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arXiv:1510.04325 · Physica Scripta

Propagation of a probe pulse inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency

Pablo Barberis-Blostein, Omar Aguilar Loreto

Published May 13, 2015• 2 citations
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Abstract

We obtain a partial differential equation for a pulse travelling inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a three-level BEC in Λ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.

DOI
10.1088/0031-8949/90/6/068008

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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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Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level $\ensuremath{\Lambda}$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\ensuremath{\Omega}}_{\ensuremath{\mu}}$, as in standard EIT systems. Tunneling between the wells at the frequency $g$ provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by $g$. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.

arXiv:0712.1805•Physical Review A•Jul 21, 2008•7 citations
We obtain a partial differential equation for a pulse travelling inside a Bose–Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a three-level BEC in Λ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.
In this paper, we investigate the propagation of a weak optical probe pulse in an f-deformed Bose- Einstein condensate (BEC) of a gas with the -type three- level atoms in the electromagnetically induced transparency (EIT) regime. We use an f- deformed generalization of an effective two- level quantum model of the three- level configuration in which the Gardiner phonon operators for BEC are deformed by an operator- valued function, f(n), of the particle- number operator n. With making use of the quantum approach of the angular momentum theory we obtain the eigenvalues and eigenfunctions of the system up to first order approximation. We consider the collisions between the atoms as a special kind of f- deformation. The collision rate k is regarded as the deformation parameter and light propagation in the deformed BEC is analyzed. In particular, we show that the absorptive and dispersive properties of the deformed condensate can be controlled effectively by changing the deformation parameter k and the total number of atoms. We find that by increasing the value of k the group velocity of the probe pulse changes, through deformed condensate, from subluminal to superluminal.
Light can be slowed down to ultraslow speeds v ia electromagnetically induced transparency in atomic Bose-Einstein condensates. This is thought to be useful for storage of quantum information for weak probe pulses. We investigate the effects of inhomogeneous density profile of the condensate on propagation of such ultraslow pulses. We find that spatial density of an atomic condensate leads to a graded refractive index profile, for an off-resonant probe pulse when condensate parameters are suitably chosen. Within the window of negligible absorption, conditions for degenerate multiple waveguide modes are determined. Both analytical and numerical studies are presented to reveal the effects of experimentally controllable parameters, such as temperature and interatomic interaction strength on the number of modes. Group velocity dispersion and modal dispersion are discussed. The effect of waveguide dispersion, in addition to usual material dispersion, on ultraslow pulses is pointed out.
In this paper, I numerically investigate the propagation of ultrashort pulses through an extended collection of multilevel systems under the condition of electromagnetically induced transparency. The transparency of a weak probe pulse is induced by a much stronger coupling pulse. In the limit of a weak probe excitation and a large number of excited states, I show that the free-induction decay signal that would naturally follow the excitation pulse is strongly suppressed, and the envelope of the probe pulse suffers a distortion in its temporal profile as the pulse propagates into the medium. This distortion is characterized by a stronger absorption of the leading edge of the pulse than that of its trailing edge. The temporal phase of the pulse, however, remains constant throughout propagation.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb^{87}\mathrm{Rb}87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
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
Electromagnetically induced transparency (EIT) is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity. Here we consider EIT in an atomic Bose-Einstein condensate (BEC) trapped in a double-well potential. A weak probe laser propagates through one of the wells and interacts with atoms in a three-level $\ensuremath{\Lambda}$ configuration. The well through which the probe propagates is dressed by a strong control laser with Rabi frequency ${\ensuremath{\Omega}}_{\ensuremath{\mu}}$, as in standard EIT systems. Tunneling between the wells at the frequency ggg provides a coherent coupling between identical electronic states in the two wells, which leads to the formation of interwell dressed states. The macroscopic interwell coherence of the BEC wave function results in the formation of two ultranarrow absorption resonances for the probe field that are inside of the ordinary EIT transparency window. We show that these new resonances can be interpreted in terms of the interwell dressed states and the formation of a type of dark state involving the control laser and the interwell tunneling. To either side of these ultranarrow resonances there is normal dispersion with very large slope controlled by ggg. We discuss prospects for observing these ultranarrow resonances and the corresponding regions of high dispersion experimentally.