Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light

TL;DR: In this article, the authors inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz.

Abstract: Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories1, 2, 3, 4 is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity.

Summary

Introduction

• In the past, these processes have made it difficult for gravitational wave detectors to reach a shot noise limited sensitivity in their most sensitive band near 150 Hz.
• Randomly scattered light reflecting back into the interferometer has to be managed at the level of 10−18 W. Past experience has shown that measured sensitivities at higher frequencies are difficult to extrapolate to lower frequencies [2].
• The measured improvement due to squeezing is well explained given the amount of squeezing injected into the interferometer and the total measured losses in the squeezed beam path, as the authors will detail later.
• With the squeezed vacuum source employed in the H1 experiment, the authors could expect to reduce the shot noise by at least a factor of 2, improving the high frequency sensitivity of Advanced LIGO.

Injection of squeezed vacuum

• A schematic of the squeezed vacuum source is shown in the grey box of Fig.
• The optical parametric oscillator (OPO) is resonant for both 1064 nm and 532 nm light.
• The interferometer reflects both fields back towards the output mode cleaner (OMC).
• The beat between the 29 MHz frequency shifted coherent beam and the interferometer beam provides an error signal which is used to control the phase of the squeezed vacuum field relative to the interferometer field.

Optical Losses

• The optical losses measured in the path from the squeezed vacuum source to the “output photodiode” are 56%.
• Slusher, R.E. et al. Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity.

AUTHOR CONTRIBUTION

• The activities of the LIGO Scientific Collaboration (LSC) cover modeling astrophysical sources of gravitational waves, setting sensitivity requirements for observatories, designing, building and running observatories, carrying out research and development of new techniques to increase the sensitivity of these observatories, and performing searches for astrophysical signals contained in the data.
• S. Dwyer, S. Chua, L. Barsotti and D. Sigg were the leading scientists on this experiment, but a number of LSC members contributed directly to its success.
• K. Kawabe supervised the integration of the squeezed vacuum source into the LIGO interferometer, with invaluable support from M. Landry and the LIGO Hanford Observatory staff.
• The LSC review of the manuscript was organized by S. Whitcomb.
• The authors declare that they have no competing financial interests.

Figures

FIG. 1. Simplified layout of the H1 interferometer with squeezed vacuum injection. The interferometer layout is described in the text, together with the main squeezer components (shown in the grey box). The green box shows a simplified representation of coherent states and squeezed states in the “in-phase” and “quadrature phase” coordinates.

FIG. 3. Comparison of possible sensitivity curves for Advanced LIGO. Projection for a squeezing-enhanced Advanced LIGO interferometer (continuous lines), using a design similar to the one described in this paper, is compared to the Advanced LIGO sensitivity tuned for high frequency performance (dashed lines). The total noise, in both cases, has been computed by considering all the main noise sources, but only thermal noise and quantum noise are shown, as they are the only relevant noise sources above 100 Hz. The total losses for the squeezed beam were assumed to be 10%, starting with 9 dB of squeezing delivered by the OPO and 35 mrad of phase noise. With the same parameters, but assuming the injection of optimal frequency dependent squeezing, quantum noise can be reduced at all frequencies as shown by the dash-dotted red line.

FIG. 2. Strain sensitivity of the H1 detector measured with and without squeezing injection. The improvement is up to 2.15 dB in the shot noise limited frequency band. Several effects cause the sharp lines visible in the spectra: mechanical resonances in the mirror suspensions, resonances of the internal mirror modes, power line harmonics, etc. As the broadband floor of the sensitivity is most relevant for gravitational wave detection, these lines are typically not too harmful. The inset magnifies the frequency region between 150 and 300 Hz, showing that the squeezing enhancement persists down to 150 Hz

Full text

,
Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed
states of light
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, J. Wang
77
, X. Wang
31
, A. Wanner
4,11
, R. L. Ward
34
, M. Was
4,11
, M. Weinert
4,11
, A. J. Weinstein
1
,
R. Weiss
15
, T. Welborn
3
, L. Wen
16
, P. Wessels
4,11
, M. West
25
, T. Westphal
4,11
, K. Wette
4,11
, J. T. Whelan
61
,
S. E. Whitcomb
1,16
, A. G. Wiseman
5
, D. J. White
38
, B. F. Whiting
8
, K. Wiesner
4,11
, C. Wilkinson
7
,
P. A. Willems
1
, L. Williams
8
, R. Williams
1
, T. Williams
62
, J. L. Willis
53
, B. Willke
4,11
, M. Wimmer
4,11
,
L. Winkelmann
4,11
, W. Winkler
4,11
, C. C. Wipf
15
, H. Wittel
4,11
, G. Woan
2
, R. Wooley
3
, J. Worden
7
, J. Yablon
43
,
I. Yakushin
3
, H. Yamamoto
1
, C. C. Yancey
27
, H. Yang
23
, D. Yeaton-Massey
1
, S. Yoshida
62
, H. Yum
43
,
M. Zanolin
46
, F. Zhang
15
, L. Zhang
1
, C. Zhao
16
, H. Zhu
21
, X. J. Zhu
16
, N. Zotov
56
, M. E. Zucker
15
, J. Zweizig
1
1
LIGO - California Institute of Technology, Pasadena, CA 91125, USA
2
SUPA, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
3
LIGO - Livingston Observatory, Livingston, LA 70754, USA
4
Albert-Einstein-Institut, Max-Planck-Institut f¨ur Gravitationsphysik, D-30167 Hannover, Germany
5
University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA
6
Stanford University, Stanford, CA 94305, USA
7
LIGO - Hanford Observatory, Richland, WA 99352, USA
8
University of Florida, Gainesville, FL 32611, USA
9
Louisiana State University, Baton Rouge, LA 70803, USA
10
University of Birmingham, Birmingham, B15 2TT, United Kingdom
11
Leibniz Universit¨at Hannover, D-30167 Hannover, Germany
12
Albert-Einstein-Institut, Max-Planck-Institut f¨ur Gravitationsphysik, D-14476 Golm, Germany
13
Montana State University, Bozeman, MT 59717, USA
14
Carleton College, Northfield, MN 55057, USA
2

15
LIGO - Massachusetts Institute of Technology, Cambridge, MA 02139, USA
16
University of Western Australia, Crawley, WA 6009, Australia
17
Columbia University, New York, NY 10027, USA
18
The University of Texas at Brownsville, Brownsville, TX 78520, USA
19
San Jose State University, San Jose, CA 95192, USA
20
Moscow State University, Moscow, 119992, Russia
21
The Pennsylvania State University, University Park, PA 16802, USA
22
Washington State University, Pullman, WA 99164, USA
23
Caltech-CaRT, Pasadena, CA 91125, USA
24
University of Oregon, Eugene, OR 97403, USA
25
Syracuse University, Syracuse, NY 13244, USA
26
Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX United Kingdom
27
University of Maryland, College Park, MD 20742, USA
28
University of Massachusetts - Amherst, Amherst, MA 01003, USA
29
The University of Mississippi, University, MS 38677, USA
30
NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
31
Tsinghua University, Beijing 100084, China
32
University of Michigan, Ann Arbor, MI 48109, USA
33
Charles Sturt University, Wagga Wagga, NSW 2678, Australia
34
Australian National University, Canberra, ACT 0200, Australia
35
The University of Melbourne, Parkville, VIC 3010, Australia
36
Cardiff University, Cardiff, CF24 3AA, United Kingdom
37
University of Salerno, I-84084 Fisciano (Salerno), Italy and INFN (Sezione di Napoli), Italy
38
The University of Sheffield, Sheffield S10 2TN, United Kingdom
39
Inter-University Centre for Astronomy and Astrophysics, Pune - 411007, India
40
Southern University and A&M College, Baton Rouge, LA 70813, USA
41
University of Minnesota, Minneapolis, MN 55455, USA
42
California Institute of Technology, Pasadena, CA 91125, USA
43
Northwestern University, Evanston, IL 60208, USA
44
The University of Texas at Austin, Austin, TX 78712, USA
45
MTA-Eotvos University, ‘Lendulet’ A. R. G., Budapest, 1117 Hungary
46
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
47
National Astronomical Observatory of Japan, Tokyo 181-8588, Japan
48
University of Adelaide, Adelaide, SA 5005, Australia
49
Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
50
University of Southampton, Southampton, SO17 1BJ, United Kingdom
51
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
52
SUPA, University of Strathclyde, Glasgow, G1 1XQ, United Kingdom
53
Abilene Christian University, Abilene TX 79699, USA
54
Hobart and William Smith Colleges, Geneva, NY 14456, USA
55
University of Sannio at Benevento, I-82100 Benevento, Italy and INFN (Sezione di Napoli), Italy
56
Louisiana Tech University, Ruston, LA 71272, USA
57
Andrews University, Berrien Springs, MI 49104, USA
58
McNeese State University, Lake Charles, LA 70609, USA
59
California State University Fullerton, Fullerton CA 92831, USA
60
Trinity University, San Antonio, TX 78212, USA
61
Rochester Institute of Technology, Rochester, NY 14623, USA
62
Southeastern Louisiana University, Hammond, LA 70402, USA
63
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario, M5S 3H8, Canada
64
Pusan National University, Busan 609-735, Korea
65
West Virginia University, Morgantown, WV 26505, USA
66
Hanyang University, Seoul 133-791, Korea
67
Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
68
National Institute for Mathematical Sciences, Daejeon 305-390, Korea
69
Seoul National University, Seoul 151-742, Korea
70
University of Szeged, 6720 Szeged, D´om t´er 9, Hungary
71
Perimeter Institute for Theoretical Physics, Ontario, N2L 2Y5, Canada
72
University of New Hampshire, Durham, NH 03824, USA
73
University of Cambridge, Cambridge, CB2 1TN, United Kingdom
74
American University, Washington, DC 20016, USA
75
Instituto Nacional de Pesquisas Espaciais, 12227-010 - S˜ao Jos´e dos Campos, SP, Brazil
76
University of Washington, Seattle, WA, 98195-4290, USA
77
National Tsing Hua University, Hsinchu Taiwan 300, Province of China
3

78
SUPA, University of the West of Scotland, Paisley, PA1 2BE, United Kingdom
79
The George Washington University, Washington, DC 20052, USA
80
Raman Research Institute, Bangalore, Karnataka 560080, India
81
Universidad Nacional de Cordoba, Cordoba 5000, Argentina
82
IISER-Kolkata, Mohanpur West. Bengal 741252, India
83
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
84
RRCAT, Indore MP 452013, India
85
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India and
86
Tata Institute for Fundamental Research, Mumbai 400005, India
Nearly a century after Einstein first predicted
the existence of gravitational waves, a global net-
work of earth-based gravitational wave obser-
vatories [1–4] is seeking to directly detect this
faint radiation using precision laser interferom-
etry. Photon shot noise, due to the quantum
nature of light, imposes a fundamental limit on
the attometer level sensitivity of the kilometer-
scale Michelson interferometers deployed for this
task. Here we inject squeezed states to improve
the performance of one of the detectors of the
Laser Interferometer Gravitational-wave Obser-
vatory (LIGO) beyond the quantum noise limit,
most notably in the frequency region down to 150
Hz, critically important for several astrophysi-
cal sources, with no deterioration of performance
observed at any frequency. With the injection
of squeezed states, this LIGO detector demon-
strated the best broadband sensitivity to gravita-
tional waves ever achieved, with important impli-
cations for observing the gravitational wave Uni-
verse with unprecedented sensitivity.
A fundamental limit to the sensitivity of a Michelson
interferometer with quasi-free mirrors comes from the
quantum nature of light, which reveals itself through two
fundamental mechanisms: photon counting noise (shot
noise), arising from statistical fluctuations in the arrival
time of photons at the interferometer output; and radia-
tion pressure noise, which is the recoil of the mirrors due
to the radiation pressure arising from quantum fluctua-
tions in the photon flux. Both sources can be attributed
to the quantum fluctuations of the electromagnetic vac-
uum field, or vacuum fluctuations, that enter the inter-
ferometer [5, 6].
An electromagnetic field can be described by two non-
commuting conjugate operators that are associated with
field amplitudes that oscillate out of phase with each
other by 90
◦
, labeled as “in-phase” and “quadrature
phase” [7]. A coherent state of light (or vacuum, if the
coherent amplitude is zero) has equal uncertainty in both
quadratures, with the uncertainty product limited by the
Heisenberg uncertainty principle. For a squeezed state,
the uncertainty in one quadrature is decreased relative to
that of the coherent state (see green box in Fig. 1). Note
that the uncertainty in the orthogonal quadrature is cor-
respondingly increased, always satisfying the Heisenberg
inequality.
The vacuum fluctuations that limit the sensitivity
of an interferometric gravitational wave detector enter
through the antisymmetric port of the interferometer,
mix with the signal field produced at the beamsplitter
by a passing gravitational wave, and exit the antisym-
metric port to create noise on the output photodetec-
tor. Caves [5, 6] showed that replacing coherent vacuum
fluctuations entering the antisymmetric port with cor-
rectly phased squeezed vacuum states decreases the “in-
phase” quadrature uncertainty, and thus the shot noise,
below the quantum limit. Shortly after, the first exper-
iments showing squeezed light production through non-
linear optical media achieved modest but important re-
ductions in noise at high frequencies [8] [9]. However,
squeezing in the audiofrequency region relevant for grav-
itational wave detection and control schemes for locking
the squeezed phase to that needed by the interferometer
were not demonstrated until the last decade [10] [11] [12].
Since then, squeezed vacuum has been used to enhance
the sensitivity of a prototype interferometer [13]. The
600-m long GEO600 detector [14] has deployed squeez-
ing since 2010, achieving improved sensitivity at 700 Hz
and above.
An important motivation for the experiment we
present here was to extend the frequency range down
to 150 Hz while testing squeezing at a noise level close
to that required for Advanced LIGO [15]. This lower fre-
quency region is critically important for the most promis-
ing astrophysical sources, such as coalescences of black
hole and neutron star binary systems, but also poses
a significant experimental challenge. Seismic motion is
huge compared to the desired sensitivity, albeit at very
low frequencies
<
∼
1 Hz, and LIGO employs a very high
performance isolation system to attenuate the seismic
motion by several orders of magnitude. This uncovers
a set of non-linear couplings which up-convert low fre-
quency noise into the gravitational wave band. In the
past, these processes have made it difficult for gravita-
tional wave detectors to reach a shot noise limited sen-
sitivity in their most sensitive band near 150 Hz. Any
interactions between the interferometer and the outside
world have to be kept at an absolute minimum. For in-
stance, randomly scattered light reflecting back into the
4

interferometer has to be managed at the level of 10
−18
W.
Past experience has shown that measured sensitivities at
higher frequencies are difficult to extrapolate to lower
frequencies [2]. For the first time, we employ squeezing
to obtain a sensitivity improvement at a gravitational
wave observatory in the critical frequency band between
150 Hz and 300 Hz. Similarly important, we observed
that no additional noise above background was added
by our squeezed vacuum source, firmly establishing this
quantum technology as an indispensable technique in the
future of gravitational wave astronomy.
The experiment was carried out toward the end of 2011
on the LIGO detector at Hanford, Washington, known
as “H1”. The optical layout of the detector is shown in
Fig. 1. The interferometer light source (“H1 laser”) is
a Nd:YAG laser (1064 nm) stabilized in frequency and
intensity. A beam splitter splits the light into the two
arms of the Michelson, and Fabry-Perot cavities increase
the phase sensitivity by bouncing the light ≈ 130 times
in each arm. The Michelson is operated on a dark fringe,
thus most of the light is reflected from the interferometer
back to the laser. A partially transmitting mirror be-
tween the laser and the beam splitter forms the power-
recycling cavity, which increases the power incident on
the beam splitter by a factor of 40. In order to isolate
them from terrestrial forces such as seismic noise, the
power recycling mirror, the beam splitter, and the arm
cavity mirrors are all suspended as pendula on vibration-
isolated platforms.
A passing gravitational wave produces a differential
change in the lengths of the arm cavities (generally, one
arm gets shorter while the orthogonal arm gets longer),
causing a signal field to appear at the antisymmetric port
proportional to the wave amplitude.
For unperturbed arm length L, a gravitational wave of
amplitude h (in dimensionless units of strain) induces a
differential change in arm length ∆L = hL. For typical
astrophysical sources from 10 to 100 Mpc away, such as
the inspiral and merger of binary neutron stars or black
holes, terrestrial detectors must measure strains at the
level of 10
−21
or smaller.
A full description of this interferometer (and its sis-
ter interferometer in Livingston, LA) can be found in
Ref. [2]. A number of crucial modifications have been
made since then that enable the implementation and
testing of squeezing. In particular, the signal readout
has been changed from a heterodyne to a homodyne sys-
tem [16], where we actively operated the Michelson in-
terferometer with a small offset from a dark fringe to
send about 30 mW of light to the antisymmetric port to
act as the homodyne reference beam. An output mode-
cleaner (OMC in Fig. 1) was also installed to prevent
light in higher order optical modes and at different radio-
frequency offsets from reaching the readout photodetec-
tor. Moreover, the available laser power was increased
from 10 W to 20 W. This resulted in 15 W of light
power reaching the interferometer, 600 W impinging on
the beamsplitter and 40 kW stored in the interferometer
arm cavities. These modifications resulted in a factor of
2 improvement in sensitivity above 500 Hz over the 2009
configuration.
The grey box of Fig. 1 shows a simplified schematic
of the squeezed vacuum source. A sub-threshold op-
tical parametric oscillator (OPO) in a bow-tie config-
uration [17] [18] produces the squeezed vacuum state.
Light at 532 nm pumps the OPO and produces squeezed
vacuum at 1064 nm via parametric downconversion in
a second-order nonlinear PPKTP crystal placed in the
OPO cavity. The “pump laser” for the squeezed vac-
uum source is phase-locked to the “H1 laser” and it emits
1064 nm light which drives the second harmonic gener-
ator (SHG) to produce light at 532 nm. The “control
laser” is phase-locked to the “pump laser” to generate
a frequency shifted coherent beam which enters the in-
terferometer through the “output Faraday isolator”, to-
gether with the squeezed vacuum. The interferometer
reflects both fields back towards the OMC, and the beat
between the frequency shifted coherent beam and the in-
terferometer beam is detected by the “squeezing angle
control photodiode” to control the phase of the squeezed
vacuum field relative to the interferometer field [11]. The
OMC filters out the frequency shifted coherent beam,
while the squeezed vacuum reaches the “output photodi-
ode”.
During the experiment reported here, the LIGO H1
detector was configured as it was during its most sen-
sitive scientific run S6 [19] concluded in October 2010.
Shot noise was the limiting noise source above 400 Hz
and contributed significantly to the total noise down to
150 Hz [2]. Radiation pressure noise was negligible, com-
pletely masked by other noise sources.
The significantly improved sensitivity due to squeezing
in this experiment is shown in Fig. 2. The performance
without squeezing shown by the red curve was compara-
ble at high frequency to the best sensitivity H1 reached
during S6. The blue curve shows the improvement in
the sensitivity resulting from squeezing, with a 2.15 dB
(28%) reduction in the shot noise. This constitutes the
best broadband sensitivity to gravitational waves ever
achieved. To achieve the same improvement, a 64% in-
crease in the power stored in the arm cavities would
have been necessary, but this power increase would be
accompanied by the significant limitations of high power
operation [15, 20]. The measured improvement due to
squeezing is well explained given the amount of squeezing
injected into the interferometer and the total measured
losses in the squeezed beam path, as we will detail later.
A reduction in the total losses would therefore directly
translate in a larger shot noise suppression.
Equally important, the squeezed vacuum source did
not introduce additional technical noise in any frequency
band. This required paying particular attention in the
5

Frequently asked questions

Q1. What are the main losses in the optical parametric oscillator?

The dominant loss sources are: mode mismatch between the squeezed beam and the OMC cavity (25% ± 5%), scatter and absorption in the OMC (18% ± 2%), and absorption and imperfect polarization alignment in the Faraday isolators (with total losses of 20% ± 2%). 

Q2. What is the phase of the squeezed vacuum?

The beat between the 29 MHz frequency shifted coherent beam and the interferometer beam provides an error signal which is used to control the phase of the squeezed vacuum field relative to the interferometer field. 

Q3. What is the recent research on the physics of aqueous quantum states?

Search for gravitational waves from low mass compact binary coalescence in LIGO’s sixth science run and Virgo’s science runs 2 and 3. 

Q4. What is the optical loss in the vacuum?

The 1064 nm ‘control laser” is phase-locked to the “pump laser” to generate a 29 MHz frequency shifted coherent beam which co-propagates with the squeezed vacuum beam, entering the interferometer through the “output Faraday isolator”. 

Q5. How much light is pumped to the vacuum source?

It is typically pumped with about 40 mW of 532 nm light, where the thresh-old for spontaneous sub-harmonic generation is near 95 mW. 

Q6. Who was the lead scientist on the LIGO experiment?

N. SmithLefebvre, M. Evans, R. Schofield and C. Vorvick kept the LIGO interferometer at its peak sensitivity and supported the integration of the squeezed vacuum source, with contributions from G. Meadors and D. Gustafson. 

Q7. What is the squeezing angle of the vacuum laser?

1. The 1064 nm “pump laser” is phase-locked to the “H1 laser” and it drives the second harmonic generator (SHG) to produce light at 532 nm. 

Q8. What is the name of the paper?

New J. Phys. 11 073032 (2009)The authors gratefully acknowledge the support of the United States National Science Foundation for the construction and operation of the LIGO Laboratory and the Science and Technology Facilities Council of the United Kingdom, the Max-Planck-Society, and the State of Niedersachsen/Germany for support of the construction and operation of the GEO600 detector. 

Q9. What is the cause of the mode mismatch?

The mode mismatch between the squeezed beam and the output mode cleaner (OMC) is mainly caused by a complicated optical train in the vacuum envelope, which precluded improving the mode matching on a time scale compatible with this experiment. 

Q10. what is the reason for the loss in the LIGO H1 detector?

Most of these losses are due to the fact that the LIGO H1 detector was not initially designed for injection of squeezed states, and the squeezing injection path was retrofitted within the original LIGO optical layout. 

Q11. What is the reason for the large optical losses in the OMC?

The losses in the OMC itself are also larger than expected, and they are believed to be due to scatter and absorption inside the mode cleaner cavity.