PI: Selim M. Shahriar / Northwestern University

PAC Meeting, Nov. 2006, MIT NU and TAMU Proposal /Shahriar,Scully,Zubairy

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PI: Selim M. Shahriar / Northwestern University

Collaborative Research: A White Light Cavity using Anomalous Dispersion for High-Sensitivity, Broadband

Operation of the Next-Generation LIGO System

CoPIs: Marlan Scully / Texas A&M UniversitySuhail Zubairy / Texas A&M University


PART 1: Scientific Merit of the Proposed Work


• L=m/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

WHITE LIGHT CAVITY: BASIC IDEA

vac

n

( )( )( , , )o o on


WHITE LIGHT CAVITY: Anomalous Dispersion/Fast-Light

• Condition for WLC:

[ / 2 /( )]vac on C n remains constant as the frequency is varied around

• This simply implies an anomalous dispersion:

( )0

o o

o

o

nn n

vac

n

( )( )( , , )o o on

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

/ ; [ ( ) / ] 0o

g o g gv C n n n

n

n


WHITE LIGHT CAVITY: Linewidth

-3 -2 -1 0 1 2 30

500

1000

1500

2000

2500

3000

frequency(MHz)

cavi

ty b

uild

up

empty cavityWLC• WLC Linewidth is given in general by:

n

n

/WLC o gn

• Ideal WLC (ng=0) has an infinite linewidth

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

• For ng=0, this limits the WLC linewidth to:

2 1/3[ ]WLC DIS o

WLC

o

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

1 /gn L


• 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:

WHITE LIGHT CAVITY: Enhanced Sensitivity

( )( )( , , )o o on

/o gn

• For ideal WLC (ng=0), no amount of frequency shift restores resonance

2 / 3DIS o oΔω= [2Γ / Δω ] .Δω• In practice, the enhanced sensitivity is given by:


• Postive Dispersion (Slow Light) Reverses the Effects

OPPOSITE EFFECT UNDER POSITIVE DISPERSION

( )( )( , , )o o on

/o gn

• The sensitivity to cavity length change is highly reduced:

• Linewidth becomes narrower (ng>>0) :

/SL o gn

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OBVIOUS CANDIDATE FOR WLC: Resonant Two-level System

|1

|2

, = - o

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 1011

0.9

1

1.1

ind

ex

-8 -6 -4 -2 0 2 4 6 8 10

x 1010

0

0.05

0.1

0.15

ab

sorp

. -8 -6 -4 -2 0 2 4 6 8 10

x 1010

-20

-10

0

x 104

detuningg

rou

p in

de

x

normal dispersion Anomalousdispersion

o

R1n

IR i,EP

2

o22

o2o

2

oR42

2

En

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

L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).

Inside pulse delayed by:

T=L/Vg-L/C=(ng-1)L/C

Inside pulse advanced by:

-T=(1-ng)L/C

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Dual-Frequency PumpProbe

F=2

F=3

5S1/2

5P3/2

Optical pump

OUR SCHEME FOR SLOW AND FAST LIGHT IN ONE SYSTEM

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ANOMALOUS DISPERSION : BASIC EXPERIMENT

o

Pump fieldsPump fieldsEE11, E, E22

ProbeProbe

|1>

|2>

|3>

F=2

F=3

5S1/2

5P3/2

Optical Optical pumppump

o

Pump fieldsPump fieldsEE11, E, E22

ProbeProbe

|1>

|2>

|3>

F=2

F=3

5S1/2

5P3/2

Optical Optical pumppump

Opticalpump

AOM Probe

Shielded Rbcell

BS

Oscilloscope

Pumps

PBS

Gain

Filter

Balancedmixer

Glanpolarizer

Polarizer

D1

D2 Phase sensitive

heterodyne

Opticalpump

AOM Probe

Shielded Rbcell

BS

Oscilloscope

Pumps

PBS

Gain Gain

Filter

Balancedmixer

Glanpolarizer

Polarizer

D1

D2 Phase sensitive

heterodyne

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-6 -4 -2 0 2 4 60

0.5

1

1.5

2

frequency (MHz)

Mag

. (a.

u.)

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4x 10

-9

frequency (MHz)

n

f = 8 MHz, x14 (11.7dB)x11.8 (10.7dB)x8.8 (9.4 dB)x5.8 (7.6dB) x3.5 (5.4dB)x2.3 (3.6dB)

f = 8 MHz, x14 (11.7dB)x11.8 (10.7dB)x8.8 (9.4 dB)x5.8 (7.6dB) x3.5 (5.4dB)x2.3 (3.6dB)

ng ~ 0, n' ~ 4.13 x 10-16

Bi-frequencygain

Negative CADdispersion

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.

Heterodyne Dispersion Measurement: Bi-frequency Raman Gain

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Tuning Anomalous Dispersion to Vanishing Group Index

-3 -2 -1 0 1 2 3 4 5 6-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-6

(MHz)

Inde

x ch

ange

(

n)

= 2 MHz2.5 MHz3 MHz4 MHz

= 2 MHz2.5 MHz3 MHz4 MHz

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4-3000

-2500

-2000

-1500

-1000

-500

0

Pump separation, (MHz)

Gro

up i

ndex

(n g)

exp. datanum. extrapolation

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DISPERSIVE MEDIUM IN A RESONATOR

Cavity Resonance Cavity Resonance

ConditionCondition ((cc= = oo))

Dispersive Medium

Pump

Probe

Opticalpump

Cavitylock

= medium length

Phase-sensitivedetection

Probe frequency ()o

Probe frequency ()o

Probe frequency ()o

Probe frequency ()o

Pos. Dispersion

Neg. Dispersion

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DISPERSIVE MEDIUM IN A RESONATOR

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-10 -5 0 5 10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

frequency (MHz)

mag

. (a.

u.)

-6 -4 -2 0 2 4 6 80

0.2

0.4

0.6

0.8

1

1.2

frequency (MHz)

cavi

ty tr

ansm

issi

on

-/500 /400

Pos. Disp.: Linewidth Narrowing and Reduced Sensitivity

Experiment

Simulation

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-30 -20 -10 0 10 20 300

2

4

6

8

0.1

0.2

frequency (MHz)

c =

o

c >

o

c <

o

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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0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

o

o

Frequency Shifts and Group Index Dependence


WLC Demonstration using Double-Gain Anomalous DispersionWLC Demonstration using Double-Gain Anomalous Dispersion

-15 -10 -5 0 5 10 150

0.05

0.1

0.15

0.2

probe frequency (MHz)

mag

. (a.

u.)

cavity reson.f = 23 MHz19 MHz12 MHz8 MHz

-10 -5 0 5 100

0.2

0.4

0.6

0.8

1

1.2

1.4

frequency(MHz)

f= 30 MHz, ng=0.283

empty cavitywhite light cavity

Experiment Simulation

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-20 -15 -10 -5 0 5 10 15 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

frequency(MHz)

mag

.(a.

u.)

f= 30 MHz, ng=0.396

ECWCdispersion

-20 -15 -10 -5 0 5 10 15 20-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

frequency(MHz)

mag

.(a.

u.)

f= 30 MHz, ng=0.114

ECWCdispersion

Effect of Group Index on WLC BroadeningEffect of Group Index on WLC Broadening

ng = 0.396

ng = 0.114

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-20 -15 -10 -5 0 5 10 15 20-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

frequency(MHz)

mag

.(a.

u.)

f= 30 MHz, ng=0.0011,FSR = 300 MHz

-20 -15 -10 -5 0 5 10 15 20-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

frequency(MHz)

mag

.(a.

u.)

f= 30 MHz, ng=0.0011,FSR = 187 MHz

Effect of Reduced FSR of the CavityEffect of Reduced FSR of the Cavity

FSR = 300 MHz

FSR = 187 MHz

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Effect of Cavity Path Length Variation: Enhanced SensitivityEffect of Cavity Path Length Variation: Enhanced Sensitivity

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Effect of Cavity Path Length Variation: Enhanced SensitivityEffect of Cavity Path Length Variation: Enhanced Sensitivity


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.


Nd:YAGLaser PRM

SRM

DET.

BSM

BASIC FEATURES OF ADVANCED LIGO


Limitation of Advanced LIGO: Sensitivity-Bandwidth Product

IntracavityIntensity

GW Frequency

Narrowband Operation

Broadband Operation


GW Frequency


WLC Operation


GW Frequency


Broadband Operation


GW Frequency


WLC Operation

DetectorSignal

• Sensitivity-Bandwidth Product is fixed by system parameters

• Sensitivity is of paramount importance for Advanced LIGO design

• Problem for inherently broadband and chirped sources

• Several ideas have been proposed to solve this problem. These include (i) Simply broadband dual recycling (ii) Frequency agile interferometers that can follow a chirp, and (iii) input/output cavity techniques that can make optimal filters for specific source spectra. Our approach seems the simplest, and is to be compared/contrasted with these as part of this proposal


Enhancing Sensitivity-Bandwidth Product with WLC

Nd:YAGLaser MP

MS

DET.

BSM

WLC-DE


Enhancing Sensitivity-Bandwidth Product with WLC


GW Frequency


Broadband Operation


GW Frequency


WLC Operation


GW Frequency


Broadband Operation


GW Frequency


WLC Operation

DetectorSignal

DetectorSignal

WithoutWLC

WithWLC


Concern: WLC needs to be demonstrated for Nd:YAG frequency

Probe

Pump1

Pump2

Photorefractive crystal

AOM3f = fo + f

AOM2f = fo - f

AOM1f = fo

C-axis

Cavity

Probe

Pump1

Pump2

Photorefractive crystal

AOM3f = fo + f

AOM2f = fo - f

AOM1f = fo

C-axis

Cavity

• 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


PART 3: Capability of the proposing team to execute the proposed research


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


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/quant-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



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).



Texas A&M 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


PI at Texas A&M 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).


PI at Texas A&M University: Marlan Scully

Five Other Significant Publications:

1. M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University Press, 1997), 648 pp; second printing (1999), third priniting (2001), fourth printing (2002), Chinese edition (2001), Russian translation (2003).2. Murray Sargent III, Marlan O. Scully and Willis E. Lamb, Jr., Laser Physics, (Addison-Wesley Publishing, 1974), 432pp.3. Marlan O. Scully and Willis E. Lamb, Jr., “Quantum Theory of an Optical Maser. I. General Theory”, Phys. Rev. 159, 208 (1967).4. O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping Light via Hot Atoms”, Phys. Rev. Lett., 86, 628 (2001).5. P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light”, Phys. Rev. Lett. 96, 163603 (2006).


PART 4: Outreach potential of the proposed work


Outreach Potential at Northwestern University

• Undergraduate students at NU may register for project courses as electives in partial fulfillment of their degree requirement. These courses typically involve a project that fits in with the faculty member’s research in the form of laboratory work, analysis, or computer simulation. We know personally of many instances in which this experience has prompted students’ first thoughts of pursuing a graduate degree in science. Undergraduates also will be involved in research during the summer through the Research Experience for Undergraduates (REU) program at NU, and through senior thesis and honors projects.

• Efforts will be made to broaden minority student representation in science and engineering through NU programs. The university participates in the National Consortium for Graduate Degrees for Minorities in Engineering and Science (GEM) and awards fellowships to qualified students. NU also participates in the Illinois Minority Graduate Program for those students interested in teaching. NU Summer Research Opportunity Program (SROP) provides underrepresented minority sophomores and juniors majoring in the social sciences, humanities, communications, biological sciences, physical sciences, and engineering an opportunity for direct involvement in research. The program is eight weeks in length, and includes faculty-supervised research, enrichment activities that prepare undergraduates for graduate school (i.e, GRE preparation, graduate school application workshop, writing workshops, etc.).


Outreach Potential at Texas A&M University

• Pathways to the Doctorate Program at Texas A&M University at College Station: The goal of the Pathways Program is to attract high achieving students within the Texas A&M University (TAMU) System to pursue careers in research and higher education. This program has established a broad range of communication channels and activities such as seminars and workshops, inter-institutional exchange programs, a mentoring program and an annual research symposium with System-wide participation. The Pathways Program enables us to contact and recruit top students from a variety of geographical, socio-economic, racial, ethnic, and cultural environments, through a partnership within the Texas A&M System that consists of nine universities, such as Prairie View A&M (a HBCU-Historically black colleges and universities), Texas A&M University - Corpus Christi (a HSI, Hispanic-serving institutions), Texas A&M University Kingsville (a HSI), and Texas A&M International University (a HSI). We expect our association with these schools through the Pathways Program to help with recruitment of students from underrepresented groups into our graduate program.

• A recruiting committee regularly visits traditionally black and hispanic American institutions and participates regularly in the National Conference of Black Physics Students. These initiatives have been successful as the minority enrolment has climed up substantially.

Documents

PI: Selim M. Shahriar / Northwestern University