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Quantum Optical Aspects of Topological Phases, Such as Berry's Phase

R. Y. Chiao

Published Nov 10, 1993• 0 citations

Abstract

The contract was for performing experiments on a recently discovered topological phase factor known as 'Berry's phase.' We proposed to examine this phase at both the quantum and classical levels, in its various manifestations. The goals of this contract were successfully accomplished; in particular, we succeeded in demonstrating this phase at the single photon level, thereby demonstrating that this phase did not originate at the classical level. Possible applications of this phase were explored. A two-photon light source, in the form a parametric down-converter of uv laser photons into highly correlated red photons was successfully constructed, and coincidence counting techniques were successfully applied to the detection of the conjugate signal and idler red photons. This formed the experimental basis for the examination of not only Berry's phase, but of the energy-time uncertainty relations, the Franson experiment, the measurement of the tunneling time of the photon, the quantum eraser, and other optical phenomena closely related to the Einstein-Podolsky- Rosen 'paradox.'

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Berry's phases in optics have been studied extensively, and examples are typically discussed in quantum-mechanical terms. To our knowledge, however, experimental demonstrations have been performed only at the classical level. We report the first observation of a Berry's phase at the single-photon level. In particular, we investigated Pan-charatnam's phase,1 which is acquired whenever light is taken through a closed cycle of polarization states, e.g., with various retardation plates. Correlated pairs of linearly-polarized photons were produced by parametric fluorescence in a UV-pumped KDP crystal. One of each pair was directed into a photomultiplier tube (PMT1). The other was directed into a Michelson interferometer, one arm of which contained two quarter-wave plates, that was used to generate a Berry's phase.

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The contract was for performing experiments on a recently discovered topological phase factor known as 'Berry's phase.' We proposed to examine this phase at both the quantum and classical levels, in its various manifestations. The goals of this contract were successfully accomplished; in particular, we succeeded in demonstrating this phase at the single photon level, thereby demonstrating that this phase did not originate at the classical level. Possible applications of this phase were explored. A two-photon light source, in the form a parametric down-converter of uv laser photons into highly correlated red photons was successfully constructed, and coincidence counting techniques were successfully applied to the detection of the conjugate signal and idler red photons. This formed the experimental basis for the examination of not only Berry's phase, but of the energy-time uncertainty relations, the Franson experiment, the measurement of the tunneling time of the photon, the quantum eraser, and other optical phenomena closely related to the Einstein-Podolsky- Rosen 'paradox.'

Berry's phases in optics have been studied extensively, and examples are typically discussed in quantum-mechanical terms. To our knowledge, however, experimental demonstrations have been performed only at the classical level. We report the first observation of a Berry's phase at the single-photon level. In particular, we investigated Pan-charatnam's phase,1 which is acquired whenever light is taken through a closed cycle of polarization states, e.g., with various retardation plates. Correlated pairs of linearly-polarized photons were produced by parametric fluorescence in a UV-pumped KDP crystal. One of each pair was directed into a photomultiplier tube (PMT1). The other was directed into a Michelson interferometer, one arm of which contained two quarter-wave plates, that was used to generate a Berry's phase.

At what level of energy does a classical experiment become quantum mechanical? Where does classical electromagnetic theory apply and where do we have to turn to quantum optics? Is there a sharp line between these two models? And if so: why, and why at this level? Or if not: what are the common features of the formalisms, and what are the di erences? With our upcoming experimental work, we hope to be able to gain some insight into these challenging questions. The starting point is an investigation of the results from an ordinary Bell type experiment showing entanglement between two photons, where the photons has been generated using spontaneous parametric down conversion, and the same experiment but with a classical source where two highly attenuated pulses are combined. Here we will present in detail our planned experiment.

Two landmark photon correlation effects, the Einstein-Podolsky-Rosen (EPR) correlation in a quantum entangled source and the Hanbury-Brown-Twiss (HBT) correlation in a thermal light source, have long attracted great attention from the physics community. Here, we report the experimental generation of an all-purpose photon-correlation source called holographic thermal light, including both HBT-type and EPR-like correlations, with thermal photons over a wide spectral range (from UV to IR) and a typical polarization combination. All two-photon correlations are established in the framework of linear optics. Interestingly, the topological structures of the diffraction patterns of the sources are very similar to those in type-I and type-II spontaneous parametric down-conversion (SPDC) processes. Holographic thermal light with multiple degrees of freedom will establish a quantum-inspired, high-brightness, low-cost classical demonstration platform capable of facilitating various quantum imaging applications at the single-photon level.

Barreto Lemos et al. [Nature 512, 409-412 (2014)] reported an experiment in which a non-degenerate parametric downconverter and a non-degenerate optical parametric amplifier--used as a wavelength-converting phase conjugator--were employed to image object transparencies in a manner akin to ghost imaging. Their experiment, however, relied on single-photon detection, rather than the photon-coincidence measurements employed in ghost imaging with a parametric downconverter source. More importantly, their system formed images despite the photons that passed through the object never being detected. Barreto Lemos et al. interpreted their experiment as a quantum imager, as assuredly it is, owing to its downconverter's emitting entangled signal and idler beams. We show, however, that virtually all the features of their setup can be realized in a quantum-mimetic fashion using classical-state light, specifically a pair of bright pseudothermal beams possessing a phase-sensitive cross correlation. Owing to its much higher signal-to-noise ratio, our bright-source classical imager could greatly reduce image-acquisition time compared to that of Barreto Lemos et al.'s quantum system, while retaining the latter's ability to image with undetected photons.