Entangled State What Do We Measure

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Entangled State What Do We Measure?
Yanhua Shih Quantum Optics Laboratory Department
of Physics University of Maryland, Baltimore
County Baltimore, MD 21250 ONR, NSF, NASA-CASPR
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Quantum Optics Laboratory Department of
Physics University of Maryland, Baltimore
County Baltimore, MD 21250 Experiment
Yanhua Shih Theory Morton H. Rubin
Graduate Research Assistants M. DAngelo, A.D.
Valencia, G. Scarcelli, S. Thanvanthri, J.M.
Wen Visiting Research Scientists V. Berardi,
M.C. Chekhova, A. Garuccio, S.L. Gompers, X.H.
He, S.P. Kulik, H.Y. Zhang
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Quantum Optics Laboratory
Remote Clock Synchronization Experiment January
2003
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One of the most surprising consequences of
quantum mechanics is the entanglement of two or
more distance particles. Even though we still
have questions in regard to fundamental issues of
the entangled quantum systems, quantum
entanglement has started to play important roles
in practical applications. Entangled states
have been introduced for different metrology
measurements, for example, the study of group
velocity (hot topic!). Do we really measure
the group velocity? If not, what do we
measure?
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A beautiful experiment
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Typical language used to explain the
result the overlap of the two photons wave
packets when they are brought together at a beam
splitter (Similar language can be found in
some early papers from my group too.)
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Group Velocity A Classical Concept
Coherent Superposition
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In a dispersive medium, each mode of w
propagates with its own phase velocity w/k.
The coherent superposition of all the possible
modes result in a wavepacket or pulse. The
envelope of the wavepacket propagates with
group velocity, u0dw/dkw0 , which may be
less, equal, or greater then c. No envelope
--gt no group velocity.
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Two-photon state (SPDC)
Pure state, coherent superposition of all
possible two-photon amplitudes.
Corresponding to a 2-D wavepacket.
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The subsystems
Statistical mixture No wavepacket is defined
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No wavepacket, no group velocity!
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What do we measure?
The following may be interested to this workshop
(1) Photon counting related correlation and
calibration.
(2) Energy-momentum related correlation and
calibration.
(3) Space-time correlation measurement of G(2)
G(2) the probability of locating a photon at
(t1, r1) and its twin at (t2, r2).
(4) Using two-photon interferometer to measure,
indirectly, certain parameters (usually in
the form of sum or difference) related
to the optical paths.
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Direct measurement of G(2)
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Two-photon Interferometer
Two-photon interference pattern will be
obtained when the optical paths are manipulated.
Basically, the pattern is determined by the
self-convolution of the biphoton wavepacket,
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Convolution of the biphoton wavepackets Either in
t1-t2 or t1t2 direction
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Conclusion Even through an entangled
two-photon state (pure state) provides complete
information of the correlation between the
subsystems. The two-photon measure-ment may not
give any information about an individual
subsystem. It may simply not be there as we
thought.