# Presentation: 063395

## 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

## 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. D’Angelo, 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

## Quantum Optics Laboratory

- Remote Clock Synchronization Experiment
- January 2003

**Quantum Optics Laboratory**

##     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?

## A beautiful experiment:

## Typical language used to explain the result:

- “...the overlap of the _two photon’s wave packets_ when they are brought together at a beam splitter...”
- (Similar language can be found in some early papers from my group too.)

## Group Velocity

- A Classical Concept

*Coherent Superposition*

## * The “envelope” of the wavepacket propagates with “group velocity”, u0=ddk, which may be less, equal, or greater then c.

- * The “envelope” of the wavepacket propagates with “group velocity”, *u**0**=d****dk*****, which may be less, equal, or greater then c.
- * No “envelope”  no “group velocity”.

## Two-photon state (SPDC):

- * Pure state, coherent superposition of all possible two-photon amplitudes.
- * Corresponding to a 2-D wavepacket.

## The subsystems:

- Statistical mixture
- No wavepacket is defined

## No wavepacket, no “group velocity”! 

## What do we measure?

- The following may be interested to this workshop:

- (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.

- (1) Photon counting related correlation and calibration.

- (2) Energy-momentum related correlation and calibration.

## * Direct measurement of G(2):

- * Direct measurement of G(2):

## * 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,

## Convolution of the biphoton wavepackets

- Either in t1-t2 or t1+t2 direction

## 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.