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Quantum Optics Seminar

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

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  1. Quantum Optics Seminar Talya Vaknin

  2. Quantization of the electromagnetic field • Fock states and Fock space • Coherent states • Squeezed states • Coherent representation of Thermal states

  3. 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

  4. Canonical momentum of the jth mode

  5. Annihilation (absorption) operator Creation operator

  6. Fock states • Single mode of frequency Eigenstate Eigenvalue

  7. Normalization • Complete set • Multi mode fields

  8. 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.

  9. Fock representation of the coherent state Minimum uncertainty

  10. 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

  11. Complete set A resolution of the identity operator 1 in terms of coherent state projectors: Over- complete set

  12. Displacement operator

  13. Squeezed states • Squeezing a single mode field

  14. Vacuum state Coherent state Squeezed state with reduced phase uncertainty Squeezed state with reduced amplitude uncertainty

  15. The unitary squeeze operator

  16. Two photon coherent state

  17. Coherent representation of Thermal states • Density operator • Fock state representation- exponent • Coherent state representation- Gaussian distribution (Distribution function)

  18. 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)

  19. Minimum uncertainty

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