Heisenberg limited sagnac interferometry
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PHYSICS. Heisenberg Limited Sagnac Interferometry. AZIZ KOLKIRAN , G.S. AGARWAL Oklahoma State University, 2007 APS March Meeting, A33 Focus Session: Quantum Limited Measurements, Monday March 5 th ,2007, 9:48-10:00am. Sagnac phase shift. Sagnac interferometer with classical fields.

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Heisenberg Limited Sagnac Interferometry

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Heisenberg limited sagnac interferometry

PHYSICS

Heisenberg Limited Sagnac Interferometry

AZIZ KOLKIRAN, G.S. AGARWAL

Oklahoma State University,

2007 APS March Meeting,

A33 Focus Session: Quantum Limited Measurements,

Monday March 5th,2007, 9:48-10:00am


Heisenberg limited sagnac interferometry

Sagnac phase shift.


Heisenberg limited sagnac interferometry

Sagnac interferometer with classical fields.

Beam splitter transmission and reflection coefficients


Heisenberg limited sagnac interferometry

Single-photon Sagnac interferometer*

*G Bertocchi, O Alibart, D B Ostrowsky, S Tanzilli and P Baldi, J. Phys. B: At. Mol. Opt. Phys. 39 (2006) 1011–1016


Heisenberg limited sagnac interferometry

Can we improve the resolution by using quantum states of light?

experimentally employed by single photons coming from a spontaneous down-converter

Bertocchi G. et al, “Single photon Sagnac interferometry”, J. Phys. B39, 1011 (2006)


Heisenberg limited sagnac interferometry

Use of entangled photon pairs from down-conversion.

pump

NL

Fig. 4

input state from the down-conversion process:

r is the interaction parameter (a.k.a. squeezing parameter)

of entangled pair production from vacuum


Heisenberg limited sagnac interferometry

Can we improve the resolution further by using

multi-photon entanglement?

Fig. 5

are transmission and reflection

probabilities at the beam splitters


Heisenberg limited sagnac interferometry

Can we turn the fringes into ones with equal height**?

Fig. 6

**see also T. Nagata, et al. Science 316, 726-729, (2007).


Heisenberg limited sagnac interferometry

4-photon interference using asymmetric beam splitters*

The experiment

B. H. Liu, F. W. Sun, Y. X. Gong, Y. F. Huang, G. C. Guo, and Z. Y. Ou

Optics Letters, Vol. 32, Issue 10, pp. 1320-1322 (2007).


Heisenberg limited sagnac interferometry

How does this work?

Non-classical

Fock state

phase shifter

phase shifter

classical field

For two-photon coincidence detection (Fig. 4), the state, after entering and completing the path, evolves into the following:

For four-photon coincidence detection (Fig. 5 and 6), the state, after entering and completing the path, evolves into the following:

This term leads to unequal fringes in the detection setup given by Fig. 5

Only this part contributes to the detection in the setup given by Fig. 6

All interferometric schemes using the maximally correlated entangled states show

the phase sensitivity equal to 1/N, which is the Heisenberg limit.


Heisenberg limited sagnac interferometry

Conclusions

  • Use of PDC light in SI leads to 2- and 4-fold increase in the sensitivity depending on the detection mechanism.

  • We think that the experiment should be feasible, because single photons have already been used from a down-converter in SI and in many experiments 2- and 4-photon interference effects have been observed.

  • If successful, it could be a stimulating application in the field of quantum metrology.


Heisenberg limited sagnac interferometry

Opt. Express 15, 6798-6808 (2007).


Heisenberg limited sagnac interferometry

Current work in progress


Heisenberg limited sagnac interferometry

Quantum Interferometric Optical Lithography:

Exploiting Entanglement to Beat the Diffraction Limit

20% at large gain

G. S. Agarwal, R. W. Boyd, E. M. Nagasako, and S. J. Bentley, Phys. Rev. Lett. 86, 1389 (2001),

comment on A.N. Boto, et al., Phys. Rev. Lett. 85, 2733 (2000).


Heisenberg limited sagnac interferometry

Quantum Imaging and Sensing Using Coherent Beam Stimulated Parametric Down conversion

SETUP: Using an input from non-degenerate stimulated parametric down-conversion for the determination of phase via photon-photon correlations.

RESULTS: Stimulated emission enhanced visibility of two-photon counts for various phases of the coherent field with respect to the gain factor g. The pump phase is fixed at . The modulus of the coherent field is chosen such that the coincidences coming from SPDC and the coherent fields are equal to each other. The dashed line shows the visibility for the case of photons produced by spontaneous parametric down-conversion.

Aziz Kolkiran and G S Agarwal, in preparation


Heisenberg limited sagnac interferometry

Future work

Interaction free measurements (non-distortion quantum

interrogation) using entangled photons

How to optically detect the presence of something without photons hitting it.

two-level

atom

25% chance of detecting the bomb without explosion. By using different beam splitter reflectivity's R, this can be made 50%.

Elitzur A. C. and Vaidman L. (1993). Quantum mechanical interaction-free measurements. Found. Phys. 23, 987-97.


Heisenberg limited sagnac interferometry

Future work

Interaction free measurements (non-distortion quantum

interrogation) using entangled photons

Entangled source

object (three level atom)


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