Quantum Interferometry

Quantum Interferometry Using Coherent Beam Stimulated Parametric Down-conversion

The process of spontaneous parametric down conversion has been a work horse for the last two decades in understanding a variety of issues in quantum physics and in applications in the field of imaging. In particular one question of great importance is the issue of the resolution in imaging and this is still being addressed [L. A. Gatti et al Phys. Rev. A 70 013802 (2004); B. I. Erkmen, and J. H. Shapiro, quant-ph/0612070v1]. Dowling and coworkers proposed [A. N. Boto et al Phys. Rev. Lett. 85, 2733 (2000)] a very new idea to improve the sensitivity of resolution by using detectors that work on two photon absorption and by using special class of states called NOON states.

It is easy to produce NOON states experimentally with two photons by using a very low gain parametric down converter. In this case the resolution is improved by a factor of two.

However the probability of two photon absorption is very low and, as I learnt, several laboratories are working on materials which would have high efficiency for two photon absorption. Some years ago Boyd’s group [G. S. Agarwal et al Phys. Rev. Lett. 86, 1389, (2001)] examined Dowling et al’s proposal for the case of down conversion with high gain and found that one indeed has a resolution improvement by a factor two however the visibility goes down to 20% as the down converter saturates [G. S. Agarwal et al J. Opt. Soc. Am. B, 24, 270 (2007)]. Clearly we need to find methods that can remove the handicap of having to work with smaller visibilities.

We propose a new idea [DOI: 10.1364/OE.16.006479 ] using stimulated parametric processes along with spontaneous ones to produce resolution improvement while at the same time maintaining high visibility at large gains of the parametric process. We use coherent beams at the signal and the idler frequencies. We further find that the phases of coherent fields can also be used as tuning knobs to control the visibility of the pattern. We believe that the use of stimulated processes along with spontaneous ones would change our landscape as far as fields of imaging and quantum sensors are concerned.

Figure 1 : Using an input from non-degenerate stimulated parametric down-conversion for the determination of phase via photon-photon correlations.
Figure 2 : Stimulated emission enhanced two-photon counts for various phases of the coherent field at the gain factor g=2. The horizontal line shows the interferometric phase. The pump phase is fixed at . The counts are in units of two-photon coincidence rates coming from spontaneous down-conversion process. 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 two-photon counts for the case of spontaneous process. Here, the counts for the case of spontaneous process (dashed line) is multiplied by a factor of 103.

Heisenberg Limited Sagnac Interferometry with Higher Order Entanglement

When two electromagnetic waves counter-propagate along a circular path in rotation they experience different travel times to complete the path. This induces a phase shift between the two counter-propagating waves proportional to the angular velocity of the rotation. This phase difference is called as the Sagnac effect [Sagnac G, “L’ether lumineux demontre par l’effect du vent relatif d’ether dans un interferometre en rotation uniforme," C. R. Acad. Sci. 157, 708–710 (1913)] and in addition to its scientific importance, it has numerous practical applications such as detection and high-precision measurement of rotation in satellites, spaceships and long range missiles. It was studied and used in optics only with lasers until the new work [Bertocchi G, Alibart O, Ostrowsky D B, Tanzilli S, and Baldi P, “Single-photon Sagnac interferometer," J. Phys. B 39, 1011–1016 (2006)] where they demonstrated the single-photon interference in the fiber Sagnac interferometer using spontaneous parametric down conversion as the source of single photons. However, it turns out that the results of interference are no different than with classical sources. Thus a natural question would be –what is the nature of interference if we replace the single photon source by entangled photon pair source. This is what we examine in detail. We find that the sensitivity of Sagnac interferometer could be considerably improved by using entangled photons. By using down-converted photons, we designed a Sagnac interferometer [DOI: 10.1364/OE.15.006798] capable of detecting phase shifts which has four-fold increase in sensitivity with respect to conventional methods. Sagnac interferometers are used in many applications such as gyroscopes to detect high-precision measurement of rotation and their sensitivity is very crucial in satellites, spaceships and long range missiles.

Figure 3: Sagnac interferometer with classical fields
Figure 4: Sagnac interferometer with entangled photons and coincidence detection.