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Vestnik of Samara University Natural Science Series

QUANTUM THEORY OF SPONTANEOUS SCATTERING OF LIGHT AND COHERENT STATES OF THREE-DIMENSIONAL LORENTZ GROUP

Alexander V. Gorokhov, Дмитрий Иванович Умов

Published Jun 16, 2011• 0 citations
Publisher

Abstract

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.
DOI
10.18287/2541-7525-2011-17-2-171-178

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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.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
The importance of photon pair generation can never be overemphasized. It has formed the basis of most fundamental quantum optical experiments like Bell-experiments, quantum teleportation and entanglement swapping. However for considerable number of years Quantum Mechanics in general has remained largely theoretical and within the four corners of laboratories. Quantum Key Distribution is one of the first quantum applications to break this barrier. It provides us with unconditionally secured communication by providing us with efficient alternative to classical cryptography. This study forms part of the effort in realizing efficient way of generating photon pairs through the Spontaneous Parametric Down-Conversion process using a nonlinear crystal cut for type-I phase matching. After generating the photon pairs, the paper examined how they can be detected efficiently. We measured the rate of single photon generation (up to 200 kHz) as well as the rate at which they are detected in coincidence (150 coincidences per second). We further investigated a quantum interference effect (the Hong-Ou-Mandel effect) which classical wave theory has failed to describe. This effect has numerous applications in scalable quantum networks and in linear quantum computing. Finally, a remarkable conversion efficiency of 2.2