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Molecular Crystals and Liquid Crystals

Simulating Quantum-Mechanical Barrier Tunneling Phenomena with a Nematic-Liquid-Crystal-Filled Double-Prism Structure

Andreas C. Liapis, George M. Gehring, Svetlana G. Lukishova, Robert W. Boyd

Published May 24, 2014• 6 citations
Publisher

Abstract

We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hänchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.

DOI
10.1080/15421406.2014.918084

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We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hänchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.
We present here our results on using liquid crystals in experiments with nonclassical light sources: (1) single-photon sources exhibiting antibunching (separation of all photons in time), which are key components for secure quantum communication systems, and (2) entangled photon source with photons exhibiting quantum interference in a Hong-Ou- Mandel interferometer. In the first part, cholesteric liquid crystal hosts were used to create definite circular polarization of antibunched photons emitted by nanocrystal quantum dots. If the photon has unknown polarization, filtering it through a polarizer to produce the desired polarization for quantum key distribution with bits based on polarization states of photons will reduce by half the efficiency of a quantum cryptography system. In the first part, we also provide our results on observation of a circular polarized microcavity resonance in nanocrystal quantum dot fluorescence in a 1-D chiral photonic bandgap cholesteric liquid crystal microcavity. In the second part of this paper with indistinguishable, time-entangled photons, we demonstrate our experimental results on simulating quantum-mechanical barrier tunnelling phenomena. A Hong-Ou-Mandel dip (quantum interference effect) is shifted when a phase change was introduced on the way of one of entangled photons in pair (one arm of the interferometer) by inserting in this arm an electrically controlled planar-aligned nematic liquid crystal layer between two prisms in the conditions close to a frustrated total internal reflection. By applying different AC-voltages to the planar-aligned nematic layer and changing its refractive index, we can obtain various conditions for incident photon propagation – from total reflection to total transmission. Measuring changes of tunnelling times of photon through this structure with femtosecond resolution permitted us to answer some unresolved questions in quantum-mechanical barrier tunnelling phenomena.
We present here our results on using liquid crystals (LCs) in experiments with nonclassical light sources: (1) single-photon sources exhibiting antibunching (separation of all photons in time), which are key components for secure quantum communication systems and (2) entangled photon source with photons exhibiting quantum interference in a Hong–Ou–Mandel interferometer. In the first part, both nematic and cholesteric liquid crystal (CLC) hosts were used to create definite linear or circular polarization of antibunched photons emitted by different types of single emitters (dye molecules, nanocrystal quantum dots (NQDs), nanodiamonds with color centers, etc.). If the photon has unknown polarization, filtering it through a polarizer to produce the desired polarization for quantum key distribution with bits based on polarization states of photons will reduce by half the efficiency of a quantum cryptography system. In the first part, we also provide our results on observation of a circular polarized microcavity resonance in NQD fluorescence in a 1-D chiral photonic bandgap CLC microcavity. In the second part of this paper with indistinguishable, time-entangled photons, we demonstrate our experimental results on simulating quantum mechanical barrier tunneling phenomena. A Hong–Ou–Mandel dip (quantum interference effect) is shifted when a phase change was introduced on the way of one of entangled photons in pair (one arm of the interferometer) by inserting in this arm an electrically controlled planar-aligned nematic LC layer between two prisms in the conditions close to a frustrated total internal reflection. By applying different AC-voltages to the planar-aligned nematic layer and changing its refractive index, we can obtain various conditions for incident photon propagation – from total reflection to total transmission. Measuring changes of tunneling times of photon through this structure with femtosecond resolution permitted us to answer some unresolved questions in quantum mechanical barrier tunneling phenomena.
We report a prediction for the delay measured in an optical tunneling experiment using Hong-Ou-Mandel (HOM) interference, taking into account the Goos-Hänchen shift generalized to frustrated total internal reflection situations. We precisely state assumptions under which the tunneling delay measured by an HOM interferometer can be calculated. We show that, under these assumptions, the measured delay is the group delay, and that it is apparently 'superluminal' for sufficiently thick air gaps. We also show how an HOM signal with multiple minima can be obtained, and that the shape of such a signal is not appreciably affected by the presence of the optical tunneling zone, thus ruling out the explanation of the anomalously short tunneling delays in terms of a reshaping of the wavepacket as it goes through the tunneling zone. Finally, we compare the predicted tunneling delay to a relevant classical delay and conclude that our predictions involve no non-causal effect.
The propagation of the quantum states of light in dispersive and anisotropic media is a fundamental problem in quantum optics. We present a unified theoretical framework for the propagation of the quantum states of light in voltage-controlled nematic liquid crystals, incorporating both material dispersion and electrically tunable birefringence. By treating photons as finite-bandwidth wave packets, we derive analytical expressions for group velocoity, temporal walk-off, and phase evolution of orthogonally polarized modes. The results demonstrate that nematic liquid crystals can serve as electrically tunable quantum photonic devices capable of manipulating photon arrival times, polarization correlations, and temporal indistinguishability of entangled photon pairs. These results show the direct relevance to quantum communication and photonic quantum information processing.
Frustrated total internal reflection is considered as the classical analog of quantum-mechanical tunneling. Here the tunneling time in frustrated total internal reflection is discussed. It is shown that the phase time allows for vanishing and negative barrier traversal times. The tunneling time is shown to be dominated by a time scale based on the Goos-H\"anchen shift. The role of further nonspecular deformations of the transmitted beam is addressed. The resulting tunneling times are compared with experimental data.