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

Historical Zeno Paradox

Quantum Zeno Effect TimePosition T P(right)

Quantum Zeno Effect TimeP(right)

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

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

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

Experimental difficulties

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

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 m (10 -3 atomic radius)! Cavity: position of the mirrors must be stable at the range of 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 bar 0.2 Hz 0.1 ~100V = 0.2 Hz P Pump Thermal contractions: (1kg) K 0.2 Hz

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

Results Injection watched with QND measurements: time

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

Results

Results Perfect agreement!

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

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

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

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

Wigner Function (Phase space)

Wigner Function (Phase space)

Wigner Function

Statistical mixture

Wigner Function Schrödinger Cat

Wigner Function

Simple parity measurement !

Size of the cat

Observing the decoherence 2 200

Size of the cat

Atom chip experiment

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.

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

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

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

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

Wigner functions of Schrödingers cats

Residual problem Dephasing per photon / Number of photons

No quantum Zeno effect for thermal photons and decays

Zeno Effect for quadratic growth Time

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

Quantum Zeno Effect

Graphes de wigner