About my research
Quantum imaging and sensing using coherent beam stimulated parametric down-conversion
Heisenberg limited Sagnac interferometry
Towards Heisenberg limit in magnetometry with parametric down-converted photons
Quantum properties of a nanomechanical oscillator
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research

I have been working on research problems at the cutting edge in Quantum Optics . In particular, I have focused on Heisenberg limited measurements with entangled light . This is a subject which is currently of great interest as it can lead not only to new fundamental results but also to new types of sensors working at quantum level.
The field of quantum limited measurements in quantum optics is at the threshold of a major technological breakthrough with potentially many applications in ultra-sensitive measurements. Utilizing the strong, unusual correlation properties of entangled light sources one can design interferometers that can detect phase shifts beyond the so-called quantum noise limit , which according to semi-classical theory is the ultimate lower noise level for optical measurements.

Quantum Imaging and Sensing 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 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.


FIG1.: Using an input from non-degenerate stimulated parametric down-conversion for the determination of phase via photon-photon correlations.

FIG2: 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 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.

I1=|E1|2(1-cosf)

FIG1. Sagnac interferometer with classical fields

P4 ~ (1-cos4f)

FIG2. Sagnac interferometer with entangled photons and coincidence detection.

Towards Heisenberg Limit in Magnetometry with Parametric Down-converted Photons

In this paper, we present an analysis of how parametric down converted photons could be useful in getting better spectroscopic information about the medium. We demonstrate how the improvement in magneto-optical rotation (MOR) of light could be realized by employing non-collinear down conversion geometry as shown in Fig. 1. We calculate the resolution that can be achieved in the MOR's both by use of coherent light and down converted light. The sensitivity depends on whether the two-photon or four-photon coincidence detection is used. We show that four-photon coincidence detection by the use of non-collinear type-II PDC light in MOR's increases the sensitivity by a factor of four in compared to coherent light. We also give an argument that minimum rotation uncertainty scales to Heisenberg limit by the use of down converted photons. Our results apply to sources with arbitrary pumping of the nonlinear crystal which is used in the production of PDC photons.

FIG1: Setup for the Magneto-optical rotation of light using type-II PDC photons in non-collinear geometry.

 

Quantum Optics of Nanomechanical Oscillator Near The Instability Point

Another upcoming area with many new exciting results concerns the existence of quantum effects at macroscopic level. Creating and manipulating quantum states in a macroscopic mechanical system would address issues, such as the physics of decoherence, that are of fundamental importance. There are also potential applications to quantum computing and communication, quantum-limited displacement, force, and mass sensing. From a scientific perspective, nanomechanical oscillators are the leading candidates in a current worldwide effort to observe quantum behavior. The previous works mostly concerned variety of methods and techniques in the stable linear regime of the oscillator. In line with the work in quantum optics on squeezing, one can consider studying the squeezed states of the nanomechanical oscillator. There are proposals that consider producing squeezing by modulating the spring constant. Here in this work, I analyzed the situation in the new regime near to the Euler buckling instability point where the nonlinearity effects take place. By numerically solving the Schrodinger equation, I showed the existence of amplitude squeezing in Nanomechanical oscillator having an externally controlled Euler buckling nonlinearity. Although the observation would be experimentally challenging, what makes me very interested in this problem is that the prospect of exploring tunable quantum squeezing in nanomechanical oscillators and the connection to the Euler buckling instability are intriguing. In future, I am planning to work on this problem in more detail. One interesting investigation can be to couple the nanomechanical oscillator with its externally controlled nonlinearity to a two level Cooper-pair box system. The detection of the Cooper-pair box in special states would give rise to a variety of states of the mechanical oscillator such as a combination of cat states and squeezed states.

FIG.1:Schematic diagram of the freely suspended nanomechanical beam of total length L, width w and thickness d. The beam is clamped at both ends. A static, mechanical force F0 compresses the beam in longitudinal direction controlling the nonlinearity. An ac-driving force can be used to excite the beam to transverse vibrations.

Publications

  1. “Resolution of objects within subwavelength range by using the near field of a dipole,PDF” Aziz Kolkıran and G. S. Agarwal, Optics Letters, Vol. 37, Iss. 12, pp. 2313–2315 (2012). 2010 ISI Impact Factor: 3.318
  2. "Amplitude Noise Reduction in a Nano-mechanical Oscillator," Aziz Kolkiran and G. S. Agarwal,Mathematical and Computational Applications 16, 290-300 (2011).
  3. "Quantum Imaging Using Coherent Beam Stimulated Parametric Down-conversion, PDF" Aziz Kolkiran and G. S. Agarwal, Opt. Express 16, 6479-6485 (2008).
  4. 2010 ISI Impact Factor: 3.753
  5. "Heisenberg limited Sagnac interferometry, PDF" Aziz Kolkiran and G. S. Agarwal, Opt. Express 15, 6798-68 (2007). 2010 ISI Impact Factor: 3.753
  6. "Towards the Heisenberg limit in magnetometry with parametric down-converted photons, PDF" Aziz Kolkiran and G. S. Agarwal, Phys. Rev. A 74, 053810 (2006). 2010 ISI Impact Factor: 2.861
  7. "Quantum properties of a nano-mechanical oscillator, PDF" Aziz Kolkiran and G. S. Agarwal, [eprint cond-mat/0608621].
  8. "Machines and quantum logic,"Aziz Kolkiran, A popular science article in Turkish, Journal of Science and Technology 400, 81 (2001).

International Conferences and Workshops / Seminars and Colloquia

  1. "Heisenberg Limited Sagnac Interferometry with Higher Order Entanglement" contributed joint poster, OSA Topical Meeting, International Conference on Quantum Information (ICQI) and Ninth Conference on Coherence in Quantum Optics (CQO9) , Rochester, New York, 10 --15 June,2007.
  2. "Heisenberg limited Sagnac interferometry,"contributed talk in the focus session on quantum limited measurements, American Physical Society March meeting, Denver, Colorado, 5 – 9 March, 2007.
  3. "Towards Heisenberg limit in magnetometry with parametric down-converted photons," contributed talk in the session on precision and quantum enabled measurements, Frontiers in Optics 2006/Laser Science XXII, The 90th Optical Society of America Annual Meeting, Rochester, New York, 8 – 12 October, 2006.
  4. "Towards Heisenberg limit in magnetometry with parametric down-converted photons," contributed poster, International Focus Workshop on Linear Optical Quantum Information Processing (LOQuIP), Baton Rouge, Louisiana, 9 - 12 April, 2006.
  5. "Heisenberg limited magnetometry," Departmental Seminar, Journal Club on Statistical Mechanics, Condensed Matter Physics and Optics, Department of physics, Oklahoma State University, Stillwater, Oklahoma, March 24th, 2006.
  6. "Squeezing in a nano-mechanical oscillator," contributed poster, 12th Central European Workshop on Quantum Optics (CEWQO) 2005, Ankara, Turkey, 6 - 9 June , 2005.
  7. IEEE/LEOS Summer Topicals 2004 on Whispering Gallery Mode Microcavities, San Diego, California, 28 - 30 June, 2004.
  8. "A teleportation scheme by using the GHZ state," contributed poster, QIP 2001: Fourth Workshop on Quantum Information Processing, Amsterdam, Netherlands, 9 – 12 January, 2001.
  9. Annual Winter Schools on Topology and Physics, three years in sequence, organized by The Scientific and Technical Research Council of Turkey, Izzet Baysal University, Bolu, Turkey, February 1995, 1996, 1997.

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