermitian counterpart of dynamical tunnelling induced by a localised absorbing region in a symmetric confining potential. The absorbing region, described by an imaginary potential barrier, induces an effective double-well structure with a pair of long-lived states that have little population in the barrier. In contrast to the periodic tunnel oscillations through a real barrier, the system slowly evolves towards equal population of the two sides, while the absorbing region remains only weakly populated. We demonstrate this generic mechanism in two continuous potentials, and capture its essence analytically in a minimal 3×33\times 33×3 matrix model. We propose a realistic optical waveguide setup for the experimental observation of the effect.
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We numerically study coherent tunneling oscillations of the particles between two levels in a double-well potential in the presence of anharmonic periodic potentials. Extremely short driving pulses modify the tunneling coefficient to ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}A$, where $\ensuremath{\kappa}$ is the bare tunneling coefficient without the driving field and AAA is the pulse area of the driving wave form. The modulation amplitude of the ${\ensuremath{\kappa}}_{\mathit{eff}}$ gradually decreases as the driving wave form becomes broad and is given by ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}{J}_{0}(A)$ for the sinusoidal modulation, where J0(x){J}_{0}(x)J0​(x) denotes the ordinary Bessel function of order zero. Theoretical derivation of the effective tunneling coefficient ${\ensuremath{\kappa}}_{\mathit{eff}}=\ensuremath{\kappa}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}A$ is also shown for a periodic $\ensuremath{\delta}$ kick with alternating sign by means of the transfer matrix formula.
The analog between an optical waveguide coupler and the quantum-mechanical double-well problem is established. Well-known results of the quantum-mechanical system are applied to the waveguide system. This way of thinking of the waveguide system provides a quick understanding of the coupling mechanism and provides new interpretations of results obtained from Maxwell’s equations. Just as ray opticals give insight into certain types of optics problems, we believe that the tunneling interpretation will give new insight into the field of guided light waves.