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Dark State Effects and Optical Fields in EIT Media * J.H. Eberly and V.V. Kozlov,

Dark State Effects and Optical Fields in EIT Media * J.H. Eberly and V.V. Kozlov, University of Rochester, USA, and University of Ulm, Germany

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Dark State Effects and Optical Fields in EIT Media * J.H. Eberly and V.V. Kozlov,

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  1. Dark State Effects and Optical Fields in EIT Media * J.H. Eberly and V.V. Kozlov, University of Rochester, USA, and University of Ulm, Germany Background and update on recent results -- the Dark State, matched pulses in 3-level resonance, dark fields and dressed field propagation, Dark Area Theorem, trapped pi phase jumps, matched-pulse impossibility. * Research supported by NSF PHY00-72359 and a grant from Corning, Inc.

  2. Puzzle in Pisa. Why did the fluorescence stop in Gozzini’s experiment? Why is there a steady state? Optical pumping paradox, 1976. 2-phtn. res. Upper level empty and nothing re-excites the pumped population. “Bright” Rabi freq.

  3. How to think about the Dark State, exploit it for Good (world peace, free lunch, etc.) Note backward ordering Or, how about moving the pulses through the atoms ??

  4. What happens to the Dark State when the two pulses move through the medium? (strong and coherent pulses, each almost resonant with an absorbing transition in the medium) For that matter, what happens when a single strong pulse goes through a medium with a resonant transition?

  5. McCall-Hahn Self-Induced Transparency (2p pulses, SIT, 1967) Harris, et al., Electromagnetically Induced Transparency (matched pulses, EIT, 1987) --- why so long?? No-shape matched pulses out Two pulses in Any shape in Sech shape out

  6. Special two-pulse analog to SIT discovered: three-level “simultons,” Sech shapes out Arbitrary shapes in Konopnicki & JHE, 1981

  7. Matched pulses out Zero Dark State out Arbitrary Dark State in

  8. Matched pulses in & out, but... Final state is totally Dark VVK & JHE, Opt. Comm. 179, 85 (2000)

  9. Pulse areas are puzzling Arbitrary state in, but totally Dark out VVK & JHE, Opt. Comm. 179, 85 (2000)

  10. Many examples are found of both matched and mis-matched pulse pairs that change, to become matched after propagation. Dark State wins. Except for perfect simultons, all examples have |D|2 = 1 at the output.

  11. Two-pulse propagation in EIT media -> new wave equation & analytic solutions Usual reduced wave equations for envelopes of real pulses. Inhomog. lineshape New wave eqn. for Dark Field envelope via Dark Area q(z,t) The averaging over inhomogeneous broadening (implied by the brackets) permits the right side to be reduced to a function of q(z) in the domain t >> T*. This is the key. JHE & VVK, PRL 88, 243604 (2002)

  12. AND THIS LEADS TO THE DARK AREA THEOREM: JHE & VVK, PRL 88, 243604 (2002)

  13. Approximations made in deriving the Dark Area Theorem are upheld in computer simulations. Log Q shows linear behavior in pulse tails. Area correctly predicts matched pulse ratios. Experiments are awaited in media with inhomogeneous broadening -- e.g., Doppler-broadened low-pressure vapors, solids that support echoes, rare-earth insulators. Envelope ratio is 1.6 ~ √3 Negative envelope ratio correctly predicted

  14. Normal physical pulse envelopes The consequences of the “unphysical” nature of dark Rabi frequency are surprising. The typical EIT scenario turns out to be unstable in a way similar to the simulton instability -- it depends on a very specially smooth input in order to reach the standard matched-pulse output. The reason for non-matching is that both D = 1 and D = -1 lead to the finally stable condition |D|2 = 1, but D = ±1 are not compatible with each other. Physical pulses can produce a normal Bright pulse envelope, but a Dark pulse envelope that is quite strange. Dark state amplitude values are pinned by dark envelope phase reversals. Bright pulse Dark pulse

  15. Summary of the moment -- coherent pulse propagation in three-level media, 2003 The physical fields try to become matched The Dark fields develop delta-function spikes. The Dark Area is forced to make 2p jumps

  16. Here’s an old list of papers that may be useful for an overview of the combined histories of 3-level effects, including pulse-pair propagation, the Dark State, anti-intuitive excitation, and the beginning of EIT theory. A few handouts are available. A updated list is in preparation and will be available via inquiry to eberly@pas.rochester.edu.

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