Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\ensuremath{\epsilon}(\mathbf{r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system-and-bath Hamiltonian of quantum optics. The field dynamics is investigated using the input-output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

[1]  C. cohen-tannoudji,et al.  Atom-photon interactions , 1992 .

[2]  García,et al.  Observation of photon localization in a three-dimensional disordered system. , 1991, Physical review letters.

[3]  Y. Fyodorov,et al.  Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invariance , 1997 .

[4]  S. Barnett,et al.  Quasi mode theory of macroscopic canonical quantization in quantum optics and cavity quantum electrodynamics , 1999 .

[5]  S. Stenholm,et al.  Quantum Langevin theory of excess noise in lasers , 1999, quant-ph/9904060.

[6]  P. Kumar,et al.  Photon statistics of random lasers with resonant feedback. , 2001, Physical review letters.

[7]  U. Fano.  Effects of Configuration Interaction on Intensities and Phase Shifts , 1961 .

[8]  J. Jackson,et al.  Classical Electrodynamics, 2nd Edition , 1975 .

[9]  Herman Feshbach,et al.  A Unified Theory of Nuclear Reactions, II , 1962 .

[10]  G. Nienhuis,et al.  Quantized mode of a leaky cavity , 2000 .

[11]  G. Nienhuis,et al.  Derivation of a Hamiltonian for photon decay in a cavity , 2000 .

[12]  P. T. Leung,et al.  Quasinormal-mode expansion for waves in open systems , 1998 .

[13]  F. Dittes,et al.  The decay of quantum systems with a small number of open channels , 2000 .

[14]  S. Barnett,et al.  Quantum theory of cavity quasimodes , 1988 .

[15]  Vogel,et al.  Resonators in quantum optics: A first-principles approach. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Wolf,et al.  Weak localization and coherent backscattering of photons in disordered media. , 1985, Physical review letters.

[17]  C. Beenakker.  Random-matrix theory of quantum transport , 1996, cond-mat/9612179.

[18]  I. Senitzky.  Dissipation in Quantum Mechanics. The Harmonic Oscillator , 1960 .

[19]  K. Yoshino,et al.  Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions , 1998 .

[20]  R. Glauber,et al.  Quantum optics of dielectric media. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[21]  Vladimir Zelevinsky,et al.  Dynamics and statistics of unstable quantum states , 1989 .

[22]  Claude Mahaux,et al.  Shell-model approach to nuclear reactions , 1969 .

[23]  A. Lagendijk,et al.  Observation of weak localization of light in a random medium. , 1985, Physical review letters.

[24]  C. Beenakker,et al.  Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium , 2000, cond-mat/0003262.

[25]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[26]  Diederik Wiersma,et al.  Laser physics: The smallest random laser , 2000, Nature.

[27]  C. Beenakker.  Thermal radiation and amplified spontaneous emission from a random medium , 1998, quant-ph/9806072.

[28]  Vogel,et al.  Action of passive, lossless optical systems in quantum optics. , 1987, Physical review. A, General physics.

[29]  Reibold,et al.  Strong damping and low-temperature anomalies for the harmonic oscillator. , 1985, Physical review. A, General physics.

[30]  B. Mehlig,et al.  EIGENVECTOR STATISTICS IN NON-HERMITIAN RANDOM MATRIX ENSEMBLES , 1998 .

[31]  Robert P. H. Chang,et al.  Investigation of random lasers with resonant feedback , 2001 .

[32]  Grunér,et al.  Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[33]  F. Haake,et al.  Field quantization for chaotic resonators with overlapping modes. , 2001, Physical review letters.

[34]  Roberto Righini,et al.  Localization of light in a disordered medium , 1997, Nature.

[35]  H. Ritsch,et al.  Unexpected role of excess noise in spontaneous emission , 2002 .

[36]  Xu,et al.  Spatial confinement of laser light in active random media , 2000, Physical review letters.

[37]  J. Y. Xu,et al.  Transition from amplified spontaneous emission to laser action in strongly scattering media , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  M. Scully,et al.  Why is the Laser Line So Narrow? A Theory of Single-Quasimode Laser Operation , 1973 .

[39]  H. Ritsch,et al.  QUANTIZED ATOM-FIELD DYNAMICS IN UNSTABLE CAVITIES , 1999 .

[40]  Philip W. Anderson,et al.  The question of classical localization A theory of white paint , 1985 .

[41]  P. Sheng,et al.  Introduction to Wave Scattering, Localization and Mesoscopic Phenomena. Second edition , 1995 .

[42]  R. Loudon,et al.  Quantum theory of optical pulse propagation through an absorbing and dispersive slab , 1997 .

[43]  K. Efetov,et al.  Supersymmetry in Disorder and Chaos , 1996 .

[44]  Robert P. H. Chang,et al.  Random laser action in semiconductor powder , 1999 .