Phase Selection in Interference of Non-Classical Sources

Ofer Firstenberg, Yoav Sagi, Moshe Shuker,

Amit Ben-Kish, Amnon Fisher, Amiram RonDepartment of Physics, Technion - Israel Inst. of Tech.

Advanced Methods in Plasma and Optics

In honor of Amnon Fisher’s 70th birthday

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

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

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

Fock State Interference ||ψψ00=|=|NN aa| | NNbb

• 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

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-

A Generic Two-Source Interference System

Intensity detectors

LinearSuperposition

Source A

Source B

Y. Sagi, O. Firstenberg, A. Fisher, A. Ron, Phys. Rev. A. 67, 033811 (2003).

Canonicaltransformation

A Generic Two-Source Interference System

Source A

Source B

.

Y. Sagi, O. Firstenberg, A. Fisher, A. Ron, Phys. Rev. A. 67, 033811 (2003).

States of the Composed Modes• Coherent State

• Fock State

States of the Composed Modes• Coherent State

• Fock State

• Fock state in the composed mode

Oscillating “phase state”

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)

A Scheme for QND Measurementof Interference using Cavity QED

|e

|g

0Atom 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

Off-Resonance Coupling ( « )

• Negligible absorption probability (QND).

• Light shift and Lamb shift.

Ramsey Interferometery

1

0.5

0

1

0.5

0

“g” Probability

“e” Probability

Transforming phase difference to excitation probabilities…

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 to after atoms.

B.C. Sanders et. al., Phys. Rev. A. 68 (4), 042329 (2003)

“Amount of information” in a single atom, determined by the interaction

strength and duration.

Simulation:

• Dynamics is not affected by the measurement.

• Detections follow the interference signal.

Initial Coherent state

~80 Atoms per cycle

Simulation:Initial Fock state

• The symmetric state evolves into an oscillating state.

• Detections identical to the coherent case!

~80 Atoms per cycleFock Coherent

No Atoms No AtomsAtomsAtoms per cycle

3

16

80

405

1026

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.

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.

Thank You.