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Journal of Experimental and Theoretical Physics Letters

Screw-type transparency in a three-level medium

Igor V. Kazinets, Boris G. Matisov, I. E. Mazets

Published Jun 1, 1998• 1 citation
Publisher

Abstract

A solution is obtained for the system of Maxwell-Schrödinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.

DOI
10.1134/1.567768

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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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A solution is obtained for the system of Maxwell-Schrödinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.
We present a new exact solution of Maxwell-Schrodinger set of equations. This solution describes propagation of a laser pulse through a (Lambda) -type medium, where the initial atomic state is prepared in the form of spatially-varying coherent superposition of low-energetic states. The solution describes a new type of transparency, which is characterized by a transformation of frequency of the incident pulse. Specifically, this type of transparency can be used for creation of an 'optical key' and a frequency converter.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\ensuremath{\Lambda}$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\ensuremath{\omega}}_{1}∕{\ensuremath{\omega}}_{2}=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\ensuremath{\pi}$, for pulse frequencies close to resonance with the transitions of a three-level $\ensuremath{\Lambda}$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\ensuremath{\omega}}_{13}∕{\ensuremath{\omega}}_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\ensuremath{\Lambda}$-type system by competition effects between optical transitions.
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
In the present paper, we examine the propagation of frequency-chirped laser pulses through a medium of Lambda atoms, pulses that are capable of producing adiabatic population transfer between the stable states. We compare the propagation of these pulses to their propagation in a medium of two-level atoms, and show that the distortion of the pulses is greatly reduced in the three-level case. In effect, there exists a transparency phenomenon for frequency-chirped laser pulses propagating in the three-level medium that is somewhat similar to electromagnetically induced transparency. It is concluded that the population transfer induced by chirped pulses does populate the excited state during the process to a slight extent, even if the transfer is perfectly adiabatic. Thus the transparency of the medium is also imperfect, the pulse is eventually distorted and its capability to produce the population transfer is lost, even in the perfectly adiabatic limit.