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QED (quantum-electrodynamical) theory of excess spontaneous emission noise

Peter W. Milonni

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

The results of a quantum-electrodynamical theory of excess spontaneous emission noise in lossy resonators will be presented. The Petermann K factor'' does not enter into the spontaneous emission rate of a single atom in the cavity. The QED theory allows different interpretations of the K factor, and we use this fact to justify semiclassical analyses and to provide in one example a simple derivation of K in terms of the amplification of the quantum vacuum field entering the resonator through its mirrors. 17 refs.

Related papers

QED theory of excess spontaneous emission noise

Peter W. Milonni

The results of a quantum-electrodynamical theory of excess spontaneous emission noise in lossy resonators will be presented. The " Petermann K factor" does not enter into the spontaneous emission rate of a single atom in the cavity. The QED theory allows different interpretations of the K factor and we use this fact to justify semiclassical analyses and to provide in one example a simple derivation of K in terms of the amplification of the quantum vacuum field entering the resonator through its mirrors.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1991•1 citation

Theory of excess noise in unstable resonator lasers

Claus Lamprecht, Helmut Ritsch

We theoretically investigate the quantum dynamics of an unstable resonator laser. Compared to a stable cavity laser of equal gain and loss it exhibits a K-fold enhanced linewidth. This excess noise factor K is a measure of the nonorthogonality of the resonator eigenmodes and amounts to an enlargement of the quantum vacuum fluctuations. Using a quantum treatment starting from first principles based on the nonorthogonal eigenmodes, we put previous theoretical predictions onto a more firm ground. While we find a position-dependent enhancement of the spontaneous emission rate into an empty mode of only $\sqrt{K},$ the constructive quantum interference of the spontaneous emission with a single oscillating mode lets the Petermann excess noise factor K reappear in the phase diffusion (laser linewidth). Hence locally enhanced spontaneous emission as well as noise enhanced by interference (amplified spontaneous emission) play an equal role in the origin of excess noise.

Physical Review A•Nov 18, 2002•4 citations

Cavity quantum electrodynamics

Partha Ghose

Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.

Cambridge University Press eBooks•Apr 29, 1999•0 citations

Excess noise in gain-guided amplifiers

Ivan Deutsch, J. C. Garrison, Ewan M. Wright

A second-quantized theory of the radiation field is used to study the origin of the excess noise observed in gain-guided amplifiers. We find that the reduction of the signal-to-noise ratio is a function of the length of the amplifier, and thus the enhancement of the noise is a propagation effect arising from longitudinally inhomogeneous gain of the noise rather than from an excess of local spontaneous emission. We confirm this conclusion by showing that the microscopic rate of spontaneous emission into a given non-power-orthogonal cavity mode is not enhanced by the Petermann factor. In addition, we illustrate the difficulties associated with photon statistics for this and other open systems by showing that no acceptable family of photon-number operators corresponds to a set of non-power-orthogonal cavity modes.

Journal of the Optical Society of America B•Jun 1, 1991•35 citations

Spontaneous Emission of an Atom in a Cavity with Nonorthogonal Eigenmodes

Yuh‐Jen Cheng

The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.

Physical Review Letters•Aug 30, 2006•11 citations

Unexpected role of excess noise in spontaneous emission

Claus Lamprecht, Helmut Ritsch

A single inverted two-level atom is used as a theoretical model for a quantum noise detector to investigate fundamental properties of excess noise in an unstable optical resonator. For a symmetric unstable spherical mirror cavity, we develop an analytic quantum description of the field in terms of a complete set of normalizable biorthogonal quasimodes and adjoint modes. Including the interaction with a single two-level atom leads to a description analogous to the Jaynes-Cummings model with modified coupling constants. One finds a strong position and geometry-dependent atomic decay probability proportional to the square root $\sqrt{K}$ of the excess noise factor K at the cavity center. Introducing an additional homogeneous gain one recovers the K-fold emission enhancement that has been predicted before for the linewidth of an unstable cavity laser. We find that excess noise may be viewed as a spatial redistribution of the field quantum noise inside the resonator. Taking a position average of the atomic decay rate over the cavity volume leads to a cancellation of the excess noise enhancement.

Physical Review A•Jan 4, 2002•9 citations
The results of a quantum-electrodynamical theory of excess spontaneous emission noise in lossy resonators will be presented. The Petermann K factor'' does not enter into the spontaneous emission rate of a single atom in the cavity. The QED theory allows different interpretations of the K factor, and we use this fact to justify semiclassical analyses and to provide in one example a simple derivation of K in terms of the amplification of the quantum vacuum field entering the resonator through its mirrors. 17 refs.
The results of a quantum-electrodynamical theory of excess spontaneous emission noise in lossy resonators will be presented. The " Petermann K factor" does not enter into the spontaneous emission rate of a single atom in the cavity. The QED theory allows different interpretations of the K factor and we use this fact to justify semiclassical analyses and to provide in one example a simple derivation of K in terms of the amplification of the quantum vacuum field entering the resonator through its mirrors.
We theoretically investigate the quantum dynamics of an unstable resonator laser. Compared to a stable cavity laser of equal gain and loss it exhibits a K-fold enhanced linewidth. This excess noise factor K is a measure of the nonorthogonality of the resonator eigenmodes and amounts to an enlargement of the quantum vacuum fluctuations. Using a quantum treatment starting from first principles based on the nonorthogonal eigenmodes, we put previous theoretical predictions onto a more firm ground. While we find a position-dependent enhancement of the spontaneous emission rate into an empty mode of only K,\sqrt{K},K​, the constructive quantum interference of the spontaneous emission with a single oscillating mode lets the Petermann excess noise factor K reappear in the phase diffusion (laser linewidth). Hence locally enhanced spontaneous emission as well as noise enhanced by interference (amplified spontaneous emission) play an equal role in the origin of excess noise.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
A second-quantized theory of the radiation field is used to study the origin of the excess noise observed in gain-guided amplifiers. We find that the reduction of the signal-to-noise ratio is a function of the length of the amplifier, and thus the enhancement of the noise is a propagation effect arising from longitudinally inhomogeneous gain of the noise rather than from an excess of local spontaneous emission. We confirm this conclusion by showing that the microscopic rate of spontaneous emission into a given non-power-orthogonal cavity mode is not enhanced by the Petermann factor. In addition, we illustrate the difficulties associated with photon statistics for this and other open systems by showing that no acceptable family of photon-number operators corresponds to a set of non-power-orthogonal cavity modes.
The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.
A single inverted two-level atom is used as a theoretical model for a quantum noise detector to investigate fundamental properties of excess noise in an unstable optical resonator. For a symmetric unstable spherical mirror cavity, we develop an analytic quantum description of the field in terms of a complete set of normalizable biorthogonal quasimodes and adjoint modes. Including the interaction with a single two-level atom leads to a description analogous to the Jaynes-Cummings model with modified coupling constants. One finds a strong position and geometry-dependent atomic decay probability proportional to the square root K\sqrt{K}K​ of the excess noise factor K at the cavity center. Introducing an additional homogeneous gain one recovers the K-fold emission enhancement that has been predicted before for the linewidth of an unstable cavity laser. We find that excess noise may be viewed as a spatial redistribution of the field quantum noise inside the resonator. Taking a position average of the atomic decay rate over the cavity volume leads to a cancellation of the excess noise enhancement.