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Heisenberg Limited Sagnac Interferometry

PHYSICS. Heisenberg Limited Sagnac Interferometry. AZIZ KOLKIRAN , G.S. AGARWAL Oklahoma State University, 2007 APS March Meeting, A33 Focus Session: Quantum Limited Measurements, Monday March 5 th ,2007, 9:48-10:00am. Sagnac phase shift. Sagnac interferometer with classical fields.

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Heisenberg Limited Sagnac Interferometry

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  1. PHYSICS Heisenberg Limited Sagnac Interferometry AZIZ KOLKIRAN, G.S. AGARWAL Oklahoma State University, 2007 APS March Meeting, A33 Focus Session: Quantum Limited Measurements, Monday March 5th,2007, 9:48-10:00am

  2. Sagnac phase shift.

  3. Sagnac interferometer with classical fields. Beam splitter transmission and reflection coefficients

  4. Single-photon Sagnac interferometer* *G Bertocchi, O Alibart, D B Ostrowsky, S Tanzilli and P Baldi, J. Phys. B: At. Mol. Opt. Phys. 39 (2006) 1011–1016

  5. Can we improve the resolution by using quantum states of light? experimentally employed by single photons coming from a spontaneous down-converter Bertocchi G. et al, “Single photon Sagnac interferometry”, J. Phys. B39, 1011 (2006)

  6. Use of entangled photon pairs from down-conversion. pump NL Fig. 4 input state from the down-conversion process: r is the interaction parameter (a.k.a. squeezing parameter) of entangled pair production from vacuum

  7. Can we improve the resolution further by using multi-photon entanglement? Fig. 5 are transmission and reflection probabilities at the beam splitters

  8. Can we turn the fringes into ones with equal height**? Fig. 6 **see also T. Nagata, et al. Science 316, 726-729, (2007).

  9. 4-photon interference using asymmetric beam splitters* The experiment B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, G. C. Guo, and Z. Y. Ou Optics Letters, Vol. 32, Issue 10, pp. 1320-1322 (2007).

  10. How does this work? Non-classical Fock state phase shifter phase shifter classical field For two-photon coincidence detection (Fig. 4), the state, after entering and completing the path, evolves into the following: For four-photon coincidence detection (Fig. 5 and 6), the state, after entering and completing the path, evolves into the following: This term leads to unequal fringes in the detection setup given by Fig. 5 Only this part contributes to the detection in the setup given by Fig. 6 All interferometric schemes using the maximally correlated entangled states show the phase sensitivity equal to 1/N, which is the Heisenberg limit.

  11. Conclusions • Use of PDC light in SI leads to 2- and 4-fold increase in the sensitivity depending on the detection mechanism. • We think that the experiment should be feasible, because single photons have already been used from a down-converter in SI and in many experiments 2- and 4-photon interference effects have been observed. • If successful, it could be a stimulating application in the field of quantum metrology.

  12. Opt. Express 15, 6798-6808 (2007).

  13. Current work in progress

  14. Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit 20% at large gain G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, Phys. Rev. Lett. 86, 1389 (2001), comment on A.N. Boto, et al., Phys. Rev. Lett. 85, 2733 (2000).

  15. Quantum Imaging and Sensing Using Coherent Beam Stimulated Parametric Down conversion SETUP: Using an input from non-degenerate stimulated parametric down-conversion for the determination of phase via photon-photon correlations. RESULTS: Stimulated emission enhanced visibility of two-photon counts for various phases of the coherent field with respect to the gain factor g. The pump phase is fixed at . The modulus of the coherent field is chosen such that the coincidences coming from SPDC and the coherent fields are equal to each other. The dashed line shows the visibility for the case of photons produced by spontaneous parametric down-conversion. Aziz Kolkiran and G S Agarwal, in preparation

  16. Future work Interaction free measurements (non-distortion quantum interrogation) using entangled photons How to optically detect the presence of something without photons hitting it. two-level atom 25% chance of detecting the bomb without explosion. By using different beam splitter reflectivity's R, this can be made 50%. Elitzur A. C. and Vaidman L. (1993). Quantum mechanical interaction-free measurements. Found. Phys. 23, 987-97.

  17. Future work Interaction free measurements (non-distortion quantum interrogation) using entangled photons Entangled source object (three level atom)

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