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Tomographic Approach to Quantum States of Electromagnetic Radiation and Spin States

Explore the accuracy and operational use of optical homodyne tomography in quantum states. Learn about spin tomography, MuSR, uncertainty relations, and advancements towards microwaves.

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Tomographic Approach to Quantum States of Electromagnetic Radiation and Spin States

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  1. Tomographic approach to quantum states of electromagnetic radiation and spin states Sergey Filippov Moscow Institute of Physics and Technology

  2. Outline • Accuracy and operational use of optical homodyne tomograms • Towards microwaves • Evolution and – product • Spin tomography and MuSR

  3. Outline • Accuracy and operational use of optical homodyne tomograms • Towards microwaves • Evolution and – product • Spin tomography and MuSR

  4. Homodyne tomography

  5. Homodyne tomography

  6. Homodyne tomography

  7. Homodyne tomography

  8. Homodyne tomography

  9. Homodyne tomography 0

  10. Tomography in phase space Wigner function

  11. Experimental data: how to get the probability density correctly?

  12. Experimental data: example of a coherent state

  13. Experimental data: example of a SPACS ?

  14. Detector efficiency • Coherent: • SPACS:

  15. Purity: how to calculate? • Tomographic approach: ? ?

  16. Accuracy

  17. Experimental data: mismatch • Coherent • SPACS

  18. Reasons and Consequences

  19. Further frontiers • Checking uncertainty relations with definite precision • Purity-dependent URs • State-extended URs • Entropic enequalities

  20. Towards microwaves

  21. “Heterodyne” detection

  22. Moments’ calculation Linear amplifier

  23. Calculation of moments: noise influence

  24. Revealing true moments Relations with the Wigner function

  25. Relation between the tomogram and the ordered moments State purity

  26. Uncertainty relations

  27. Two phase spaces: the relation

  28. State evolution: an example • [Phys. Rev. A, 2011]

  29. “Lattice” phase space

  30. Star product on the “lattice” phase space

  31. Star product kernel

  32. Evolution in the “lattice” phase space [J. Phys. A, 2012]

  33. Spin systems

  34. Muon • Charge • Mass • Spin • Magnetic moment • Mean decay time • Decay channels

  35. Directional diagram of decay positrons

  36. Spin tomogram

  37. Probability Stern-Gerlach (1922) 43

  38. Muon spin tomography • Spin • Spin projection • Angular moment operators , • Tomogram • “Dequantizer”

  39. Decay diagram and tomogram

  40. Experimental setups

  41. Muons in matter

  42. Two-spin tomography • Unitary spin tomogram • Two-spin tomogram • Reconstruction procedure

  43. Reduced tomogram

  44. Hyperfine interaction • Initial state • Initial tomogram • Tomogram evolution • Evolution of the reduced tomogram

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