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Simulation of “Slow Light” and the beginnings of Quantum Memory Herbert Weller C’06

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17 m/s 3x10 8 m/s or 300000000 m/s Olympic Sprinter E/M Wave in a Vacuum

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See Demos

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The Circuit Instead of a medium we have the length Δx for each phase Shifter circuit. Or the “distance” passed per unit time.

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Phase Shifter Transfer Function The circuit provides a group delay T for a signal limited to a bandwidth of 1/T The circuit provides a group delay T for a signal limited to a bandwidth of 1/T T=2RC

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Group Velocity Java Applet http://gregegan.customer.netspace.net.au /APPLETS/20/20.html http://gregegan.customer.netspace.net.au /APPLETS/20/20.html http://gregegan.customer.netspace.net.au /APPLETS/20/20.html http://gregegan.customer.netspace.net.au /APPLETS/20/20.html

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Group velocity in terms of k to the left and in terms of ω below

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Wave propagation @ different velocities

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“Slow Light” or a low group velocity happens when the group index is large “Fast light” occurs when the group index is less than one.

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Kramers-Kronig Relation A change in absorption over a narrow spectral range must be accompanied by a change in refractive index over the same narrow range. A change in absorption over a narrow spectral range must be accompanied by a change in refractive index over the same narrow range.

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Material Resonance

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Dispersion with in the Spectral line Absorption grey, refractive index blue Absorption grey, refractive index blue

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What is Electromagnetically Induced Transparency (EIT)?

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Material Resonance

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Two “dipole allowed” transitions and one “dipole non- allowed”

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Formal Mathematical explanation of group velocity, wave propagation, and the EIT condition, overhead projector. Formal Mathematical explanation of group velocity, wave propagation, and the EIT condition, overhead projector. Senior Seminar Math.pdf Senior Seminar Math.pdf

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Formal Mathematical relation of the circuit and the slow light system and the limitations of that system, overhead projector. Formal Mathematical relation of the circuit and the slow light system and the limitations of that system, overhead projector.

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Spectrum Condition The descretized equation only works when the wave is smooth enough that the changes over Δx can be negated. The descretized equation only works when the wave is smooth enough that the changes over Δx can be negated. or

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Circuit Configuration SW1SW2RT=2RC V d =1/T ONON 476kΩ 0.078s13/s ONOFF 909kΩ 0.15s6.7/s OFFOFF 10MΩ 1.6s.062/s

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Constant propagation speed

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Decrease in propagation speed

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Increase in Propagation Speed

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EIT condition violation

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“Stopped Pulse”

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Future Possibilities Quantum Memory? (Possibility) Quantum Memory? (Possibility) Faster than Light Data Transmission (not a possibility with this method) Faster than Light Data Transmission (not a possibility with this method) Laser Transmission with out absorption through walls or thick heterogeneous gases (not a possibility) Laser Transmission with out absorption through walls or thick heterogeneous gases (not a possibility)

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Questions

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Acknowledgements Sarah Matthews @ TTI International Sarah Matthews @ TTI International Christi Sessions @ TRS Telco Christi Sessions @ TRS Telco Dr. Peterson Dr. Peterson Wave Propagation and Group Velocity, Leon Brillouin, 1960 Wave Propagation and Group Velocity, Leon Brillouin, 1960 Classical Electrodynamics, John David Jackson, 3 rd Ed., 1999 Classical Electrodynamics, John David Jackson, 3 rd Ed., 1999 Simulation of Slow Light with Electronic Circuits, Am J. Phys Simulation of Slow Light with Electronic Circuits, Am J. Phys Demonstration of Negative Group Delays in a simple electronic circuit, Am J. Phys. 70, T. Nakanishi, K Sugiyama, and M. Kitano Demonstration of Negative Group Delays in a simple electronic circuit, Am J. Phys. 70, T. Nakanishi, K Sugiyama, and M. Kitano Negative Group Delay and Superluminal Propagation: An Electronic Circuit Approach, IEEE Journal of Selected topics in Quantum Electronics, Vol. 9, NO. 1, M. Kitano, T. Nakanishi, K. Sugiyama Negative Group Delay and Superluminal Propagation: An Electronic Circuit Approach, IEEE Journal of Selected topics in Quantum Electronics, Vol. 9, NO. 1, M. Kitano, T. Nakanishi, K. Sugiyama “Slow” and “Fast” Light, Robert W. Boyd, Progress in Optics, Vol 43, 2002 “Slow” and “Fast” Light, Robert W. Boyd, Progress in Optics, Vol 43, 2002 Electromagnetically Induced Transparency, S. Harris, Physics Today, July 1997 Electromagnetically Induced Transparency, S. Harris, Physics Today, July 1997

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Announcements EXAM 3 will be returned at the END of class! Homework for tomorrow… (Ch. 20, Probs. 22, 24, & 26) Office hours… MW 12:30-1:30 pm TR.

Announcements EXAM 3 will be returned at the END of class! Homework for tomorrow… (Ch. 20, Probs. 22, 24, & 26) Office hours… MW 12:30-1:30 pm TR.

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