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Annual Meeting Optical Society of America

Effects of quantum noise on modulation spectroscopy

David A. Holm, Murray Sargent

Published Jan 1, 1985• 0 citations
Publisher

Abstract

AM and FM modulation spectroscopies1,2 have been used to study the properties of matter as well as for applications such as reading out optical memories.3 Advances in the accuracy of these methods have turned what used to be an academic subject, quantum noise, into a practical consideration. For example, memory readout fields must be very weak to keep the medium from heating up too much and quantum noise puts a lower limit on the readout field strength. Similarly if weak modulation sidebands are used to study coherent dips via AM spectroscopy, quantum noise becomes relevant. We use our quantum theory of multiwave mixing4 to predict the effects of quantum noise on these problems. We find that, for modulation frequencies about equal to the Rabi frequency for the strong wave, spontaneous emission contributes a pronounced AM component that might be confused with the appearance of a hole in reading out optical memories. In AM spectroscopy we find that the coherent dips are partly filled in by spontaneous emission.

DOI
10.1364/oam.1985.fn2

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AM and FM modulation spectroscopies1,2 have been used to study the properties of matter as well as for applications such as reading out optical memories.3 Advances in the accuracy of these methods have turned what used to be an academic subject, quantum noise, into a practical consideration. For example, memory readout fields must be very weak to keep the medium from heating up too much and quantum noise puts a lower limit on the readout field strength. Similarly if weak modulation sidebands are used to study coherent dips via AM spectroscopy, quantum noise becomes relevant. We use our quantum theory of multiwave mixing4 to predict the effects of quantum noise on these problems. We find that, for modulation frequencies about equal to the Rabi frequency for the strong wave, spontaneous emission contributes a pronounced AM component that might be confused with the appearance of a hole in reading out optical memories. In AM spectroscopy we find that the coherent dips are partly filled in by spontaneous emission.
In the presence of a high-finesse cavity, the resonance fluorescence spectrum can be altered by stimulated emission and multiwave mixing processes. We show that under some conditions it is possible for spontaneous emission to induce conjugate fields similar to semiclassical phase conjugation, requiring the use of the multiwave quantum theory described in earlier papers in this series. The theory is applicable to laser spectroscopy and optical bistability. We present explicit spectra and suggest possible experimental tests. In particular we find a quantum limit for FM spectroscopy that shows that even if the medium under study leaves the FM phase and amplitude relationships intact according to semiclassical theory, spontaneous emission can create an AM component detectable in a square-law detector.
This dissertation formulates and applies a theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse variations. The resonance fluorescence spectrum in a high finesse optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Our analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular we determine a quantum limit to the semiclassical theory of FM modulation spectroscopy. Finally, we derive the corresponding theory for the two-photon, two-level medium. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem. We discuss the role of the Stark shifts on the emission spectrum and show how the Rayleigh scattering is markedly different.
Over the past three years we have developed a quantum theory of multiwave mixing designed to determine effects of quantum noise on laser and optical bistability instabilities, pump/probe saturation spectroscopy, AM and FM modulation spectroscopy, and phase conjugation. The theory treats a classical pump field and one or two quantum-mechanical sidemode fields interacting with one- or two-photon, two-level media. The theory1 produces a master equation for the reduced sidemode density operator able to describe all of the above phenomena in a uniform way closely related to the corresponding semiclassical theories. It has led to a number of significant predictions about the effects of spontaneous emission on laser spectroscopy and optical instabilities.
Due to improvements in detector sensitivity, quantum noise is known to be the limiting factor of many lasers and other optical devices. In this work we present a fully quantum mechanical theory of multiwave mixing to study the effects of spontaneous emission noise on three- and four- wave mixing. The foundations of this theory have been presented in a series of papers1-3 demonstrating how such diverse topics as resonance fluorescence, saturation spectroscopy, phase conjugation, and squeezed states of light share a common origin.
The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.