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Phase Selection in Interference of Non-Classical Sources Ofer Firstenberg, Yoav Sagi, Moshe Shuker, Amit Ben-Kish, Amnon Fisher, Amiram Ron Department of Physics, Technion - Israel Inst. of Tech. Advanced Methods in Plasma and Optics In honor of Amnon Fisher’s 70 th birthday

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Outline The chronicles of two-source interference A generic two-source interference system and its oscillating “phase state” A scheme for quantum-non-demolition (QND) measurement of interference. Simulating the emergence of oscillating states. Conclusions

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Observations of Two-Source Interference 1949: Independent microwave beams (Hull) 50’s: Incoherent light (Forrester; Brown & Twist) 60’s: Independent lasers Temporal (Javan et. al.) Spatial (Magyar & Mandel) Attenuated lasers (Paul et. al.; Radloff) “Each photon interferes only with itself. Interference between two independent photons never occurs” Dirac, 1930

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Non-Classical Sources Interference Spontaneous emission from two atoms (Dicke, Richter) or more (Fano, Mandel) Late 80’s: Observation of two photons interference using PDC (Mandel, Franson) “…The two radiating atoms could be extremely far apart … and still exhibit this correlation effect. … It should be remembered, however, that both atoms are coupled to the same electromagnetic field. In the process of emitting the first photon, this common coupling results in the excitation of correlation states between the two atoms.” Dicke, 1964

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|ψ 0 =|N a | N b Fock State Interference |ψ 0 =|N a | N b Expectation values read no interference. Trajectory formalism show interference: –Continuous damping subjects non-unitary evolution –Photon detections described by “jump” operators –Environment modes are ignored. phase is chosen randomly. Y-T. Chough, PRA 55, 3143 (1997).K. Molmer, PRA. 55, 3195

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BEC Interference Y. Castin, J. Dalibard, Phys. Rev. A, 55, 4330 (1997). J. Javanainen, S.M. Yoo, Phys. Rev. Lett. 76, 161 (1996). M.R. Andrews, C.G. Townsend, H.-J. Miesner, D.S. Durfee, D.M. Kurn, W. Ketterle, SCIENCE 275, 637 (1997). - Initial state is disputed -

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A Generic Two-Source Interference System Intensity detectors Linear Superposition Source A Source B Y. Sagi, O. Firstenberg, A. Fisher, A. Ron, Phys. Rev. A. 67, (2003).

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Canonical transformation A Generic Two-Source Interference System Source A Source B. Y. Sagi, O. Firstenberg, A. Fisher, A. Ron, Phys. Rev. A. 67, (2003).

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States of the Composed Modes Coherent State Fock State

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States of the Composed Modes Coherent State Fock State Fock state in the composed mode Oscillating “phase state”

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The oscillating “phase state” Definite total photon number 100% visibility oscillation, with Does the system evolve towards that kind of state in the Fock interference experiments? (Molmer, 1997)

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A Scheme for QND Measurement of Interference using Cavity QED |e |g 00 Atom Field S. Haroche, J.M. Raimond, Advances in Atom. Molec. & Opt. Phys. Supplement 2, p. 123 (1994). Atoms as detectors Perfect mirrors (lossless) Two cavities (or single cavity with two nearly- degenerate modes) Spatial overlap

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Off-Resonance Coupling ( « ) Negligible absorption probability (QND). Light shift and Lamb shift. Spatial overlap

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Ramsey Interferometery “g” Probability “e” Probability Transforming phase difference to excitation probabilities…

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The Bernoulli Trial Process Each atom improves the estimation of intensity. Uncertainty of the estimation after K atoms is Same result was obtained for photo-detectors Effective detection (maximum of ) decreases our uncertainty toafter atoms. B.C. Sanders et. al., Phys. Rev. A. 68 (4), (2003) “Amount of information” in a single atom, determined by the interaction strength and duration.

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Simulation: Dynamics is not affected by the measurement. Detections follow the interference signal. Initial Coherent state ~80 Atoms per cycle

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Simulation: Initial Fock state The symmetric state evolves into an oscillating state. Detections identical to the coherent case! ~80 Atoms per cycle Fock Coherent

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No Atoms Atoms Atoms per cycle Emergence of the Oscillating Phase State Robust emergence of stable oscillations with 100% visibility. State stabilized after atoms, when the uncertainty is Oscillation phase is distributed uniformly.

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Conclusions Two Fock states will always show interference when the composed modes are measured: Initial independent Fock state has large number uncertainty in the composed mode. The decrease of the uncertainty induce an evolution to a stable oscillating phase state. The measured intensity is random, and hence the relative phase.

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Thank You.

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