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arXiv:0907.2289 · Journal of the Physical Society of Japan

Observation of Geometric Phases in Quantum Erasers

H. Kobayashi, Shuhei Tamate, Toshihiro Nakanishi, Kazuhiko Sugiyama, Masao Kitano

Published Feb 25, 2011• 18 citations
arXivHTMLPDF

Abstract

We introduce a simple experiment involving a double-slit interferometer by which one can learn basic concepts of quantum interference such as which-path marking, quantum erasers, and geometric phases. Each of them exhibits seemingly mysterious phenomena in quantum physics. In our experiment, we use the double-slit interference of visible light with the polarization as an internal state to demonstrate the disappearance of fringes by which-path marking, recovery of interference using quantum erasers, and the rapid shifting of the fringe pattern induced by the geometric phase. We also present a simple theoretical analysis of an interferometer with an internal state.

DOI
10.1143/jpsj.80.034401

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We introduce a simple experiment involving a double-slit interferometer by which one can learn basic concepts of quantum interference such as which-path marking, quantum erasers, and geometric phases. Each of them exhibits seemingly mysterious phenomena in quantum physics. In our experiment, we use the double-slit interference of visible light with the polarization as an internal state to demonstrate the disappearance of fringes by which-path marking, recovery of interference using quantum erasers, and the rapid shifting of the fringe pattern induced by the geometric phase. We also present a simple theoretical analysis of an interferometer with an internal state.
This experiment explores the quantum phenomenon known as the Quantum Eraser, using a variation of Young’s Double Slit experiment. Young’s Double Slit experiment demonstrates that light acts as a wave by creating an interference pattern when diffracted through two slits. If one measures which of the two slits the photons pass through, then the interference pattern is replaced by a single bright spot, as would be expected for particle-like behaviour. The “Quantum Eraser” eliminates the measurement on the photons, thereby reintroducing the interference pattern observed in Young’s original experiment. The experiment’s first stage saw Young’s Double Slit experiment recreated and an interference pattern was observed. Upon adding two orthogonally polarized filters, the photon’s path was measured, and the interference pattern was removed. By then adding a third filter which was polarized 45O relative to both other polarisers, the interference pattern was somewhat restored. For each experiment, the heights of the peaks in the interference patterns were compared to each other to examine the quality of the reproduced interference pattern based on the original double slit interference pattern. This comparison gave a quantitative result that demonstrated that the Quantum Eraser was able to restore the interference pattern to within 5 standard errors, thereby exemplifying the effect that changing the measurement conditions affects the final measurement.
We report a quantum eraser experiment which actually uses a Young double slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)]. One photon of an entangled pair is incident on a Young double slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under ``delayed erasure'' circumstances.
Youngs double slit experiment is one of the most celebrated achievements in quantum and classical optics; it provides experimental proof of the wave-particle duality of light. When the paths of the double slit are marked with orthogonal polarizations, the path information is revealed and no interference pattern is observed. However, the path information can be erased with a complimentary analysis of the polarization. Here we use hybrid entanglement between photons carrying orbital angular momentum and polarization to show that, just as in Young's experiment, the paths (OAM) marked with polarization do not lead to interference. However, when introducing the eraser (polarizer) which projects the polarization of one of the entangled photons onto a complementary polarization basis, the OAM (paths) are allowed to interfere, leading to the formation of azimuthal fringes whose frequency is proportional to the OAM content carried by the photon.
The quantum eraser experiment was revisited, using entangled photons of visible light in a Hong-Ou-Handel type interferometer with a magnitude two orders higher than before in count rates. We introduced which-path information by polarization and subsequently erasied this information by means of polarizers in front of detectors. It was found that the visibility of the interference fringe is revived from 0% to 88% as the polarizers are changed from 0 ∘^{\circ}∘ to 45 ∘^{\circ}∘ .
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90\ifmmode^\circ\else\textdegree\fi{}. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
The concept of a Hamiltonian-independent geometric phase which depends only on the path of the evolution in parameter space is well established in a broad spectrum of physical phenomena. Recently it has been extended to the so-called `off-diagonal' geometric phase, which is associated with the off-diagonal matrix elements of the evolution. Here we present a polarized neutron interferometer experiment which for the first time allows an explicit observation and quantitative determination of off-diagonal geometric phase shifts: Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.