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  • 6:40 AM, Wednesday, 22 Jan 2020


Course Postgraduate
Semester Electives
Subject Code PH666
Subject Title Statistical and Quantum Optics

Syllabus

Introduction to probability theory, properties of probabilities, random variabes and probability distribution, generating functions, examples of probability distributions, Gaussian probability distribution, central limit theorem, multivariate Gaussian distribution. Random processes, statistical ensembles, stationarity and ergodicity, properties of autocorrelation function, spectral properties of stationary random processes, orthogonal representation of a random process, Wiener Khinchine theorem, Karhunen–Loeve expansion.

Second order coherence theory of scalar wave fields, temporal coherence, spatial coherence, the laws of interference, the mutual coherence function and the complex degree of coherence, cross spectral density, partial coherence and spectral degree of coherence, Wigner function, propagation of cross–spectral density and mutual coherence in free space, the van Cittert–Zernike theorem and its application in stellar interferometry.

Elementary theory of polarization of stochastic electromagnetic beams. Polarized, unpolarized, and partially polarized light. Partially polarized light and the degree of polarization. Stokes parameters and the Poincare sphere. Unified theory of polarization and coherence. Spectral degree of coherence and stochastic electromagnetic beams, generalized stokes parameters.

Position and momentum kets, displacement operator. Wave functions in position and momentum space, the uncertainty principle. Simple harmonic oscillator, annihilation and creation operators, Fock basis, time evolution. Coherent, squeezed, and thermal states of a single–mode. Quantization of the electromagnetic field.

Represention of a state, Fock basis expansion, coherent state expansion, diagonal representation, Wigner phase space density, and the Q function, s-ordered quasi-probability. Normal, symmetric, and anti–normal ordering of operators. Classical and non-classical states of radiation with examples.

Field correlation functions, properties of correlation functions, correlation functions and optical coherence. Photon correlation measurements, photon counting measurements, Intensity – intensity correlation g2 (τ). The quantum mechanical beam-splitter, the quantum mechanical amplifier. Two-mode squeezed vacuum.

Text Books

Same as Reference

References

1. Statistical Optics, J. W. Goodman, Wiley–Interscience, 2000. (units 1, 2, and 3).
2. Optical Coherence and Quantum Optics, L. Mandel and E. Wolf, Cambridge University Press, 1995. (units 1, 2, and 3).
3. Introduction to theory of coherence and polarization of light, E. Wolf, Cambridge University Press, 2007. (units 2 and 3).
4. Modern Quantum Mechanics, J. J. Sakurai, Pearson Education, 2009. (unit 4).
5. Optical Coherence and Quantum Optics, L. Mandel and E. wolf, Cambridge University Press, 1995. (units 4, 5, and 6).
6. Quantum Optics, D. F. Walls and G. J. Milburn, Springer, 2007. (units 4, 5, and 6).
7. The quantum theory of light, R. Loudon, Oxford university press, 2000. (units 4, 5, and 6).