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Tomographic approach to quantum states of electromagnetic radiation and spin states. Sergey Filippov. Moscow Institute of Physics and Technology. Outline. Accuracy and operational use of optical homodyne tomograms Towards microwaves Evolution and – product Spin tomography and MuSR.
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Tomographic approach to quantum states of electromagnetic radiation and spin states Sergey Filippov Moscow Institute of Physics and Technology
Outline • Accuracy and operational use of optical homodyne tomograms • Towards microwaves • Evolution and – product • Spin tomography and MuSR
Outline • Accuracy and operational use of optical homodyne tomograms • Towards microwaves • Evolution and – product • Spin tomography and MuSR
Tomography in phase space Wigner function
Experimental data: how to get the probability density correctly?
Detector efficiency • Coherent: • SPACS:
Purity: how to calculate? • Tomographic approach: ? ?
Experimental data: mismatch • Coherent • SPACS
Further frontiers • Checking uncertainty relations with definite precision • Purity-dependent URs • State-extended URs • Entropic enequalities
Moments’ calculation Linear amplifier
Revealing true moments Relations with the Wigner function
Relation between the tomogram and the ordered moments State purity
State evolution: an example • [Phys. Rev. A, 2011]
Evolution in the “lattice” phase space [J. Phys. A, 2012]
Muon • Charge • Mass • Spin • Magnetic moment • Mean decay time • Decay channels
Probability Stern-Gerlach (1922) 43
Muon spin tomography • Spin • Spin projection • Angular moment operators , • Tomogram • “Dequantizer”
Two-spin tomography • Unitary spin tomogram • Two-spin tomogram • Reconstruction procedure
Hyperfine interaction • Initial state • Initial tomogram • Tomogram evolution • Evolution of the reduced tomogram