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Physical Review A

Enhancement of nonlinear-optical signals under coherent-population-trapping conditions

Harshawardhan Wanare, G. S. Agarwal

Published Jul 1, 1998• 20 citations
Publisher

Abstract

We develop a nonperturbative approach to study the generation of nonlinear signals in a coherently prepared medium. Specifically, we study the process ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}+({\ensuremath{\omega}}_{2}+\ensuremath{\Omega})$, in a system prepared in a coherent-population-trapping state. We calculate enhancement factors of the order of $\ensuremath{\sim}{10}^{2}$ in the generated signal, under a variety of conditions thus supplementing the work of Jain et al. [Phys. Rev. Lett. 77, 4326 (1996)]. Our approach also enables us to study other related issues. We demonstrate the existence of pulse matching at higher probe powers.

DOI
10.1103/physreva.58.598

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Propagation of a laser pulse in a three-level cascade atomic medium under conditions of electromagnetically induced transparency

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We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such i.e., the effect is established. Under conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, Lasers without inversion: interference of dressed lifetime-broadened states, Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb, Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, speed reduction to 17 metres per second in an ultracold atomic gas, Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening, Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach, J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, Matched Optical Solitary Waves for Three- and Five-Level Systems, Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, Preparation energy for electromagnetically induced transparency, Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency, Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, Dynamical control of pulse propagation in electromagnetically induced transparency, Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium, Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, Propagation and nonlinear generation dynamics in a coherently prepared four-level system, Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, Controlling the propagation of broadband light pulses by Induced Transparency, Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, Pulse propagation in a medium of ?-type atoms, Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency, Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach, Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, Transmission of dressed fields in three-level media, Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium, Phys. Rev. A 1 (1970) 1604. CrossRef

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Coherent population trapping and vast enhancement of the efficiency of resonant three-wave mixing in isotropic media

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Propagation of a laser pulse in a three-level cascade atomic medium under conditions of electromagnetically induced transparency

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We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such medium, i.e., the EIT effect is established. Under EIT conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, "Lasers without inversion: interference of dressed lifetime-broadened states", Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, "Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb", Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, "EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening", Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, "Matched Optical Solitary Waves for Three- and Five-Level Systems", Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, "Preparation energy for electromagnetically induced transparency", Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, "Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency", Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, "Dynamical control of pulse propagation in electromagnetically induced transparency", Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, "Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium", Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, "Propagation and nonlinear generation dynamics in a coherently prepared four-level system", Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, "Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency", Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, "Pulse propagation in a medium of ?-type atoms", Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, "Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency", Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, "Transmission of dressed fields in three-level media", Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, "Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium", Phys. Rev. A 1 (1970) 1604. CrossRef

Photonics Letters of Poland•Sep 30, 2016•6 citations
We develop a nonperturbative approach to study the generation of nonlinear signals in a coherently prepared medium. Specifically, we study the process \ensuremathω1\ensuremath−\ensuremathω2+(\ensuremathω2+\ensuremathΩ){\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}+({\ensuremath{\omega}}_{2}+\ensuremath{\Omega})\ensuremathω1​\ensuremath−\ensuremathω2​+(\ensuremathω2​+\ensuremathΩ), in a system prepared in a coherent-population-trapping state. We calculate enhancement factors of the order of \ensuremath∼102\ensuremath{\sim}{10}^{2}\ensuremath∼102 in the generated signal, under a variety of conditions thus supplementing the work of Jain et al. [Phys. Rev. Lett. 77, 4326 (1996)]. Our approach also enables us to study other related issues. We demonstrate the existence of pulse matching at higher probe powers.
To achieve a high degree of quantum noise squeezing, an optical cavity is often employed to enhance the interaction time between light and matter. Here, we propose to utilize the effect of coherent population trapping (CPT) to directly generate squeezed light without any optical cavity. Combined with the slow propagation speed of light in a CPT medium, a coherent state passing through an atomic ensemble with a high optical density (OD) can evolve into a highly squeezed state even in a single passage. Our study reveals that noise squeezing of more than 10 dB can be achieved with an OD of 1000, which is currently available in experiments. A larger OD can further increase the degree of squeezing. As the light intensity and two-photon detuning are key factors in the CPT interaction, we also demonstrate that the minimum variance at a given OD can be reached for a wide range of these two factors, showing the proposed scheme is flexible and robust. Furthermore, there is no need to consider the phase-matching condition in the CPT scheme. Our introduction of high OD in atomic media not only brings a long light-matter interaction time comparable to optical cavities, but also opens an alternative avenue in the generation of squeezed light for quantum interface.
An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.
We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such i.e., the effect is established. Under conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, Lasers without inversion: interference of dressed lifetime-broadened states, Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb, Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, speed reduction to 17 metres per second in an ultracold atomic gas, Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening, Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach, J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, Matched Optical Solitary Waves for Three- and Five-Level Systems, Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, Preparation energy for electromagnetically induced transparency, Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency, Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, Dynamical control of pulse propagation in electromagnetically induced transparency, Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium, Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, Propagation and nonlinear generation dynamics in a coherently prepared four-level system, Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, Controlling the propagation of broadband light pulses by Induced Transparency, Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, Pulse propagation in a medium of ?-type atoms, Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency, Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach, Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, Transmission of dressed fields in three-level media, Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium, Phys. Rev. A 1 (1970) 1604. CrossRef
We study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such medium, i.e., the EIT effect is established. Under EIT conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, "Lasers without inversion: interference of dressed lifetime-broadened states", Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, "Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb", Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, "EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening", Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, "Matched Optical Solitary Waves for Three- and Five-Level Systems", Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, "Preparation energy for electromagnetically induced transparency", Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, "Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency", Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, "Dynamical control of pulse propagation in electromagnetically induced transparency", Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, "Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium", Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, "Propagation and nonlinear generation dynamics in a coherently prepared four-level system", Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, "Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency", Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, "Pulse propagation in a medium of ?-type atoms", Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, "Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency", Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, "Transmission of dressed fields in three-level media", Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, "Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium", Phys. Rev. A 1 (1970) 1604. CrossRef