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Physical Review A

Coherent phenomena due to double-dark states in a system with decay interference

Antonios Fountoulakis, Andreas Terzis, Emmanuel Paspalakis

Published Mar 15, 2006• 30 citations
Publisher

Abstract

We theoretically analyze the interaction of a quantum system with a single ground state and three excited states that interacts with a pulsed laser field. The three excited states decay outside of the system to the same state. The dynamics of the system is studied by solving the coupled Maxwell-Schr\"odinger equations. We first present conditions for obtaining dark states of the system. These dark states lead to the phenomenon of coherent population trapping for strong applied fields. In addition, the existence of dark states leads to transparency at two different frequencies of a probe field. Slow light, at two different frequencies, can also occur. We present analytical results and verify those results with numerical solutions of the coupled Maxwell-Schr\"odinger equations.

DOI
10.1103/physreva.73.033811

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We analytically and numerically investigate the response of an open Λ-type atomic system to a probe laser field, where one of the atomic transition is coupled with a double-band radiation reservoir and high- Q defect modes formed by atomic doping. This system can be transparent to a weak probe field being two-photon resonant with the frequency of the defect modes or one of the two band edges, and the high- Q defect modes can even induce an atom–field coherent population trapping (CPT) state without involving the excited state of the atom, in spite of the background decay of the excited state of the atom. The steady-state properties of this CPT are independent of the smoothness feature of the density of modes (DOM) at band edges. However, the CPT never occurs in the absence of any defect even if the DOM is singular at both band edges. We also find that the background decay of the second ground state of the atom will destroy the CPT and increase the probe absorption, but the atomic coherence induced by the defect modes is more robust than that induced by the band edges. The transient properties of the CPT are also studied.

Journal of Optics B Quantum and Semiclassical Optics•Apr 27, 2004•11 citations
We theoretically analyze the interaction of a quantum system with a single ground state and three excited states that interacts with a pulsed laser field. The three excited states decay outside of the system to the same state. The dynamics of the system is studied by solving the coupled Maxwell-Schr"odinger equations. We first present conditions for obtaining dark states of the system. These dark states lead to the phenomenon of coherent population trapping for strong applied fields. In addition, the existence of dark states leads to transparency at two different frequencies of a probe field. Slow light, at two different frequencies, can also occur. We present analytical results and verify those results with numerical solutions of the coupled Maxwell-Schr"odinger equations.
We analyze the steady state and transient properties of the polarization and of the electronic population in a triple semiconductor quantum well structure with tunneling induced interference. We first derive the dark states of the system and show that this structure can lead to double dark states. Then, we show that under the dark state conditions the system can exhibit tunneling induced transparency, slow light, transient gain without inversion and coherent population trapping. The dynamics of the polarization and of the electronic population, as well as the total trapped electronic population in the system, are found to be depended on which dark state condition is satisfied.
The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.
We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled from the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can be completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. In particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases, in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and $\ensuremath{\Lambda}$-type three-level atoms and two nonidentical two-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in $\ensuremath{\Lambda}$-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.
We analyze the effects of partial coherence of ground-state preparation on two-pulse propagation in a three-level $\ensuremath{\Lambda}$ medium, in contrast to previous treatments that have considered the cases of media whose ground states are characterized by probabilities (level populations) or by probability amplitudes (coherent pure states). We present analytic solutions of the Maxwell-Bloch equations, and we extend our analysis with numerical solutions to the same equations. We interpret these solutions in the bright and dark dressed-state basis, and show that they describe a population transfer between the bright and dark state. For mixed-state $\ensuremath{\Lambda}$ media with partial ground-state phase coherence the dark state can never be fully populated. This has implications for phase-coherent effects such as pulse matching, coherent population trapping, and electromagnetically induced transparency (EIT). We show that for partially phase-coherent three-level media, self-induced transparency dominates EIT and our results suggest a corresponding three-level area theorem.
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 analytically and numerically investigate the response of an open Λ-type atomic system to a probe laser field, where one of the atomic transition is coupled with a double-band radiation reservoir and high- Q defect modes formed by atomic doping. This system can be transparent to a weak probe field being two-photon resonant with the frequency of the defect modes or one of the two band edges, and the high- Q defect modes can even induce an atom–field coherent population trapping (CPT) state without involving the excited state of the atom, in spite of the background decay of the excited state of the atom. The steady-state properties of this CPT are independent of the smoothness feature of the density of modes (DOM) at band edges. However, the CPT never occurs in the absence of any defect even if the DOM is singular at both band edges. We also find that the background decay of the second ground state of the atom will destroy the CPT and increase the probe absorption, but the atomic coherence induced by the defect modes is more robust than that induced by the band edges. The transient properties of the CPT are also studied.