Extreme optomechanically induced transparency
Extreme Optomechanically Induced Transparency by
Timothy Paul Bodiya
w7
zC::
Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of
M Cr')
ci)
Masters of Science in Physics
;
2
o
at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted A uthor ............................ Department of Physics February 9, 2015
Signature redacted C ertified by .......................... Nergis Mavalvala Curtis (1963) and Kathleen Marble Professor of Astrophysics Thesis Supervisor
Signature redacted Accepted by..................is............. Krishna Rajagopal Associate Department Head for Education
-5
101
100
10
12
frequency [Hz]
Figure 4-7: Transfer function of the cavity feedback filter board,
FFB-
* Mechanical resonance frequency, Qm " Mechanical mode damping, Fm " Pump power, P " Detuning, A " Total cavity loss, or FWHM of the cavity,
'tot
Because we are detuned, the asymmetric sideband response of the cavity gives information about both, A and
IZtot.
The narrowband transfer functions will give
information about m, Qm, and Fm. The fitting procedure is as follows: 1. Fit the wideband transfer functions at power P for A and Ktot. 2. Using the values of A and ntt from the wideband fit, we fit the narrowband transfer function for m, Qm, rm. The fitting routine fits for all parameters, but both
'tot
and A are restricted to be within one percent of values from the
wideband transfer function. 60
5
In Figures 4-8, and 4-9 we show plots of a representative wideband and narrowband fit along with the fit residuals. As seen in the plots, the data is fit extremely well. Figure 4-10 is a plot of the OMIT feature as a function of power. In this plot, we see how the OMIT dip increases as a function of power and the OMIT linewidth also increases. Also apparent from the figure, the dip gets deeper and wider as the power is increased. This can be seen in more detail in Figure 4-12 where the linewidth of the dip is plotted as a function of power. Extracting the cooperativity from all of the different power levels gives the plot in Figure 4-11. The fitted value of 0.035 0.005 calculatd using the fit agrees quite well with the predicted value of 0.031 Figure 4-13 which shows how the different fit parameters varied as a
parameters.
function of power. We extract a value of '
of 10.7 kHz
0.18 kHz. The reduced is 23.8
-,
9.6 grams. The mechanical loss,
mass of the oscillator is 133 grams
mHz t 3.2 mHz, corresponding to a quality factor of 1.2 x 106. This is approximately what is to be expected from fused silica. Probe Tranemission_
0 .44-
C13,
-
e
---
-
-
-20
D
t
. .--..
1
I 00II
.
-20 -120-
-
-8 -
0
104
r-100
--
---
-400.1
-0.05
01 1
005
0
60 s-80
-120-0.1
10
-0.05
0
0.05
0.1
Freuenc-y
Figure 4-8: A sample wideband fit. Hfere the input power was 61 mW.
61
zu
C -1 C In
10 -2(
-3( 2.7521
2.7523
a)
01
2.7523 x 10 Data .- Fit
-0.02
0
-0.1 -0.05
0
0.02
3ln.
20
a) U)
10
0 0~
0'
L;
2.7521
2.7523 Frequency
2.7523 x 10
.
3. .....
i
0.05 0.1
Figure 4-9: A sample narrowband fit. Here the input power was 1180 mW.
Probe Transmission L.
*
-
100
30
481.5 mW 640 mW 774.5 mW 0 1180.5 mW
............ ............
10-2
L.
-
61 mW
o 121.5 mW o 242.5 mW
-1.5
-1
-0.5
-1.5
-1
-0.5
0.5
1
1.5
0.5 0 Frequency (Hz)
1
1.5
0
-5 0 --10
-c
0--is
0-
Figure 4-10: A plot of the OMIT dip as a function of power.
62
50 *Data -- Fit -> 0.035x + -0.85
40
-oI'
300-
-
10 10400
200
0
1200
1000
800 600 Input Power (mW)
Figure 4-11: A plot of the cooperativity as a function of the power. As you can see this is very well fit by a linear curve with a slope of 0.035. This compares very well 0.005 obtained from the average fitted values of m, to a calculated value of 0.031
A, Itot, and
Fm.
0.8
1-
0.6--
0.5 --
eData STheory Optickle-
o.3 0.2
0.10.1
0.2
0.3
0.4
0.6
0.5
0.7
0.8
0.9
1
Power(W)
Figure 4-12: A plot of the linewidth of the OMIT feature as a function of laser power found in three different ways. The red line has a slope of 0.7239 and the linewidth is extracted from the measured data. The blue line has a slope of 0.7041 and is calculated using the fit parameters in a theoretical model. Finally, the green curve is calculated using the fit parameters and inputting them into Optickle, an interferomter modelling program. Optickle generates OMIT curves and then the linewidth is measured from those curves. As shown from the plot, the data is linear as a function of power which is what we expect and follows very closely to the predicted slope give by the blue line.
63
,150 E cc
a,)
140
...................... ......... * .... ma=3.7g.... ... mean =133.7 g std =9.6 g
CO)
E 130 C
Z 200
400
600
800
1000
Input Power (mW) . mean = 23.8 mHz
" .5
b)
std =3.2 mHz
S4 0.5
I?
3
200
400
600
800
1000
Input Power (mW)
I . mean = 10.7 kHz
11
std = 0.2 kHz
0.8
.............. .
10.6 200
400
600
.. 1000
800
Input Power (mW) -0.96
d)i|
. mean = -0.96
-0.98
std = 0.01 200
400
600
1000
800
Input Power (mW) Figure 4-13: Plots of the fit parameters for a) modal mass m, b)
A as a function of the power. 64
-,
c) N'o and d)
Chapter 5 Future Directions In the previous chapters, we have described the theory behind OMIT, along with an experimental setup that has measured the smallest OMIT linewidth known to us. OMIT has a wide variety of applications, but many are dependent on the width of the OMIT feature since this provides a timescale. At larger OMIT linewidths (on the order of 10 to 100 Hz), OMIT offers the possibility of creating a tunable filter cavity for quantum noise.
This has many
applications for gravitational wave detection and there has been a theoretical study done in 117]. In addition, the base linewidth of the OMIT filter cavity should be less than the minimum required for the system. In this sense, our system with its extremely narrow linewidth is ideal. On the other hand, at some point the intensity noise of the control laser will become an issue for quantum mechanical applications, so the system needs to be designed to minimize this effect. For a system to work as a quantum noise filter, there are much more stringent requirements on both the pump laser and the mechanical system.
Usually, for a
gravitational wave detector filter cavity, the relevant quantity is the optical loss per length.
This is due to the fact that a filter cavity uses the optical linewidth to
rotate the quadrature of the input quantum noise. This linewidth can be changed via changing the length or changing the loss per roundtrip in the cavity. To use OMIT in place of an optical cavity in this situation requires that the mechanical system be in the quantum ground state. The physical reason for this can be seen by looking at the 65
OMIT level diagram in relation to a standard optical cavity. Looking at the OMIT level diagram shows that linewidth of the OMIT cavity is defined by the intrinsic mechanical loss and broadening due to saturation of the OMIT dip. From this perspective, to use OMIT for a filter cavity in gravitational wave detection, the mechanical linewidth needs to lower than the linewidth of the arm cavities. This way the cavity can be tuned through the linewidth of the arm cavity while still operating in a saturated regime. To put some numbers on this, the Advanced LIGO arm cavity pole is at around 40 Hz, so the mechanical oscillator would possibly have a linewidth of around 40 Hz. Since this value is very high it could be artificially changed by replacing the mechanical oscillator with another optomechanical system where the frequency of the optomechanical oscillator are defined via an optical spring and optical damping. Another possible way to use OMIT with small mechanical linewidths is to use the OMIT dip as a reference to lock two lasers together, similar to frequency stabilization. In this case the linewidth would be as small as possible, neglecting other noise sources. Using the OMIT dip as a reference has one crucial difference as compared to a fixed reference cavity: the OMIT dip uses a pump laser to mediate the interaction. This means that any frequency shift of the pump laser will change the relative width of the OMIT dip. Therefore, OMIT will allow for locking two lasers relative to each other very tightly as defined by the mechanical linewidth, but not absolute frequency stabilization.
66
Bibliography [1]
G. S. Agarwal and S. Huang. Electromagnetically induced transparency in mechanical effects of light. Physical Review A, 81(4):041803, April 2010.
12] T. Baba. Slow light in photonic crystals. Nature Photonics, 2:465-473, 08 2008.
[31
Eric D. Black. An introduction to pound drever hall laser frequency stabilization. American Journal of Physics, 69(1):79-87, 2001.
[4] K.-J. Boller, A. Imamolu, and S. E. Harris. Observation of electromagnetically induced transparency. Phys. Rev. Lett., 66:2593-2596, May 1991.
15]
Alessandra Buonanno and Yanbei Chen. Signal recycled laser-interferometer gravitational-wave detectors as optical springs. Phys. Rev. D, 65:042001, Jan 2002.
[6] J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Grbblacher, M. Aspelmeyer, and 0. Painter. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 478:89-92, October 2011.
[7]
Y. Chen. Macroscopic quantum mechanics: theory and experimental concepts of optomechanics. Journal of Physics B Atomic Molecular Physics, 46(10):104001, May 2013.
[81
LIGO Scientific Collaboration. Observation of a kilogram-scale oscillator near its quantum ground state. New Journal of Physics, 11(7):073032, 2009.
[9] Thomas Corbitt. Quantum Noise and Radiation Pressure Effects in High Power Optical Interferometers. PhD thesis, MIT, 2008. [10] Thomas Corbitt, Yanbei Chen, Edith Innerhofer, Helge Miiller-Ebhardt, David Ottaway, Henning Rehbein, Daniel Sigg, Stanley Whitcomb, Christopher Wipf, and Nergis Mavalvala. An all-optical trap for a gram-scale mirror. Phys. Rev. Lett., 98:150802, Apr 2007. [11] Thomas Corbitt, David Ottaway, Edith Innerhofer, Jason Pelc, and Nergis Mavalvala. Measurement of radiation-pressure-induced optomechanical dynamics in a suspended fabry-perot cavity. Phys. Rev. A, 74:021802, Aug 2006. 67
[12] M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and 0. Painter. Optomechanical crystals. Nature, 462:78-82, November 2009.
[13]
Michael Fleischhauer, Atac Imamoglu, and Jonathan P. Marangos. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys., 77:633-673, Jul 2005.
[14] S. Gigan, H. R. B6hm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Biuerle, M. Aspelmeyer, and A. Zeilinger. Self-cooling of a micromirror by radiation pressure. Nature, 444:67-70, November 2006. [15] T. J. Kippenberg, S. M. Spillane, and K. J. Vahala. Demonstration of ultra-highq small mode volume toroid microcavities on a chip. Applied Physics Letters, 85(25):6113-6115, 2004. [16] Mikhail D. Lukin, Michael Fleischhauer, Marlan 0. Scully, and Vladimir L. Velichansky. Intracavity electromagnetically induced transparency. Opt. Lett., 23(4):295-297, Feb 1998. [17] Yiqiu Ma, Stefan L. Danilishin, Chunnong Zhao, Haixing Miao, W. Zach Korth, Yanbei Chen, Robert L. Ward, and D. G. Blair. Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction. Phys. Rev. Lett., 113:151102, Oct 2014.
118] William Marshall, Christoph Simon, Roger Penrose, and Dik Bouwmeester. Towards quantum superpositions of a mirror. 2003.
[19]
Phys. Rev. Lett., 91:130401, Sep
Osamu Miyakawa, Robert Ward, Rana Adhikari, Matthew Evans, Benjamin Abbott, Rolf Bork, Daniel Busby, Jay Heefner, Alexander Ivanov, Michael Smith, Robert Taylor, Stephen Vass, Alan Weinstein, Monica Varvella, Seiji Kawamura, Fumiko Kawazoe, Shihori Sakata, and Conor Mow-Lowry. Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector. Phys. Rev. D, 74:022001, Jul 2006.
[20] A. F. Pace, M. J. Collett, and D. F. Walls. Quantum limits in interferometric detection of gravitational radiation. Phys. Rev. A, 47:3173-3189, Apr 1993. [21] Jameson Rollins. Intensity stabilization of a solid-state laser for interferometric gravitational wave detectors. Master's thesis, MIT, 2004. [22] Jameson Rollins, David Ottaway, Michael Zucker, Rainer Weiss, and Richard Abbott. Solid-state laser intensity stabilization at the 10< sup>-8 level. Optics letters, 29(16):1876-1878, 2004. [23] A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and 0. Painter. Electromagnetically induced transparency and slow light with optomechanics. Nature, 472:69-73, April 2011. 68
124] J.J. Sakurai. Modern Quantum Mechanics. Addison-Wellsley, 2010. 125] A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg. Radia-
tion pressure cooling of a micromechanical oscillator using dynamical backaction. Phys. Rev. Lett., 97:243905, Dec 2006.
f261 J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds. Sideband cooling of micromechanical motion to the quantum ground state. Nature, 475:359-363, July 2011. [271 J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett., 101:197203, Nov 2008. [281 J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature, 452:72-75, March 2008. [29] D.F. Walls. Quantum Optics. Springer, 2008.
[30] Stefan Weis, Remi Riviere, Samuel DelAl'glise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, and Tobias J. Kippenberg. Optomechanically induced transparency. Science, 330(6010):1520-1523, 2010. [31] Christopher Wipf. Toward Quantum Opto-Mechanics in a Gram-Scale Suspended Mirror Interferometer. PhD thesis, MIT, 2013.
69
Timothy Paul Bodiya
w7
zC::
Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of
M Cr')
ci)
Masters of Science in Physics
;
2
o
at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted A uthor ............................ Department of Physics February 9, 2015
Signature redacted C ertified by .......................... Nergis Mavalvala Curtis (1963) and Kathleen Marble Professor of Astrophysics Thesis Supervisor
Signature redacted Accepted by..................is............. Krishna Rajagopal Associate Department Head for Education
-5
101
100
10
12
frequency [Hz]
Figure 4-7: Transfer function of the cavity feedback filter board,
FFB-
* Mechanical resonance frequency, Qm " Mechanical mode damping, Fm " Pump power, P " Detuning, A " Total cavity loss, or FWHM of the cavity,
'tot
Because we are detuned, the asymmetric sideband response of the cavity gives information about both, A and
IZtot.
The narrowband transfer functions will give
information about m, Qm, and Fm. The fitting procedure is as follows: 1. Fit the wideband transfer functions at power P for A and Ktot. 2. Using the values of A and ntt from the wideband fit, we fit the narrowband transfer function for m, Qm, rm. The fitting routine fits for all parameters, but both
'tot
and A are restricted to be within one percent of values from the
wideband transfer function. 60
5
In Figures 4-8, and 4-9 we show plots of a representative wideband and narrowband fit along with the fit residuals. As seen in the plots, the data is fit extremely well. Figure 4-10 is a plot of the OMIT feature as a function of power. In this plot, we see how the OMIT dip increases as a function of power and the OMIT linewidth also increases. Also apparent from the figure, the dip gets deeper and wider as the power is increased. This can be seen in more detail in Figure 4-12 where the linewidth of the dip is plotted as a function of power. Extracting the cooperativity from all of the different power levels gives the plot in Figure 4-11. The fitted value of 0.035 0.005 calculatd using the fit agrees quite well with the predicted value of 0.031 Figure 4-13 which shows how the different fit parameters varied as a
parameters.
function of power. We extract a value of '
of 10.7 kHz
0.18 kHz. The reduced is 23.8
-,
9.6 grams. The mechanical loss,
mass of the oscillator is 133 grams
mHz t 3.2 mHz, corresponding to a quality factor of 1.2 x 106. This is approximately what is to be expected from fused silica. Probe Tranemission_
0 .44-
C13,
-
e
---
-
-
-20
D
t
. .--..
1
I 00II
.
-20 -120-
-
-8 -
0
104
r-100
--
---
-400.1
-0.05
01 1
005
0
60 s-80
-120-0.1
10
-0.05
0
0.05
0.1
Freuenc-y
Figure 4-8: A sample wideband fit. Hfere the input power was 61 mW.
61
zu
C -1 C In
10 -2(
-3( 2.7521
2.7523
a)
01
2.7523 x 10 Data .- Fit
-0.02
0
-0.1 -0.05
0
0.02
3ln.
20
a) U)
10
0 0~
0'
L;
2.7521
2.7523 Frequency
2.7523 x 10
.
3. .....
i
0.05 0.1
Figure 4-9: A sample narrowband fit. Here the input power was 1180 mW.
Probe Transmission L.
*
-
100
30
481.5 mW 640 mW 774.5 mW 0 1180.5 mW
............ ............
10-2
L.
-
61 mW
o 121.5 mW o 242.5 mW
-1.5
-1
-0.5
-1.5
-1
-0.5
0.5
1
1.5
0.5 0 Frequency (Hz)
1
1.5
0
-5 0 --10
-c
0--is
0-
Figure 4-10: A plot of the OMIT dip as a function of power.
62
50 *Data -- Fit -> 0.035x + -0.85
40
-oI'
300-
-
10 10400
200
0
1200
1000
800 600 Input Power (mW)
Figure 4-11: A plot of the cooperativity as a function of the power. As you can see this is very well fit by a linear curve with a slope of 0.035. This compares very well 0.005 obtained from the average fitted values of m, to a calculated value of 0.031
A, Itot, and
Fm.
0.8
1-
0.6--
0.5 --
eData STheory Optickle-
o.3 0.2
0.10.1
0.2
0.3
0.4
0.6
0.5
0.7
0.8
0.9
1
Power(W)
Figure 4-12: A plot of the linewidth of the OMIT feature as a function of laser power found in three different ways. The red line has a slope of 0.7239 and the linewidth is extracted from the measured data. The blue line has a slope of 0.7041 and is calculated using the fit parameters in a theoretical model. Finally, the green curve is calculated using the fit parameters and inputting them into Optickle, an interferomter modelling program. Optickle generates OMIT curves and then the linewidth is measured from those curves. As shown from the plot, the data is linear as a function of power which is what we expect and follows very closely to the predicted slope give by the blue line.
63
,150 E cc
a,)
140
...................... ......... * .... ma=3.7g.... ... mean =133.7 g std =9.6 g
CO)
E 130 C
Z 200
400
600
800
1000
Input Power (mW) . mean = 23.8 mHz
" .5
b)
std =3.2 mHz
S4 0.5
I?
3
200
400
600
800
1000
Input Power (mW)
I . mean = 10.7 kHz
11
std = 0.2 kHz
0.8
.............. .
10.6 200
400
600
.. 1000
800
Input Power (mW) -0.96
d)i|
. mean = -0.96
-0.98
std = 0.01 200
400
600
1000
800
Input Power (mW) Figure 4-13: Plots of the fit parameters for a) modal mass m, b)
A as a function of the power. 64
-,
c) N'o and d)
Chapter 5 Future Directions In the previous chapters, we have described the theory behind OMIT, along with an experimental setup that has measured the smallest OMIT linewidth known to us. OMIT has a wide variety of applications, but many are dependent on the width of the OMIT feature since this provides a timescale. At larger OMIT linewidths (on the order of 10 to 100 Hz), OMIT offers the possibility of creating a tunable filter cavity for quantum noise.
This has many
applications for gravitational wave detection and there has been a theoretical study done in 117]. In addition, the base linewidth of the OMIT filter cavity should be less than the minimum required for the system. In this sense, our system with its extremely narrow linewidth is ideal. On the other hand, at some point the intensity noise of the control laser will become an issue for quantum mechanical applications, so the system needs to be designed to minimize this effect. For a system to work as a quantum noise filter, there are much more stringent requirements on both the pump laser and the mechanical system.
Usually, for a
gravitational wave detector filter cavity, the relevant quantity is the optical loss per length.
This is due to the fact that a filter cavity uses the optical linewidth to
rotate the quadrature of the input quantum noise. This linewidth can be changed via changing the length or changing the loss per roundtrip in the cavity. To use OMIT in place of an optical cavity in this situation requires that the mechanical system be in the quantum ground state. The physical reason for this can be seen by looking at the 65
OMIT level diagram in relation to a standard optical cavity. Looking at the OMIT level diagram shows that linewidth of the OMIT cavity is defined by the intrinsic mechanical loss and broadening due to saturation of the OMIT dip. From this perspective, to use OMIT for a filter cavity in gravitational wave detection, the mechanical linewidth needs to lower than the linewidth of the arm cavities. This way the cavity can be tuned through the linewidth of the arm cavity while still operating in a saturated regime. To put some numbers on this, the Advanced LIGO arm cavity pole is at around 40 Hz, so the mechanical oscillator would possibly have a linewidth of around 40 Hz. Since this value is very high it could be artificially changed by replacing the mechanical oscillator with another optomechanical system where the frequency of the optomechanical oscillator are defined via an optical spring and optical damping. Another possible way to use OMIT with small mechanical linewidths is to use the OMIT dip as a reference to lock two lasers together, similar to frequency stabilization. In this case the linewidth would be as small as possible, neglecting other noise sources. Using the OMIT dip as a reference has one crucial difference as compared to a fixed reference cavity: the OMIT dip uses a pump laser to mediate the interaction. This means that any frequency shift of the pump laser will change the relative width of the OMIT dip. Therefore, OMIT will allow for locking two lasers relative to each other very tightly as defined by the mechanical linewidth, but not absolute frequency stabilization.
66
Bibliography [1]
G. S. Agarwal and S. Huang. Electromagnetically induced transparency in mechanical effects of light. Physical Review A, 81(4):041803, April 2010.
12] T. Baba. Slow light in photonic crystals. Nature Photonics, 2:465-473, 08 2008.
[31
Eric D. Black. An introduction to pound drever hall laser frequency stabilization. American Journal of Physics, 69(1):79-87, 2001.
[4] K.-J. Boller, A. Imamolu, and S. E. Harris. Observation of electromagnetically induced transparency. Phys. Rev. Lett., 66:2593-2596, May 1991.
15]
Alessandra Buonanno and Yanbei Chen. Signal recycled laser-interferometer gravitational-wave detectors as optical springs. Phys. Rev. D, 65:042001, Jan 2002.
[6] J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Grbblacher, M. Aspelmeyer, and 0. Painter. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 478:89-92, October 2011.
[7]
Y. Chen. Macroscopic quantum mechanics: theory and experimental concepts of optomechanics. Journal of Physics B Atomic Molecular Physics, 46(10):104001, May 2013.
[81
LIGO Scientific Collaboration. Observation of a kilogram-scale oscillator near its quantum ground state. New Journal of Physics, 11(7):073032, 2009.
[9] Thomas Corbitt. Quantum Noise and Radiation Pressure Effects in High Power Optical Interferometers. PhD thesis, MIT, 2008. [10] Thomas Corbitt, Yanbei Chen, Edith Innerhofer, Helge Miiller-Ebhardt, David Ottaway, Henning Rehbein, Daniel Sigg, Stanley Whitcomb, Christopher Wipf, and Nergis Mavalvala. An all-optical trap for a gram-scale mirror. Phys. Rev. Lett., 98:150802, Apr 2007. [11] Thomas Corbitt, David Ottaway, Edith Innerhofer, Jason Pelc, and Nergis Mavalvala. Measurement of radiation-pressure-induced optomechanical dynamics in a suspended fabry-perot cavity. Phys. Rev. A, 74:021802, Aug 2006. 67
[12] M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and 0. Painter. Optomechanical crystals. Nature, 462:78-82, November 2009.
[13]
Michael Fleischhauer, Atac Imamoglu, and Jonathan P. Marangos. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys., 77:633-673, Jul 2005.
[14] S. Gigan, H. R. B6hm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Biuerle, M. Aspelmeyer, and A. Zeilinger. Self-cooling of a micromirror by radiation pressure. Nature, 444:67-70, November 2006. [15] T. J. Kippenberg, S. M. Spillane, and K. J. Vahala. Demonstration of ultra-highq small mode volume toroid microcavities on a chip. Applied Physics Letters, 85(25):6113-6115, 2004. [16] Mikhail D. Lukin, Michael Fleischhauer, Marlan 0. Scully, and Vladimir L. Velichansky. Intracavity electromagnetically induced transparency. Opt. Lett., 23(4):295-297, Feb 1998. [17] Yiqiu Ma, Stefan L. Danilishin, Chunnong Zhao, Haixing Miao, W. Zach Korth, Yanbei Chen, Robert L. Ward, and D. G. Blair. Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction. Phys. Rev. Lett., 113:151102, Oct 2014.
118] William Marshall, Christoph Simon, Roger Penrose, and Dik Bouwmeester. Towards quantum superpositions of a mirror. 2003.
[19]
Phys. Rev. Lett., 91:130401, Sep
Osamu Miyakawa, Robert Ward, Rana Adhikari, Matthew Evans, Benjamin Abbott, Rolf Bork, Daniel Busby, Jay Heefner, Alexander Ivanov, Michael Smith, Robert Taylor, Stephen Vass, Alan Weinstein, Monica Varvella, Seiji Kawamura, Fumiko Kawazoe, Shihori Sakata, and Conor Mow-Lowry. Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector. Phys. Rev. D, 74:022001, Jul 2006.
[20] A. F. Pace, M. J. Collett, and D. F. Walls. Quantum limits in interferometric detection of gravitational radiation. Phys. Rev. A, 47:3173-3189, Apr 1993. [21] Jameson Rollins. Intensity stabilization of a solid-state laser for interferometric gravitational wave detectors. Master's thesis, MIT, 2004. [22] Jameson Rollins, David Ottaway, Michael Zucker, Rainer Weiss, and Richard Abbott. Solid-state laser intensity stabilization at the 10< sup>-8 level. Optics letters, 29(16):1876-1878, 2004. [23] A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and 0. Painter. Electromagnetically induced transparency and slow light with optomechanics. Nature, 472:69-73, April 2011. 68
124] J.J. Sakurai. Modern Quantum Mechanics. Addison-Wellsley, 2010. 125] A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg. Radia-
tion pressure cooling of a micromechanical oscillator using dynamical backaction. Phys. Rev. Lett., 97:243905, Dec 2006.
f261 J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds. Sideband cooling of micromechanical motion to the quantum ground state. Nature, 475:359-363, July 2011. [271 J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett., 101:197203, Nov 2008. [281 J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature, 452:72-75, March 2008. [29] D.F. Walls. Quantum Optics. Springer, 2008.
[30] Stefan Weis, Remi Riviere, Samuel DelAl'glise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, and Tobias J. Kippenberg. Optomechanically induced transparency. Science, 330(6010):1520-1523, 2010. [31] Christopher Wipf. Toward Quantum Opto-Mechanics in a Gram-Scale Suspended Mirror Interferometer. PhD thesis, MIT, 2013.
69
