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КВАНТОВАЯ ТЕОРИЯ СПОНТАННОГО ПАРАМЕТРИЧЕСКОГО РАССЕЯНИЯ СВЕТА И КОГЕРЕНТНЫЕ СОСТОЯНИЯ ТРЕХМЕРНОЙ ГРУППЫ ЛОРЕНЦА

Александр Викторович Горохов, Дмитрий Иванович Умов

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The work is devoted to applications of group-theoretic coherent states to describe the nonlinear optical effects. Important in modern quantum information process of parametric down conversion is studied. It is shown that the use of superpositions of coherent states of SU(1; 1) allows to increase the squeezing of generated photon pairs.

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The work is devoted to applications of group-theoretic coherent states todescribe the nonlinear optical effects. Important in modern quantum informationprocess of parametric down conversion is studied. It is shown that the useof superpositions of coherent states of SU(1; 1) allows to increase the squeezingof generated photon pairs.

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Исследовано управление нелинейными процессами в квантовой оптике, гамильтонианы которых обладают некомпактной группой динамической симметрии. Использована техника когерентных состояний динамической группы. Детально рассмотрен процесс спонтанного параметрического рассеяния, важный для современной квантовой информатики, в том числе и с учетом потерь вследствие взаимодействия с большим диссипативным окружением. Nonlinear processes in quantum optics controlled by Hamiltonians with a noncompact dynamical group are investigated. The technique of coherent states of the dynamical group is used. The process of spontaneous parametric down-conversion, important for the modern quantum informatics, is considered in detail takin into account the interaction with a large dissipative environment.

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Optical quantum computing, quantum information and quantum communication protocols rely on the generation of qubits encoded in optical systems, many of which can be generate via the process of spontaneous parametric down-conversion. In this thesis, we investigate down-converted states, in the context of quantum computing and quantum information. In the high gain regime, a type I down-converted state can be described as a single-mode squeezed vacuum state. We present an analysis of photon-subtracted squeezed vacuum states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent-state teleportation and entanglement swapping. In the low gain regime, the output state of a type II parametric down-converter can be approximated as containing pairs of single photons, which can be used to herald the presence of one- or two- photon Fock states in one mode, conditional on the detection of the same number of photons in the other mode. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g(2) and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We also develop a technique for controlling the joint spectral profile of the down-converted photons. By exploiting the dependence of the effective nonlinearity of a periodically poled crystal on its poling order, we tailor the nonlinearity profile and therefore the phase matching function of the down-converted photons. Finally, we consider the validity of the Taylor series expansion of the unitary operator which governs the evolution of the fields within the crystal, in comparison to the strictly correct time-ordered Dyson series expansion.

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Исследовано управление нелинейными процессами в квантовой оптике, гамильтонианы которых обладают некомпактной группой динамической симметрии. Использована техника когерентных состояний динамической группы. Детально рассмотрен процесс спонтанного параметрического рассеяния, важный для современной квантовой информатики, в том числе и с учетом потерь вследствие взаимодействия с большим диссипативным окружением. Nonlinear processes in quantum optics controlled by Hamiltonians with a noncompact dynamical group are investigated. The technique of coherent states of the dynamical group is used. The process of spontaneous parametric down-conversion, important for the modern quantum informatics, is considered in detail takin into account the interaction with a large dissipative environment.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)\chi^{(2)}χ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
Optical quantum computing, quantum information and quantum communication protocols rely on the generation of qubits encoded in optical systems, many of which can be generate via the process of spontaneous parametric down-conversion. In this thesis, we investigate down-converted states, in the context of quantum computing and quantum information. In the high gain regime, a type I down-converted state can be described as a single-mode squeezed vacuum state. We present an analysis of photon-subtracted squeezed vacuum states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent-state teleportation and entanglement swapping. In the low gain regime, the output state of a type II parametric down-converter can be approximated as containing pairs of single photons, which can be used to herald the presence of one- or two- photon Fock states in one mode, conditional on the detection of the same number of photons in the other mode. We explore the effects of spectral filtering and inefficient detection, of the heralding mode, on the count rate, g(2) and purity of the heralded state, as well as the fidelity between the resulting state and an ideal Fock state. We also develop a technique for controlling the joint spectral profile of the down-converted photons. By exploiting the dependence of the effective nonlinearity of a periodically poled crystal on its poling order, we tailor the nonlinearity profile and therefore the phase matching function of the down-converted photons. Finally, we consider the validity of the Taylor series expansion of the unitary operator which governs the evolution of the fields within the crystal, in comparison to the strictly correct time-ordered Dyson series expansion.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.