Theoretical Problems of Quantum Optics

Prof. Yu.M. Golubev

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Проблемы квантовой оптики. Часть 1:
Основные понятия и теоретические подходы

Проблемы квантовой оптики. Часть 2:
Теория субпуассноновского лазера

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The lectures are devoted to theoretical problems of the quantum optics, connected with search of a real source of non-classical (sub-Poissonian, squeezed etc.) light. It consists of four parts. The first part is introduction and reminds basic elements of quantum electrodynamics under a specific corner of sight of quantum optics. The second part is devoted to theoretical problems of photodetecting that is the important component of the quantum optics. The third part is devoted to discussion of opportunities of generation of non-classical light by lasers and microlasers. The fourth part is devoted to problems of generation of compressed light in parametrical processes.

I. Elements of quantum electrodynamics

  1. Representation of an electromagnetic field in the optical resonator as set field oscillators.

  2. Quantization of field oscillator. Creation and annihilation photon operators. Coherent states as eigen-states of the photon creation operators. The Glauber's diagonal representation. Rules of transition to diagonal representation. Antinormal diagonal representation.

  3. The Bell's inequalities for classical electromagnetic fields. Infringement of the Bell's inequalities in quantum optics.

  4. The squeezed states of an electromagnetic field.

  5. Bunching and anti-bunching of photons.

  6. Poissonian, super-Poissonian and sub-Poissonian statistics of photons.

II. Photodetecting the light

  1. Shot noise (the Shotki's current) of detecting: the nature of shot noise from the point of view of classical and quantum electrodynamics

  2. "Excess" noise of detecting. The negative excess noise for the sub-Poissonian light.

  3. A photocurrent spectrum under registration of a single mode fields. Hetero- and homo-dyning: transformation of squeezed light into the sub-Poissonian one.

III. Sub-Poissonian lasing

  1. Physical model of the sub-Poissonian laser.

  2. The basic kinetic equation for a matrix of density of a laser field of generation under regular and random excitation of the active medium.

  3. Diagonal representation of the basic kinetic equations.

  4. Approximation of small photon fluctuations (the big number of photons). The optical spectrum of laser generation connected with the phase diffusion.

  5. A photocurrent spectrum for emission of a Poissonian, super- and sub-Poissonian lasers.

  6. The theory of the microlaser on a single four level atom.

IV. Generation of the squeezed electromagnetic field in a parametrical process

  1. Parametrical mixing electromagnetic waves in the passive cavity with the nonlinear medium.

  2. Lasing with an intracavity additional parametric cell. Heterodyning of the squeezed light.