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Interferometria quântica em microcavidades

Caio Olindo de Miranda e Silva

Published Mar 21, 2002• 0 citations
OpenAlex

Abstract

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.

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Interferometria quântica com cavidades

Caio Olindo de Miranda e Silva

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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arXiv:0810.4501•Physical Review A•Nov 26, 2008•7 citations
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.
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 _.
Summary form only given. Semiconductor microcavities can be engineered to produce strong coupling between photons and quantum well excitons leading to the formation of new eigenstates called polaritons. Due to their peculiar dispersion, enabling non-equilibrium Bose-Einstein condensation [1], and their straightforward experimental accessibility, microcavity polaritons have gained considerable interest in recent years. Polariton states can be selectively populated by choosing the excitation angle and the wavelength of the excitation laser. After a lifetime of a few picoseconds the polariton decays and a photon is emitted from the cavity, carrying the complete information on the underlying polariton state. Several theoretical works [2-3] suggest that polariton-polariton interactions can be a source of non-classical photon correlations, producing photon pairs that are entangled in either the energy, the polarization, or the momentum degree of freedom. One appeal of such a system is that many parameters such as the polariton-polariton interaction strength are tunable [4] and multipartite entangled states can be created in a single device [5]. However, due to the lack of high-quality samples, experimental realisations of these schemes have been elusive so far. In this contribution, we will discuss some of our experimental work on the statistics of polariton-polariton parametric scattering. Excited polaritons can scatter in a four-wave mixing process into signal and idler states lying on a figure-eight shaped curve in k-space, where phase-matching is fulfilled. We make use of a sample with ultra narrow exciton resonances, which allows for the generation and detection of correlated light. We present our measurements of the second order correlation functions using time-correlated photon counting. We discuss in detail, how polariton quantum correlations depend on a number of experimental parameters, such as phase space location and excitation density and find that the results can be understood in the framework of the well known Bogoliubov theory for 2D Bose gases utilised for microcavity polaritons [6]. We find bunching below the parametric threshold and a slow buildup of coherence above the threshold similar to the quantum statistics of a non-degenerate optical parametric oscillator, which is well known for its nonclassical properties [7]. We discuss in particular the influence of strong background processes on the observed photon statistics.
We study different phenomena associated with single-photon propagation in optical cavities coupled through optical fibers. We first address the issue of storing and delaying single-photon wavepackets in an array of microcavities. This has possible applications in developing reliable and efficient quantum repeaters that will be utilized \n \nin building long distance quantum networks. Second, we investigate a Hong-Ou-Mandel (HOM) type of interference between two photons that are produced in two coupled atom-cavity systems. The HOM effect in this setup can test the degree of indistinguishability between photons when they are stored inside cavities. This part of the dissertation also includes the study of entanglement between atoms, cavities and atom-cavity systems induced by the photons. Finally, we focus on single-photon interactions with a tiny movable mirror in the context of quantum optomechanics. We investigate how the mechanical motion of the mirror leaves its imprints on the optical spectrum of the photon \n \nThis dissertation includes previously published and unpublished co-authored material.
We consider Mach-Zehnder and Hong-Ou-Mandel interferometers with nonclassical states of light as input, and study the effect that dispersion inside the interferometer has on the sensitivity of phase measurements. We study in detail a number of different one- and two-photon input states, including Fock, dual Fock, maximally path-entangled $\ensuremath{\mid}N,0⟩+⟨{0}_{,}N\ensuremath{\mid}$ (``N00N'') states, and photon pairs from parametric down-conversion. Assuming there is a phase shift ${\ensuremath{\phi}}_{0}$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of ${\ensuremath{\phi}}_{0}$, and then compute the Shannon mutual information between ${\ensuremath{\phi}}_{0}$ and the measurements. This provides a means of quantitatively comparing the utility of various input states for determining the phase in the presence of dispersion. In addition, we consider a simplified model of parametric down-conversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic down-conversion model.