PI: Selim M. Shahriar Northwestern University

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Collaborative Research A White Light Cavity
using Anomalous Dispersion for High-Sensitivity,
Broadband Operation of the Next-Generation LIGO
System
PI Selim M. Shahriar / Northwestern University
CoPIs Marlan Scully / Texas AM
University Suhail Zubairy / Texas AM University
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PART 1 Scientific Merit of the Proposed Work
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WHITE LIGHT CAVITY BASIC IDEA

• Lm?/2 means cavity resonance
• Normally, ? changes with frequency
• In the presence of dispersion, it is possible
  to change frequency
• without changing ?.
• There exists a particular variation of n as a
  function of ? so that
• this compensation is exact over a large range
  of frequency
• variation. The cavity then remains resonant
  over this whole range.
• This is the White Light Cavity (WLC).
• The cavity build-up factor remains unchanged

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WHITE LIGHT CAVITY Anomalous Dispersion/Fast-Lig
ht

• This simply implies an anomalous dispersion
  

• This happens to correspond to fast-light with
  infinite group velocity

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WHITE LIGHT CAVITY Linewidth

• WLC Linewidth is given in general by

• Ideal WLC (ng0) has an infinite linewidth

• In practice, the dispersion only linear over a
  finite range ?DIS

• For ng0, this limits the WLC linewidth to

?DIS

• For cavity of length L filled with a disp. med.
  of length l, the ideal WLC condition is

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WHITE LIGHT CAVITY Enhanced Sensitivity

• WLC also experiences enhanced sensitivity
• Consider a situation where L is changed by ?L
  away from resonance
• For a regular cavity, resonance is restored by
  changing frequency by
• a small ??o the measurement of ??o allows
  measurement of ?L
• For a generic White Light Cavity (WLC), the
  frequency shift
• needed to restore resonance is

• For ideal WLC (ng0), no amount of frequency
  shift restores resonance

• In practice, the enhanced sensitivity is given
  by

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OPPOSITE EFFECT UNDER POSITIVE DISPERSION

• Postive Dispersion (Slow Light) Reverses the
  Effects

• Linewidth becomes narrower (nggtgt0)

• The sensitivity to cavity length change is
  highly reduced

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OBVIOUS CANDIDATE FOR WLC Resonant Two-level
System
Problem Strong absorption at line center
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ALTERNATIVE APPROACH Double-peak Raman Gain
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature,
406, 277 (2000).
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FAST LIGHT USING ANOMALOUS DISPERSION
Inside pulse delayed by
?TL/Vg-L/C(ng-1)L/C
Inside pulse advanced by
-?T(1-ng)L/C
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature,
406, 277 (2000).
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OUR SCHEME FOR SLOW AND FAST LIGHT IN ONE SYSTEM

5P
3/2
?
Optical
pump
Dual-Frequency Pump
Probe
F3
5S
1/2
F2
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ANOMALOUS DISPERSION BASIC EXPERIMENT
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Heterodyne Dispersion Measurement Bi-frequency
Raman Gain
Note Results showing dispersion measurement
under double-gain condition for a pump frequency
separation of 8 MHz. As shown in the top figure,
the gain is adjusted to get a value of group
index close to zero.
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Tuning Anomalous Dispersion to Vanishing Group
Index
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DISPERSIVE MEDIUM IN A RESONATOR
Cavity Resonance Condition (?c ?o)
Pos. Dispersion
Neg. Dispersion
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DISPERSIVE MEDIUM IN A RESONATOR
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Pos. Disp. Linewidth Narrowing and Reduced
Sensitivity
Experiment
Simulation
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Detuned Cavity showing Reduced Sensitivity
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Simulation of Slow-Light Medium in a Resonator

• Assumes a medium with group index ng 10
• Empty cavity linewidth 10 MHz Disp.
  linewidth 1 MHz

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Frequency Shifts and Group Index Dependence
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WLC Demonstration using Double-Gain Anomalous
Dispersion
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Effect of Group Index on WLC Broadening
ng 0.396
ng 0.114
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Effect of Reduced FSR of the Cavity
FSR 300 MHz
FSR 187 MHz
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Effect of Cavity Path Length Variation Enhanced
Sensitivity
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Effect of Cavity Path Length Variation Enhanced
Sensitivity
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PART 2 Relevance to LIGO of the proposed work

• The WLC would enhance the Sensitivity-Bandwidth
  Product
• of the Advanced LIGO

• However, the design for the Advanced LIGO is
  already too firmly
• established for such a modification

• Therefore, we believe that the WLC cavity will
  be relevant to the
• Third-Generation LIGO.

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BASIC FEATURES OF ADVANCED LIGO
NdYAG Laser
PRM
BSM
SRM
DET.
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Limitation of Advanced LIGO Sensitivity-Bandwidt
h Product
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Enhancing Sensitivity-Bandwidth Product with WLC
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Enhancing Sensitivity-Bandwidth Product with WLC
Detector Signal
Without WLC
Detector Signal
With WLC
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Concern WLC needs to be demonstrated for NdYAG
frequency

• Photorefractive crystal has already been used to
  demonstrate Fast Light

• TAMU group recently showed Slow-Light with
  Photorefractive crystal

• We will use dual-frequency pump to create a
  tunable group-index anomalous
• dispersion necessary for WLC suitable for LIGO,
  using an SPS(Sn2P2S6) crystal

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PART 3 Capability of the proposing team to
execute the proposed research
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Project PI at Northwestern University Selim
Shahriar

• Has a state-of-the-art Atomic Physics and Optics
  Laboratory

• This laboratory is equipped with three
  Ti-Sapphire lasers, many diode
• lasers, stable optical tables, Nd-YAG laser,
  optical components,
• microwave components, and Sophisticated
  measurement tools.

• Has nearly fifteen years of experiment dealing
  with dispersive media

• Was the first to demonstrate slow-light in a
  solid

• Was the first to demonstrate the White Light
  Cavity using a tunable, open
• system suited for inserting in an
  interferometer such as LIGO

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Project PI at Northwestern University Selim
Shahriar
Five publications most relevant to the
proposal Demonstration of a Tunable-Bandwidth
White Light Interferometer using Anomalous
Dispersion in Atomic Vapor, G.S. Pati, M.
Messal, K. Salit, and M.S. Shahriar, Phys. Rev.
Letts. (submitted, 2006). http//arxiv.org/abs/qua
nt-ph/0610022. Demonstration of Tunable
Displacement- Measurement-Sensitivity using
Variable Group Index in a Ring Resonator, G.S.
Pati, M. Messal, K. Salit, and M.S. Shahriar,
Phys. Rev. Letts. (submitted, 2006).
http//arxiv.org/abs/quant-ph/0610023.
Ultrahigh Precision Rotation Sensing using a
Fast-Light Enhanced Ring Laser Gyroscope , M.S.
Shahriar, G.S. Pati, R. Tripathi, V. Gopal, and
M. Messal, Phys. Rev. Letts.( submitted, 2006).
http//lapt.ece.northwestern.edu/files/fast-light-
enhanced-ligo Experimental Determination of
the Degree of Enhancement in Laub-Drag Augmented
Rotation Sensing using Slow-Light in Sodium
Vapor, R. Tripathi, G.S. Pati, M. Messall, K.
Salit and M.S. Shahriar, Optics Communications
(accepted, 2006). Controllable Anomalous
Dispersion and Group Index Nulling via
Bi-Frequency Raman Gain in Rb Vapor for
Ultraprecision Rotation Sensing,, G.S. Pati, R.
Tripathi, M. Messall, V. Gopal, K. Salit and M.S.
Shahriar, Optics Letters (submitted, 2006).
http//arxiv.org/abs/quant-ph/0512260
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Project PI at Northwestern University Selim
Shahriar
Five other significant publications Observation
of Ultraslow and Stored Light Pulses in a
Solid, A. V. Turukhin, V.S. Sudarshanam, M.S.
Shahriar, J.A. Musser, B.S. Ham, and P.R.
Hemmer, Phys. Rev. Lett. 88, 023602
(2002). Long Distance, Unconditional
Teleportation of Atomic States via Complete Bell
State Measurements, S. Lloyd, M.S. Shahriar,
J.H. Shapiro, and P.R. Hemmer, Phys. Rev. Lett.
87, 167903 (2001). Self-Organization, Broken
Symmetry and Lasing in an Atomic Vapor the
Interdependence of Gratings and Gain, P.R.
Hemmer, M.S. Shahriar, D.P. Katz, N.P. Bigelow,
L. DeSalvo, and R. Bonifacio, Phys. Rev. Letts.
77, 1468 (1996). "First Observation of Forces on
Three Level Atoms in Raman Resonant Standing Wave
Optical Fields," P. Hemmer, M.S. Shahriar, M.
Prentiss, D. Katz, K. Berggren, J. Mervis,and N.
Bigelow, Physical Review Letters, 68, 3148
(1992). "Direct Excitation of Microwave-Spin
Dressed States Using a Laser Excited Resonance
Raman Interaction," M.S. Shahriar and P. Hemmer,
Physical Review Letters, 65, 1865(1990).
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Texas AM University Marlan Scully and Suhail
Zubairy

• Both are world-renowned authorities in atomic
  and optical physics

• Prof. Scully did many of the seminal work in the
  area of slow light

• Prof. Scully was the first to propose the idea
  of the WLC for this
• application

• Have a sophisticated laboratory that will be
  used to perform the work
• involving photorefractive crystals

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PI at Texas AM University Marlan Scully
Related Recent Publications 1. A. Wicht, K.
Danzmann, M. Fleischhauer, M. Scully, G. Miiller,
R.H. Rinkleff, "White-light cavities, atomic
phase coherence, and gravitational wave
detectors", Opt. Commun. 134, 431 (1997). 2. M.
O. Scully, M. S. Zubairy and M. P. Haugan,
"Proposed optical test of metric gravitation
theories", Phys. Rev. A 24, 2009 (1981). 3.
Marlan O. Scully, Enhancement of the Index of
Refraction via Quantum Coherence, Phys. Rev.
Lett. 67, 1855 (1991). 4. W. W. Chow, J.
Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W.
Schleich, and M. O. Scully, The Ring Laser Gyro,
Rev. Mod. Phys. 57, 61 (1985). 5. M. S. Zubairy,
A. B. Matsko, and M. O. Scully, "Resonant
enhancement of high order optical nonlinearities
based on atomic coherence", Phys. Rev. A 65,
043804 (2002). 6. M. O. Scully and M. S. Zubairy,
Playing tricks with slow light, Science, 301,
181 (2003).
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PI at Texas AM University Marlan Scully
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PART 4 Outreach potential of the proposed work
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Outreach Potential at Northwestern University
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Outreach Potential at Texas AM University