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Journal of Modern Optics

Gain in single and paired parametric oscillators

Reed Nessler, Hichem Eleuch, Wolfgang P. Schleich, Marlan O. Scully

Published Aug 25, 2018• 8 citations
Publisher

Abstract

The new concept of Quantum Amplification by Superradiant Emission of Radiation for generating high-frequency coherent light has produced several open questions, and one of the most important is how to determine the gain in two coupled oscillators with a parametric amplifier. In this article, we analytically derive the equation for the gain expression and state sufficient conditions to obtain gain. We also draw connections to single oscillator topics, including the Mathieu equation and the Kronig–Penney model.

DOI
10.1080/09500340.2018.1511860

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The new concept of Quantum Amplification by Superradiant Emission of Radiation for generating high-frequency coherent light has produced several open questions, and one of the most important is how to determine the gain in two coupled oscillators with a parametric amplifier. In this article, we analytically derive the equation for the gain expression and state sufficient conditions to obtain gain. We also draw connections to single oscillator topics, including the Mathieu equation and the Kronig–Penney model.
With Maxwell-Bloch equations how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency has been shown. This remarkable effect has been examined in terms of a simpler model involving two coupled oscillators, with one of them parametrically driven. We show that this coupled-oscillator model has a hidden parity-time (PT\mathcal{PT}PT) symmetry for quantum amplification by superradiant emission of radiation (QASER); we thus bring PT\mathcal{PT}PT symmetry to the realm of parametrically coupled resonators. Moreover, we find that the QASER gain arises from the broken-PT\mathcal{PT}PT-symmetry phase. We then quantize the simplified version of QASER using quantum Langevin equations. The quantum description enables us to understand how the system starts from quantum fluctuations.
Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.
Lasers and masers typically require population inversion. But with phase coherent atoms (phasers), we get lasing without inversion (e.g. 10% of the atoms excited). However, in recent work we found that it is possible to get coherent light emitted with no atoms excited, via Quantum Amplification of Superradiant Emission of Radiation (QASER). In particular, we found that by utilizing collective superradiant emission, we can generate coherent light at high frequency in the UV or x-ray bands by driving the atomic system with lower frequency source. Here, we present a simple analysis based on near-resonant QASER operation and on a multi-photon Hamiltonian obtained by, e.g. a canonical transformation.
Introduction Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.