Photon Tunneling Goes Back in Time

Aephraim M. Steinberg

Hiroki Nakamura, Gennady Mil'nikov

In the case of decay rate problem, the potential barrier separates the potentialminimum from the continuum where the system is energetically allowed to go to infinity [see Figure 1.1(b)]. The general formulation developed in Chapter 6 for tunneling splitting can be applied to the present problem with some modifications [44]. The instanton trajectoryq0(τ ) starts in the infinitely remote past at τ = −∞ frompotentialminimum and returns back to the minimum in the infinitely remote future at τ = ∞. This periodic orbit always goes through a turning point on the potential contour V (q) = 0, which can be assumed to occur at τ = 0.

R. Y. Chiao, Paul G. Kwiat, Aephraim M. Steinberg

Martin Esmann, Niklas Teichmann, Christoph Weiß

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.

Aephraim M. Steinberg

Qingyan Ma, Yufei Wang, Zhishuang Liu +1 more

Quantum walks (QWs) have been proposed as powerful tools in a broad range of fields. Discrete-time QW (DTQW) is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. Continuous-time QW (CTQW) can be shown as a limit of DTQW. Many objects, such as atoms, trapped ions etc., have been used to simulate QW. But photon, with the wave-particle duality, is easy to generate and can be easily manipulated in many platforms, such as space light circuits and integrated optical platforms. Silicon-on-insulator (SOI) integrated optics have been widely used, among these self-collimation photonic crystal shows a great potential. In this paper we propose the simulation of CTQWs and DTQWs with self-collimation photonic crystal chip fabricated on 830 nm thick top silicon SOI. Similarity between theory results and simulations are analyzed.