PROJECT-2
Low Field Nonlinear Optics (LFNLO) & Spectroscopy
(Using EIT, Slow Optical Pulses, and Cold-Atoms)
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PROJECT-2
Project Title: Enhancement of Nonlinear Optical Effects in Ultra-Cold Atoms Using Quantum Interference Effects i.e., with Electromagnetically Induced Transparency (EIT) and Slow Light Pulses
Key Words: Nonlinear Optics and Spectroscopy, Third-Order Nonlinear Susceptibility, Four-Wave Mixing (FWM), Coherent Raman Process, Quantum Interference in Atoms, Electromagnetically Induced Transparency (EIT), Slow Optical Pulse, Cold Atom Physics. Quantum Information Science (QIS), Low Field Nonlinear Optics (LFNLO), Single Photonics.
Above Figure shows Slow Optical Pulse
(After Krauss, Nature Photonics 2, 448 (2008))
Overview of this Project
Physical origin of optical nonlinearity is the quantum mechanical perturbation of valance electrons of the material medium by electric field of strong optical beam incident on the medium and nonlinear susceptibility represents the perturbative i.e., an-harmonic term in the expansion of the dielectric polarization induced by strong incident optical field in the medium (R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, Inc., Second ed. 2003). Therefore, due to perturbative nature of underlying process, magnitude of nonlinear susceptibility is extremely weak and is orders of magnitudes weaker than magnitude of linear susceptibility. Therefore, strength of nonlinear signal (or alternately the generation efficiency) of any nonlinear optical process, which depends on magnitude of nonlinear susceptibility, is also extremely weak. This is the major drawback of traditional nonlinear optics. However, nonlinear optical processes are used in many-many practical applications. Therefore, enhancement of magnitude of nonlinear susceptibility is of very high practical importance. Past and the original research on enhancement of magnitude of nonlinear susceptibility, which was done by N. Bloembergen at Harvard University, was based on technique of Resonance Enhancement. This research led to Nobel Prize for year 1981, which was awarded to N. Bloembergen (Harvard) and A. Schawlow (Stanford) (Click-(Nobel-Prize-1981)). Recent availability of new techniques of EIT (Click For: (EIT)), slow optical pulses (Click For: (Slow Pulse), and cold-atom technology provides opportunity to further greatly enhance magnitude of nonlinear susceptibility and generation efficiency of nonlinear optical processes.
Electromagnetically Induced Transparency (EIT) is a quantum interference effect (M. Fleischhauer et al., Rev. Mod. Phys. 77, 633 (2005) and Slow Pulse is optical pulse (R. W. Boyd et al., Science 326, 1074 (2009)), which propagate with group velocity far less than usual speed of light (c). Both EIT and slow pulse were invented by Stephen E. Harris at Stanford University (S. E. Harris, Phys. Today 50, No. 7, pp. 36 (1997):Download: Harris-(PT) Pdf). Although, EIT and slow pulse have found many practical applications (J. B. Khurgin and R. S. Tucker, Eds., Slow Light Science and Applications (Taylor & Francis, 2008)) but enhancement of nonlinear optical effects is one of the most important applications of electromagnetically induced transparency (EIT) (S. E. Harris et al., Phys. Rev. Lett. 64, 1107 (1990); Phys. Rev. Lett. 93, 183601 (2004); J. D. Joannopoulos et al., Nature Material 3, 211 (2004) and slow pulse (S. E. Harris et al., Phys. Rev A 68, 041801 (2003); Phys. Rev. Letts. 82, 4611 (1999); C. Monat et al., Opt. Express 17 (4), 2944 (2009)). Majority of past research on EIT and slow optical pulses had been based on investigations of the effect of quantum interference on real and imaginary parts of complex linear susceptibility, but this project focuses on investigations of the effect of quantum interference on real and imaginary parts of complex third-order nonlinear susceptibility of cold atomic matter (Nonlinear Optical Processes Using Electromagnetically Induced Transparency, S. E. Harris et al., Phys. Rev. Lett. 64, 1107 (1990): Download: Harris-(CHI-3) Pdf ).
This research project is continuation of my two different past experiments, which are on: (1) Nonlinear Optics (NLO) and Spectroscopy and (2) Electromagnetically Induced Transparency (EIT) & Lasing Without Inversion (LWI). Summary of each of these two past experiments is available in two different Pdf files, which can be downloaded. To download these Pdf files cllck on Page: PAST, which is located on TOP-ROW of this website, and then download two Pdf files: A-OHD-RIKE and B-EIT-LWI.
This project integrates techniques of nonlinear optics, electromagnetically induced transparency (EIT), cold-atom physics, and single-photon detector technology to enhance generation efficiency of four-wave mixing (FWM) process, which is a third-order nonlinear optical effect (Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984)). In this four-wave mixing (FWM) experiment, three weak input optical pulses along with multiple dressing optical fields are phase matched in a cloud of cold Cesium (Cs) atoms created in Magneto-Optical Trap (MOT). Third-order nonlinear susceptibility of cold atoms mixes three input optical fields generating a new fourth optical field at a frequency, which is algebraic sum of the frequencies of three input optical fields. Altogether, it is four-photon coherent Raman process. All three input optical pulses are tuned to resonant transitions of four-level atoms. Due to quantum interference effect caused by dressing fields, resonant absorption of all three input pulses is cancelled and linewidth of atomic transitions of cold atoms become sub-natural. With all three input optical pulses tuned to extremely narrow atomic transitions, my recent publication (P. S. Bhatia, Resonance Enhancement of Nonlinear Susceptibility of Ultracold Atoms using EIT, Phys. Rev. A) predict a very huge enhancement of magnitude of third-order nonlinear susceptibility of ultracold atoms (See Figure below), which is orders of magnitude greater than any previously reported enhancement of nonlinear susceptibility. Secondly, due to quantum interference effect caused by dressing fields, all three optical pulses are simultaneously slowed and compressed in the atomic cloud. This project deals with designing novel schemes for slowing multiple optical pulses, which are not independent but are coupled by nonlinear susceptibility of propagating medium. As a result, all three input optical pulses stay phase matched and propagate in the atomic cloud with ultraslow and equal group velocities. Group velocities of input pulses are adjusted, so that spatial length of each of these three pulses matches with physical length of atomic cloud (Nonlinear Optics at Low Light Levels, S. E. Harris et al., Phys. Rev Lett. et al., 82, 4611 (1999): Download: Harris-(LFNLO-1) Pdf & Low-Light -Level Nonlinear Optics with Slow Light, S. E. Harris et al., Phys. Rev. A 68, 041801 (2003)): Download: Harris-(LFNLO-2) Pdf. Due to ultraslow group velocities of pulses, optical energy in the pulses is compressed in space and therefore optical energy density in the atomic cloud is greatly increased. Under the condition of very huge magnitude of third-order nonlinear susceptibility together with very large optical energy density in the atomic cloud, the efficiency of nonlinear signal generated by four-wave mixing (FWM) process is greatly enhanced, so that third-order nonlinear interaction between single photon pulses and single atoms can be practiced.
This high-sensitive and extremely cared experiment requires development of very sophisticated and large-scale experimental facility in which almost every optical component is special purpose. Major hardware developments required for this experiment include creation of cold Cesium (Cs) atoms in Magneto-Optical Trap (MOT), development of injection seeded solid-state laser system that generates highly stable narrowband optical pulses tunable both in frequency and pulse-width, high precision wavemeter that can monitor operating characteristics of light pulses with frequency measurement accuracy of the order of 1 part in 10^10 (10 raise to the power +10), Superconducting Nanowire Photon Number Resolving (PNR) Single Photon Detector (SNSPD), and computer controlled gated data acquisition system based on fast electronics.
Some applications of this research are given below.
(1) Observation of nonlinear optical effects typically require high intensity light pulses, which have millions and billions of photons in them. Thanks to EIT and slow pulses that allow practicing nonlinear optical effects with only few photons approaching single photon limit. This give birth to a new field of research called Low Field Nonlinear Optics (LFNLO) or alternately Single Photonics.
(2) This project eliminates major drawbacks of traditional nonlinear optics and pushes light-matter interaction to a new regime where nonlinear optical processes can be practiced with almost same generation efficiency as linear optical processes ! Therefore, this project totally revolutionizes light-matter interaction and can bring next Nobel Prize.
(3) Results of this experiment can be used to greatly enhance Signal-to-Noise (S/N) ratio i.e. detection sensitivity of nonlinear laser spectroscopy. Therefore, this research is important for Heisenberg limited high-sensitive and high-resolution nonlinear spectroscopy of ultracold atoms and molecules. In this project, we can also study nonlinear optical properties of BEC as a new condensed matter material.
(4) This research paves the way towards new era of quantum information science (QIS) and technology in which atomic size nonlinear photonic devices are likely to operate by nonlinear interaction between single atoms and single photons. Such photonic devices are needed for development of real-world practical quantum logic gates and quantum processors required for quantum computation. Further, operation of an advanced quantum network typically requires single photons and in particular, generation & processing of quantum entangled states and quantum frequency conversion (QFC), which are central to the development of quantum networks, relies on nonlinear interaction at single photon level. Therefore, this project supports development of next generation of quantum internet.
Above Figure Shows Huge Increase in Magnitude of Third-Order Nonlinear Susceptibility of Ultra-Cold Atoms using EIT
Research Proposal Related to this Project
Short version of the research proposal related to this project is available in a Pdf file, which can be downloaded. To download this file click on the link below. Complete version of this research proposal is also available on request. This proposal is almost ready to be submitted to funding agency for attracting research funds.
Download: PROPOSAL-(AMO) Pdf
Publications Related to this Project
My selected current publications, directly related to this proposed project, are given below. Just clicking on these publications is sufficient. Note majority of my publications are single authored / first authored and further these publications are very detailed.
(Quantum Interference in Cold-Atoms)
[1] Resonance Enhancement of Nonlinear Susceptibility of Ultracold Atoms using Electromagnetically Induced Transparency (EIT),
P. S. Bhatia, Phys Rev A,
Download: 1-PUB-AMO Pdf
(Slow Optical Pulses in Cold-Atoms)
[2] Simultaneously Slowing Multiple Optical Pulses using Quantum Interference
Effect in Ultracold Atoms, P. S. Bhatia, Phys, Rev. A.
Download: 2-PUB-AMO Pdf
(High-Sensitive Nonlinear Spectroscopy of Molecules in the Fermi-Resonance Region)
[3] Highly Sensitive Optically Heterodyne, Raman induced Kerr-Effect Spectrometer using Pulsed Lasers,
P. S. Bhatia, Joe P. Holder, and John W. Keto, J. Opt. Soc. Am. B 14 (2), 263 (1997).
Download: 3-PUB-AMO Pdf
(Atomic and Molecular Spectroscopy Beyond the Standard Quantum Limit)
[4] Pressure and Power Dependence of the Optically Heterodyne Raman Induced Kerr Effect Line Shape,
P. S. Bhatia and John W. Keto, Phys. Rev. A 59, 4045 (1999).
Download: 4-PUB-AMO Pdf
(High-Precision Measurements of Atomic and Molecular Transitions)
[5] Calibration of a Computer Controlled Precision Wavemeter for use with Pulsed Lasers,
P. S. Bhatia, Craig W. McCluskey &, John W. Keto, Appl. Opt. 38 (12), 2486 (1999).
Download: 5-PUB-AMO Pdf
(Cesium Atom Spectroscopy)
[6] Laser Amplification without Population Inversion on the Line of the Cs Atomusing Semiconductor Diode Laser,
P. S. Bhatia, George R. Welch, and M. O. Scully, J. Opt. Soc. Am. B 18 (11), 1587 (2001).
Download: 6-PUB-AMO Pdf
Presentation Related to this Project
Presentation on this Project, which has selected view graphs, is available in a Pdf file, which can be downloaded. To download this Pdf file click on the link below.
Download: (VG-Project-2) Pdf
Nobel Prize Associated with this Project
Year: 1981
Nonlinear Laser Spectroscopy
Nicolaas Bloembergen (Harvard) and
Arthur Leonard. Schawlow (Stanford)
Click-(Nobel-Prize-1981)
General Readings Related to this Project
(1) Nonlinear Optics ans Spectroscopy, N. Bloembergen,
Reviews of Mod. Phys. 54 (3), 685 (1982).
Download: (READ-1) Pdf
(2) Bose-Einstein Condensation of Atomic Gases
J. R. Anglin and W. Ketterle, Nature 416, 211 (2002).
(3) Optical Frequency Metrology
Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
Download: (READ-3) Pdf
(4) Electromagnetically Induced Transparency,
S. E. Harris, Physics Today 50 (7), 36 (1997).
Download: (READ-4) Pdf
(5) Slow, Ultraslow, Stored, and Frozen Light
G. R. Welch, M. O. Scully et al., Adv. AMO Phys. 46, 191-242 (2001).
Download: (READ-5) Pdf
(6) Why Do We Need Slow Light ?
T. F. Krauss, Nature Photonics 2, 448 (2008).
Download: (READ-6) Pdf
Textbooks Related to this Project
Handbook of Nonlinear Optics
Richard L. Sutherland
Marcel Dekker, Inc., Second ed. 2003.
Introduction to Nonlinear Laser Spectroscopy
Marc D. Levenson and S. S. Kano
Revised Edition-1988
Academic Press.
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