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QND measurement of photons Quantum Zeno Effect & Schrödingers Cat Julien BERNU YEP 2007

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Historical Zeno Paradox

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Quantum Zeno Effect TimePosition T P(right)

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Quantum Zeno Effect TimeP(right)

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R1R2 Classical source Our experimental setup QND measurement of the photon number

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Coupling the cavity to a classical source Classical source The field gets a complex amplitude in phase space Complex phase space

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Coupling the cavity to a classical source Time Mean photon number Quadratic start Zeno Effect ! Coherent field:

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Experimental difficulties

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Why 1 Hz precision? Effect of a frequency noise or sideband picks on the source or the cavity: random phase for injection pulses. Complex phase space

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How? Source: Anritsu generator locked on a (very) good quartz locked on a commercial atomic clock Source: Anritsu generator locked on a (very) good quartz locked on a commercial atomic clock Cavity: position of the mirrors must be stable at the range of 10 -13 m (10 -3 atomic radius)! Cavity: position of the mirrors must be stable at the range of 10 -13 m (10 -3 atomic radius)! Sensitivity to accoustic vibrations, pressure, temperature, voltage, hudge field… Sensitivity to accoustic vibrations, pressure, temperature, voltage, hudge field… V 4 He Recycling 0.1 mbar @ 1 bar 0.2 Hz 0.1 mV @ ~100V = 0.2 Hz P Pump Thermal contractions: (1kg) 100 µK @ 0.8 K 0.2 Hz

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Results Injection watched with QND measurements: time Injection pulses (Zeno Effect) Measurement

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Results Injection watched with QND measurements: time

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Results Then with continuous measurement: Injection watched with QND measurements: Perfect control! to be removed… Zeno Effect!

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Results

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Results Perfect agreement!

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QND detection of atoms Re( ) Im( ) a single atom controls the phase of the field R1R2

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QND detection of atoms Re( ) Im( ) /2 pulse R 1 The field phase "points" on the atomic state R1R2 a single atom controls the phase of the field

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This is a "Schrödinger cat state" on off 0 +1 on off 0 +1 Schrödingers Cat

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Production of Schrödingers Cat by a simple photon number parity measurement ( phase shift per photon): Schrödingers Cat

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Wigner Function (Phase space)

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Wigner Function (Phase space)

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Wigner Function

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Statistical mixture

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Wigner Function Schrödinger Cat

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Wigner Function

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Simple parity measurement !

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Size of the cat

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Observing the decoherence 2 200

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Size of the cat

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Atom chip experiment

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Conclusion Using our QND measurement procedure, we have been able to prevent the building up of a coherent field by Quantum Zeno Effect. We can also use it to produce big Schrödinger cats and study their decoherence by measuring their Wigner function.

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Perspectives 2 cavities for non-local experiments: teleportation of atoms teleportation of atoms non-local Scrödingers cat non-local Scrödingers cat quantum corrector codes quantum corrector codes

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Thank you! The team: J. B. Samuel Deléglise Christine Guerlin Clément Sayrin Igor Dotsenko Michel Brune Jean-Michel Raimond Serge Haroche Sebastien Gleyzes Stefan Kuhr Atom chip team

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The origin of decoherence: entanglement with the environment Decay of a coherent field: the cavity field remains coherent the cavity field remains coherent the leaking field has the same phase as the leaking field has the same phase as Environment

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Decay of a "cat" state: cavity-environment entanglement: cavity-environment entanglement: the leaking field "broadcasts" phase information trace over the environment trace over the environment decoherence (=diagonal field reduced density matrix) as soon as: decoherence (=diagonal field reduced density matrix) as soon as: Environment The origin of decoherence: entanglement with the environment

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Wigner functions of Schrödingers cats

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Residual problem Dephasing per photon / Number of photons 02004006008001000 1.0 0.8 0.6 0.4 0.2 0

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No quantum Zeno effect for thermal photons and decays

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Zeno Effect for quadratic growth Time

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Results: injection Effect of a small frequency detuning between the source and the cavity: Complex phase space

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Quantum Zeno Effect

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Graphes de wigner

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