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John Wiley & Sons, Inc. eBooks

Quantum Noise in Nonlinear Optical Phenomena

R. Tanaś

Published Apr 2, 2003• 2 citations
Publisher

Abstract

In this chapter the author discusses two nonlinear optical phenomena — second-harmonic generation and parametric downconversion — drawing particular attention to the signatures of quantum fluctuations of the optical fields that can be found in the phenomena. The ubiquitous vacuum fluctuations can manifest themselves in various ways when an optical field undergoes nonlinear transformation. The two processes considered here are only examples of a rich variety of nonlinear phenomena, but they are of great practical importance and thus have been studied for years. It is not the author's intention to collect all the facts known about the two processes, but rather to select some specific effects illustrating the role of quantum character of the field in the process. He presents several theoretical methods that are used to describe quantum properties of the field and that are now available to everybody owing to common access to computers and software.

DOI
10.1002/0471231479.ch1

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In this chapter the author discusses two nonlinear optical phenomena — second-harmonic generation and parametric downconversion — drawing particular attention to the signatures of quantum fluctuations of the optical fields that can be found in the phenomena. The ubiquitous vacuum fluctuations can manifest themselves in various ways when an optical field undergoes nonlinear transformation. The two processes considered here are only examples of a rich variety of nonlinear phenomena, but they are of great practical importance and thus have been studied for years. It is not the author's intention to collect all the facts known about the two processes, but rather to select some specific effects illustrating the role of quantum character of the field in the process. He presents several theoretical methods that are used to describe quantum properties of the field and that are now available to everybody owing to common access to computers and software.
Nonlinear phenomena in quantum optics are reviewed, with particular emphasis on scientific activities in quantum optics at the Natural Science Faculty of Palacký University ln Olomouc (Czech Republic). The first section is devoted to quantum and classical methods to obtain photon statistics in higher-harmonics generation, including a method of classical trajectories. It is followed by a discussion of photon bunching and antibunching of nonstationary fields. The chapter continues with a discussion of methods for reconstruction of quantum states. Other topics covered include the process of frequency downconversion with pulses, Zeno and anti-Zeno effects based on optical parametric processes, Raman nonlinear couplers as switching elements and sources of nonclassical light for optoelectronics and photonics, and quantum cryptography. Finally, quantum spatial propagation of a two-mode squeezed light in a cubically behaved quadratic medium is treated as another feature of a two-field squeezed steady-state light, and this approach is compared with the conventional one.
The concept of squeezing, which generally implies that one quadrature component of an optical field has measured fluctuations below the vacuum limit, is generalized to higher moments of even order. Higher-order squeezing is encountered in many of the nonlinear processes that generate second-order squeezing. It is shown that the field produced in degenerate parametric downconversion is squeezed to all even orders and is intrinsically squeezed to orders 2,6,10…. Higher-order squeezing also shows up in second harmonic generation and in resonance fluorescence from an atom. However, in those cases there is no intrinsic squeezing beyond the second order, although a strong second-order squeezing effect is manifest in the higher-order moments of the field.
The interest toward strong electromagnetic confinement structures through the use of microcavities is of great interest, from both the fundamental understanding and the technological application sides. Here, we focus our attention to second order nonlinear processes inside such structures. From a basic point of view, electromagnetic confinement leads, physically, to the manipulation of vacuum field fluctuations and, formally, to an anomalous commutation relation [Ueda, M. and Imoto, N., "Anomalous commutation relation and modified spontanenous emission inside a microcavity," Phys. Rev. A, 50(1), 89-92 (1994)]. However, an attempt to probe the resulting anomaly with a beam splitter located inside a cavity is theoretically proved inadequate for this task. For this reason, parametric fluorescence (PF, parametric down conversion) and second harmonic generation (SHG) are considered as potential tools to probe vacuum field fluctuations in confinement structures. Indeed, it was recently showed that PF can be strongly intensified, by two orders of magnitude or more, when it occurs inside a high confinement (open) cavity. Therefore, PF could efficiently be used to probe the expected anomaly. Additionally, in consideration of the simplest possible experimental scheme to probe the anomaly and because it is generally admitted that SHG is the time reversal of degenerate parametric fluorescence, here our attention is also directed toward SHG. Formally, we show that the equations describing SHG and PF are not symmetrical regarding quantum noise. It turns out that, conversely to the case of PF, the intensification of vacuum field fluctuations tends to inhibit SHG. We interpret this result as due to the reduction of waves coherence induced by stronger quantum noise. In conclusion, albeit both processes could be used as probes to prove or disprove the realm of quantum anomalies, PF appears as a more convenient tool.
Statistical properties of light generated in nonlinear optical couplers are discussed. Methods suitable for the description of non-classical properties of light are mentioned; special attention is paid to generalized superposition of coherent fields and noise. Regimes suitable for non-classical light generation in various types of nonlinear couplers based on second-harmonic and second- subharmonic generation, optical parametric processes, Kerr effect as well as Raman and Brillouin processes are analyzed. Special attention is devoted to the generation of light with sub-Poissonian statistics, squeezed light, and light in purely quantum states. Role of real effects like damping of optical fields and phase mismatches is also discussed.
Quantum electrodynamics furnishes a new type of representation for the characterisation of nonlinear optical processes. The treatment elicits the detailed role and interplay of specific quantum channels, information that is not afforded by other methods. Following an illustrative application to the case of Rayleigh scattering, the method is applied to second and third harmonic generation. Derivations are given of parameters that quantify the various quantum channels and their interferences; the results are illustrated graphically. With given examples, it is shown in some systems that optical nonlinearity owes its origin to an isolated channel, or a small group of channels.