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Interferometria quântica com cavidades

Caio Olindo de Miranda e Silva

Published May 26, 2006• 0 citations

Abstract

Using type I parametric down conversion, coincidence detection and the Hong-Ou-Mandel interferometer modified with the introduction of a Fabry-Perot cavity in one of its arms, we map the temporal distribution of the photon (one of those generated by the parametric down conversion), that pass through the cavity and we also measure the displacement of the peak of its temporal distribution after the cavity, in the photon longitudinal coherence length greater than the cavity length regime. We study the opposite regime, that is, where the cavity length is greater than the photon coherence length, and we found coalescence and anti-coalescence effects. The coincidence pattern, in this regime, is formed, in general, by peaks and dips which born from a constant value platform. The platform value depends only on the mirrors (that form the cavity) transmission and reflection coefficients, and it is proportional to the number of photons that cross the cavity. We complicated a little more, still in the cavity length greater than the photons coherence length regime, putting two cavities (each one in each of the interferometer arm), and we study the coincidence pattern for this case. The coincidence pattern is essentially the same of that found for the one cavity case. One of the main differences is that at this time the platform value depends also on the cavities lengths, and do not represents the number of the photons that cross the cavities anymore. We can simulate a C-NOT gate using this apparatus.Finally, using type II parametric down conversion, we study the case of two cavities which the transmission coefficients are polarization dependents. With this apparatus it is possible to distinguish conclusively the four Bell states: +, , _+ and _.

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Using type I parametric down conversion, coincidence detection and the Hong-Ou-Mandel interferometer modified with the introduction of a Fabry-Perot cavity in one of its arms, we map the temporal distribution of the photon (one of those generated by the parametric down conversion), that pass through the cavity and we also measure the displacement of the peak of its temporal distribution after the cavity, in the photon longitudinal coherence length greater than the cavity length regime. We study the opposite regime, that is, where the cavity length is greater than the photon coherence length, and we found coalescence and anti-coalescence effects. The coincidence pattern, in this regime, is formed, in general, by peaks and dips which born from a constant value platform. The platform value depends only on the mirrors (that form the cavity) transmission and reflection coefficients, and it is proportional to the number of photons that cross the cavity. We complicated a little more, still in the cavity length greater than the photons coherence length regime, putting two cavities (each one in each of the interferometer arm), and we study the coincidence pattern for this case. The coincidence pattern is essentially the same of that found for the one cavity case. One of the main differences is that at this time the platform value depends also on the cavities lengths, and do not represents the number of the photons that cross the cavities anymore. We can simulate a C-NOT gate using this apparatus.Finally, using type II parametric down conversion, we study the case of two cavities which the transmission coefficients are polarization dependents. With this apparatus it is possible to distinguish conclusively the four Bell states: +, , _+ and _.

We herein study the rate of coincidences in a Hong–Ou–Mandel interferometer exit whose arms have been supplemented by two optical cavities which reflect the photons generated by parametric down conversion. The fourth-order correlation function at the beam-splitter exit is calculated. In the regime where the coherence length of the photons is larger than the cavities lengths, photon coalescence and anti-coalescence interferences are observed. In particular, complete anti-coalescence between photons generated by parametric down conversion Type I is evidenced. The photons reshaping as they are reflected by the cavities are also studied and path diagrams for the indistinguishable processes that lead to quantum interference are presented.

The interference of photons with the same polarization generated by spontaneous parametric down conversion in a Hong-Ou-Mandel interferometer, after one of them passed through a symmetric cavity, is demonstrated experimentally. In the regime where the cavity length is larger than the one-photon coherence length, photon coalescence and anticoalescence interference is observed. We show that by changing the cavity length, coincidence peaks can be transformed in dips and vice versa, even though the coherence length of the photon wave packet is smaller than the cavity length. The photon pair coalescence or anticoalescence at the beam splitter can be controlled by changing the length of the cavity.

Nowadays semiconducting cavities are built having thickness less than one micron, some of them filled with absorbing mediums like quantum wells, what lend to them very peculiar properties, mainly in what is referred to their interaction with light. This work is dedicated to the theoretical study, by means of interferometry, of the interaction between photons and empty microcavities, and will serve as a preliminar study for posterior experimental and theoretical works with filled microcavities. We made use of pairs of twin photons generated in type I non-colinear parametric down conversion as ligth source and the Fabry-P´erot cavity of parallel semi-mirrors as a cavity model. We also used the Hong-Ou-Mandel interferometer, puting the microcavity in one of its arms and an optic path compensator device in the other. The strong temporal correlation that exists between the twin photons enables measuring the averaged life time of the photon inside the cavity, that is, the time spent by the photon to cross it.

We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam splitter exit is calculated. In the regime where the cavities lengths are larger than the one-photon coherence length, photon coalescence and anticoalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. The construction of an optical XOR gate is discussed as an application for the Hong-Ou-Mandel interferometer with two cavities.

We study the Hong-Ou-Mandel interferometer in the regime of spontaneous parametric down-conversion with high pump beam power at the crystal. In this regime one and two photons from a pump pulsed laser beam generate one and two pairs of photons, respectively. These photons are then directed to the beam splitter of the interferometer and detected at its exit in coincidence. An interesting phenomenon is observed: The reduction of the visibility of the Hong-Ou-Mandel coincidence peak (or dip) with the increase of pump power. We study the relation between the visibility of the fourth-order interference pattern and the power of the pumping laser beam for type I and type II phase-matching crystals. Our theoretical calculations are in good agreement with the experimental results.

In the nonlinear optical process of spontaneous parametric down conversion, a laser beam incident in a nonlinear crystal, generates pairs of photons. In this process energy and momentum are conserved. This process is used in diverse studies in Quantum Optics. We worked with state of the parametric down-conversion process where two and four photons are generated. This state is used in the Hong-Ou-Mandel interferometer (HOM). The use of the HOM interferometer for studies with two entangled photons is vast. An intriguing phenomenon, observed in this and many other interferometer that uses optic pumping, is the reduction of the visibility of the tax of coincidence of photons, in the exit of the interferometer, with the increase of the power of the laser pump. In this work we study the dependence of the visibility of the standard of interference of fourth order with the power of the laser that generates the pairs of photons. Our results are in good agreement with experimental results.