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Quantum Optics Seminar. Talya Vaknin. Quantization of the electromagnetic field Fock states and Fock space Coherent states Squeezed states Coherent representation of Thermal states. Quantization of the free electromagnetic field .
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Quantum Optics Seminar Talya Vaknin
Quantization of the electromagnetic field • Fock states and Fock space • Coherent states • Squeezed states • Coherent representation of Thermal states
Quantization of the free electromagnetic field • Electromagnetic field contained in a very large cube of side L • Periodic boundary conditions • Electric field linearly polarized in the x- direction
Annihilation (absorption) operator Creation operator
Fock states • Single mode of frequency Eigenstate Eigenvalue
Normalization • Complete set • Multi mode fields
Coherent states • Eigen states of the annihilation operator • Poisson distribution of Fock states • States of minimum uncertainty product • A product of the displacement operator on the vacuum state.
Fock representation of the coherent state Minimum uncertainty
The photon distribution p(n) for a coherent state Probability that n photons will be found in the coherent state Mean number of photons Variance
Complete set A resolution of the identity operator 1 in terms of coherent state projectors: Over- complete set
Squeezed states • Squeezing a single mode field
Vacuum state Coherent state Squeezed state with reduced phase uncertainty Squeezed state with reduced amplitude uncertainty
Coherent representation of Thermal states • Density operator • Fock state representation- exponent • Coherent state representation- Gaussian distribution (Distribution function)
Bibliography • Leonard Mandel and Emil Wolf, Optical coherence and quantum optics, chap 10, 11 and 21 (Cambridge University press, Cambridge 1995) • Marlan O. Scully and M. Suhail Zubairy, Quantum Optics, chap 1 and 2 (Cambridge University press, Cambridge 1997)