Transcript Phase selection in interference of non

Advanced Methods in Plasma and Optics
In honor of Amnon Fisher’s 70th birthday
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.
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
“Each photon interferes only with itself.
Interference between two independent
photons never occurs” Dirac, 1930
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)
Non-Classical Sources Interference
Spontaneous emission from two atoms
(Dicke, Richter) or more (Fano, Mandel)
“…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
Late 80’s: Observation of two photons
interference using PDC (Mandel, Franson)
Fock State Interference |ψ0=|N a| Nb
Y-T. Chough, PRA 55, 3143 (1997).
K. Molmer, PRA. 55, 3195
• 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.
BEC Interference
Y. Castin, J. Dalibard, Phys.
Rev. A, 55, 4330 (1997).
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 -
J. Javanainen, S.M. Yoo, Phys.
Rev. Lett. 76, 161 (1996).
A Generic Two-Source Interference System
Source A
Linear
Superposition
Intensity
detectors
Source B
Y. Sagi, O. Firstenberg, A. Fisher, A. Ron, Phys. Rev. A. 67, 033811 (2003).
A Generic Two-Source Interference System
Source A
Canonical
transformation
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
(Molmer, 1997)
• Does the system evolve towards that kind of
state in the Fock interference experiments?
A Scheme for QND Measurement
of Interference using Cavity QED
|e
Atom
w0
D

w
Field
|g
Atoms as
detectors
Spatial overlap
Perfect mirrors
(lossless)
Two cavities (or single
cavity with two nearlydegenerate modes)
 S. Haroche, J.M. Raimond, Advances in Atom. Molec. & Opt. Phys. Supplement 2, p. 123
Off-Resonance Coupling ( « )
• Negligible absorption probability (QND).
• Light shift and Lamb shift.
Ramsey Interferometery
Transforming phase difference
to excitation probabilities…
“g” Probability
1
0.5
0
“e” Probability
1
0.5
0
The Bernoulli Trial Process
• Each atom improves the estimation of intensity.
Uncertainty of the estimation after K atoms is
“Amount of information” in a single atom,
determined by the interaction
strength and duration.
• Same result was obtained for photo-detectors
• Effective detection (maximum of
our uncertainty to
after
 B.C. Sanders et. al., Phys. Rev. A. 68 (4), 042329 (2003)
) decreases
atoms.
Simulation:
Initial Coherent state
~80 Atoms per cycle
• Dynamics is not
affected by the
measurement.
• Detections follow the
interference signal.
Simulation:
Initial Fock state
~80 Atoms per cycle
Fock
Coherent
• The symmetric state
evolves into an
oscillating state.
• Detections identical to
the coherent case!
Emergence of the Oscillating Phase State
Atoms per
No Atoms Atoms
No Atoms
cycle
3
Robust emergence of
stable oscillations
with 100% visibility.
16
80
405
1026
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.