Quantum correlation measurements in interferometric gravitational wave detectors
D. V. Martynov,
7
V. V. Frolov,
3
S. Kandhasamy,
16
K. Izumi,
5
H. Miao,
32
N. Mavalvala,
7
E. D. Hall,
1
R. Lanza,
7
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
C. Adams,
3
R. X. Adhikari,
1
S. B. Anderson,
1
A. Ananyeva,
1
S. Appert,
1
K. Arai,
1
S. M. Aston,
3
S. W. Ballmer,
4
D. Barker,
5
B. Barr,
6
L. Barsotti,
7
J. Bartlett,
5
I. Bartos,
8
J. C. Batch,
5
A. S. Bell,
6
J. Betzwieser,
3
G. Billingsley,
1
J. Birch,
3
S. Biscans,
1
,
7
C. Biwer,
4
C. D. Blair,
9
R. Bork,
1
A. F. Brooks,
1
G. Ciani,
10
F. Clara,
5
S. T. Countryman,
8
M. J. Cowart,
3
D. C. Coyne,
1
A. Cumming,
6
L. Cunningham,
6
K. Danzmann,
11
,
12
C. F. Da Silva Costa,
10
E. J. Daw,
13
D. DeBra,
14
R. T. DeRosa,
3
R. DeSalvo,
15
K. L. Dooley,
16
S. Doravari,
3
J. C. Driggers,
5
S. E. Dwyer,
5
A. Effler,
3
T. Etzel,
1
M. Evans,
7
T. M. Evans,
3
M. Factourovich,
8
H. Fair,
4
A. Fern ́andez Galiana,
7
R. P. Fisher,
4
P. Fritschel,
7
P. Fulda,
10
M. Fyffe,
3
J. A. Giaime,
2
,
3
K. D. Giardina,
3
E. Goetz,
12
R. Goetz,
10
S. Gras,
7
C. Gray,
5
H. Grote,
12
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
17
G. Hammond,
6
J. Hanks,
5
J. Hanson,
3
T. Hardwick,
2
G. M. Harry,
18
M. C. Heintze,
3
A. W. Heptonstall,
1
J. Hough,
6
R. Jones,
6
S. Karki,
19
M. Kasprzack,
2
S. Kaufer,
11
K. Kawabe,
5
N. Kijbunchoo,
5
E. J. King,
20
P. J. King,
5
J. S. Kissel,
5
W. Z. Korth,
1
G. Kuehn,
12
M. Landry,
5
B. Lantz,
14
N. A. Lockerbie,
21
M. Lormand,
3
A. P. Lundgren,
12
M. MacInnis,
7
D. M. Macleod,
2
S. M ́arka,
8
Z. M ́arka,
8
A. S. Markosyan,
14
E. Maros,
1
I. W. Martin,
6
K. Mason,
7
T. J. Massinger,
4
F. Matichard,
1
,
7
R. McCarthy,
5
D. E. McClelland,
22
S. McCormick,
3
G. McIntyre,
1
J. McIver,
1
G. Mendell,
5
E. L. Merilh,
5
P. M. Meyers,
23
J. Miller,
7
R. Mittleman,
7
G. Moreno,
5
G. Mueller,
10
A. Mullavey,
3
J. Munch,
20
L. K. Nuttall,
4
J. Oberling,
5
P. Oppermann,
12
Richard J. Oram,
3
B. O’Reilly,
3
D. J. Ottaway,
20
H. Overmier,
3
J. R. Palamos,
19
H. R. Paris,
14
W. Parker,
3
A. Pele,
3
S. Penn,
24
M. Phelps,
6
V. Pierro,
15
I. Pinto,
15
M. Principe,
15
L. G. Prokhorov,
25
O. Puncken,
12
V. Quetschke,
26
E. A. Quintero,
1
F. J. Raab,
5
H. Radkins,
5
P. Raffai,
27
S. Reid,
28
D. H. Reitze,
1
,
10
N. A. Robertson,
1
,
6
J. G. Rollins,
1
V. J. Roma,
19
J. H. Romie,
3
S. Rowan,
6
K. Ryan,
5
T. Sadecki,
5
E. J. Sanchez,
1
V. Sandberg,
5
R. L. Savage,
5
R. M. S. Schofield,
19
D. Sellers,
3
D. A. Shaddock,
22
T. J. Shaffer,
5
B. Shapiro,
14
P. Shawhan,
29
D. H. Shoemaker,
7
D. Sigg,
5
B. J. J. Slagmolen,
22
B. Smith,
3
J. R. Smith,
30
B. Sorazu,
6
A. Staley,
8
K. A. Strain,
6
D. B. Tanner,
10
R. Taylor,
1
M. Thomas,
3
P. Thomas,
5
K. A. Thorne,
3
E. Thrane,
31
C. I. Torrie,
1
G. Traylor,
3
G. Vajente,
1
G. Valdes,
26
A. A. van Veggel,
6
A. Vecchio,
32
P. J. Veitch,
20
K. Venkateswara,
33
T. Vo,
4
C. Vorvick,
5
M. Walker,
2
R. L. Ward,
22
J. Warner,
5
B. Weaver,
5
R. Weiss,
7
P. Weßels,
12
B. Willke,
11
,
12
C. C. Wipf,
1
J. Worden,
5
G. Wu,
3
H. Yamamoto,
1
C. C. Yancey,
29
Hang Yu,
7
Haocun Yu,
7
L. Zhang,
1
M. E. Zucker,
1
,
7
and J. Zweizig
1
(LSC Instrument Authors)
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
LIGO Livingston Observatory, Livingston, LA 70754, USA
4
Syracuse University, Syracuse, NY 13244, USA
5
LIGO Hanford Observatory, Richland, WA 99352, USA
6
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
7
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
8
Columbia University, New York, NY 10027, USA
9
University of Western Australia, Crawley, Western Australia 6009, Australia
10
University of Florida, Gainesville, FL 32611, USA
11
Leibniz Universit ̈at Hannover, D-30167 Hannover, Germany
12
Albert-Einstein-Institut, Max-Planck-Institut f ̈ur Gravitationsphysik, D-30167 Hannover, Germany
13
The University of Sheffield, Sheffield S10 2TN, United Kingdom
14
Stanford University, Stanford, CA 94305, USA
15
University of Sannio at Benevento, I-82100 Benevento,
Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
16
The University of Mississippi, University, MS 38677, USA
17
University of Michigan, Ann Arbor, MI 48109, USA
18
American University, Washington, D.C. 20016, USA
19
University of Oregon, Eugene, OR 97403, USA
20
University of Adelaide, Adelaide, South Australia 5005, Australia
21
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
22
Australian National University, Canberra, Australian Capital Territory 0200, Australia
23
University of Minnesota, Minneapolis, MN 55455, USA
24
Hobart and William Smith Colleges, Geneva, NY 14456, USA
25
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
26
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
27
MTA E ̈otv ̈os University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary
arXiv:1702.03329v1 [physics.optics] 10 Feb 2017
2
28
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
29
University of Maryland, College Park, MD 20742, USA
30
California State University Fullerton, Fullerton, CA 92831, USA
31
Monash University, Victoria 3800, Australia
32
University of Birmingham, Birmingham B15 2TT, United Kingdom
33
University of Washington, Seattle, WA 98195, USA
(Dated: February 14, 2017)
Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the
sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational wave
detectors, such as the Advanced Laser Interferometer Gravitational wave Observatory (LIGO), is
limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We
show how the quantum properties of light can be used to distinguish these noises using correlation
techniques. Particularly, in the first part of the paper we show estimations of the coating thermal
noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity
curve. We also make projections on the observatory sensitivity during the next science runs. In the
second part of the paper we discuss the correlation technique that reveals the quantum radiation
pressure noise from the background of classical noises and shot noise. We apply this technique to
the Advanced LIGO data, collected during the first science run, and experimentally estimate the
quantum correlations and quantum radiation pressure noise in the interferometer for the first time.
PACS numbers: 04.80.Nn, 95.55.Ym, 95.75.Kk, 07.60.Ly, 03.65.Ta, 42.50.Lc
I. INTRODUCTION
Interferometric gravitational wave detectors have trig-
gered extensive research in the field of quantum op-
tics [1, 2]. The standard quantum limit [3, 4], related to
the Heisenberg uncertainty principle, sets limitations on
the sensitivity of modern interferometric measurements.
These broadband noises, known as shot noise and quan-
tum radiation pressure noise (QRPN), are predicted to
limit the design sensitivity of Advanced LIGO in the fre-
quency range 10 Hz–10 kHz [5, 6].
Apart from quantum noises, the Advanced LIGO sen-
sitivity was limited by a set of classical noises during the
first observing run (O1) [7–9]. This run, lasting from
September 2015 to January 2016, culminated in two di-
rect observations of gravitational waves from binary black
hole coalescences [10–13]. Further improvement of the
observatory range requires more investigations into quan-
tum and classical noises.
Since Advanced LIGO was limited by shot noise above
100 Hz, the spectrum of classical noises is not directly
observable at these frequencies. Here, we report on the
use of correlation technique and reveal, for the first time,
the classical-noise spectrum, hidden underneath the shot
noise in Advanced LIGO. This technique explores quan-
tum properties of light, in particular the quantum corre-
lation among the optical power fluctuations in different
readout channels. We use the obtained spectrum of clas-
sical noises to estimate the Advanced LIGO sensitivity
during the next science runs, and set constraints on the
coating thermal noise [14, 15] and gas phase noise [16].
In addition to estimating classical noise, we also use
the correlation technique to probe QRPN in Advanced
LIGO, and estimate this noise experimentally. QRPN
was studied for more than thirty years [1, 17]. It has
been investigated by a number of experiments both in
the gravitational wave (GW) community [18–22], and the
optomechanics community [23–29]. To our knowledge, its
spectrum at the audio band has not yet been observed.
During O1 the level of this noise is predicted to be a factor
of
'
8
−
10 smaller compared to the current noise floor in
the frequency band 30–100 Hz; the quantum correlation,
however, allows us to reveal it for the first time.
This paper is structured as follows: In Sec. II we dis-
cuss the configuration of the Advanced LIGO interferom-
eters, and the propagation of the optical fields that are
involved in computing the power fluctuation of different
photodiode readouts. Sec. III is devoted to the investi-
gations of the classical noise spectra in Advanced LIGO
hidden below the quantum shot noise. In Sec. IV we set
an experimental estimate on the level of the QRPN using
the correlation technique.
II. OPTICAL CONFIGURATION
In this section, we introduce the optical configuration
of the interferometer, discuss how optical fields propagate
through the interferometer and beat on the photodetec-
tors.
A. The interferometer and its signal field
The Advanced LIGO detectors, shown in Fig. 1, are
Michelson–type interferometers, enhanced by four optical
cavities: a Fabry–P ́erot cavity in each arm, one at the
symmetric port and another at antisymmetric port of
the interferometer [30]. The first two arm cavities are
used to optically increase the length of each arm by a
factor of
G
arm
= 260. The latter two cavities are set
to maximize circulating power in the interferometer by a
factor of
G
prc
= 38 and optimize the frequency response
to gravitational waves in the frequency range 10 Hz –
3
10 kHz [5], respectively. This is achieved by setting the
carrier field to be anti resonant in the signal recycling
cavity [31, 32] and attenuating its power by a factor of
G
src
= 9.
100 kW
1064 nm
Laser
22W
800W
85mW
FIG. 1. Layout of an Advanced LIGO detector. The an-
notations show the optical power in use during O1. Also
shown are vacuum and laser fields entering the interferometer
through the input, output, and transmission ports. GW sig-
nal
s
as
(also includes classical noises) leaves the interferometer
through the antisymmetric port.
The frequency dependent GW signal is derived from
the difference in the two arm lengths
L
(
f
) according to
the equation
L
(
f
)
/L
0
, where
L
0
= 3995 m is the macro-
scopic length of each arm and
f
is the frequency of the
GW signal. The differential arm length signal
L
(
f
) is
derived from the power measurement
P
as
at the antisym-
metric port of the interferometer. The transfer function
Z
=
dP
as
/dL
, known as the optical response of the in-
strument [33, 34], can be written as
Z
(
f
) =
4
πG
arm
λ
(
G
prc
P
in
P
as
G
src
)
1
/
2
K
−
(
f
)
W
m
,
(1)
where
P
in
is the input power and
λ
is the laser wave-
length. The transfer function
K
−
=
f
−
/
(
if
+
f
−
) ac-
counts for the diminished response of the instrument at
high frequencies, where
f
−
is known as the differential
coupled cavity pole frequency [5] and is given by the
equation
f
−
=
T
i
c
8
πL
0
≈
360 Hz
,
(2)
where
T
i
≈
0
.
12 is the transmission of the signal recycling
cavity and
c
is the speed of light.
The differential arm length is sensed by using a par-
ticular type of homodyne readout technique, known as
DC readout [35]. In this scheme an offset ∆
L
= 10 pm
is introduced to the differential arm length to allow a
small fraction of the optical power
P
as
to leak to the
antisymmetric port. Other longitudinal degrees of free-
dom are controlled using the Pound–Drever–Hall tech-
nique [36, 37], with no intentional longitudinal offsets.
0
20
40
60
80
100
120
Time, days
90
95
100
105
110
115
120
Arm power, kW
FIG. 2. Optical power resonating in LIGO Livingston inter-
ferometer (L1) during the first science run. The power was
fluctuating by a few percents, and slightly decreased by the
end of the run due to the drift of the input power.
The main laser is capable of delivering 150 W of op-
tical power, however, only
P
in
,
0
= 22 W was used dur-
ing O1. This resulted in a circulating power of approx-
imately
P
arm
= 107 kW in each arm. Fig. 2 shows the
power fluctuation in one of the arm cavities during O1.
The variance was 3.2 kW, and the precision of the power
calibration was 5% [33]. The circulating arm power has
slightly decreased by the end of the run due to the drift
of the input power.
B. Power fluctuations as beat between DC and AC
fields
In this paper, one of the key quantities involved is the
optical power fluctuation measured by different photodi-
odes. We treat the interferometer as a linear device in
which longitudinal disturbances are linearly translated to
perturbations of the optical fields. In such a linear sys-
tem, the power fluctuation of a field at a frequency
f
can
be classically described as
P
(
f
) =
Aa
∗
(
ν
0
−
f
) +
A
∗
a
(
ν
0
+
f
)
,
(3)
where
ν
0
= 2
.
82
×
10
14
Hz is the laser (carrier) frequency,
A
is the amplitude of the carrier field at
ν
0
and
a
(
ν
0
±
f
)
are those of the sideband fields or perturbation fields at
ν
0
±
f
. The superscript “
∗
” is for complex conjugate.
Similarly, when quantizing the field, the corresponding
Heisenberg operator is equal to
ˆ
P
(
f
) =
A
ˆ
a
†
(
ν
0
−
f
) +
A
∗
ˆ
a
(
ν
0
+
f
)
,
(4)
4
where ˆ
a
and ˆ
a
†
are annihilation and creation operators of
the field, respectively. Throughout this paper we study
physical properties of the interferometer according to
the quantum formalism broadly presented in the liter-
ature [38–41].
In Advanced LIGO, the cavity mode is excited by
a laser with a large amplitude
A
s
at an angular fre-
quency
ω
0
= 2
πν
0
. The input field is normalized ac-
cording to the equation
A
s
=
√
P
in
/hν
0
, where
h
is
the Planck constant. We study the linearized dynamics
by perturbing the steady state and move into the rotat-
ing frame at
ν
0
. Correspondingly, the carrier field is at
zero frequency (DC), while the sideband fields are at fre-
quency
±
f
(AC). In the following, we shall use ˆ
a,
ˆ
b,
ˆ
c
, as
shorthand for ˆ
a
(
f
)
,
ˆ
b
(
f
)
,
ˆ
c
(
f
) and ˆ
a
†
,
ˆ
b
†
,
ˆ
c
†
, as shorthand
for ˆ
a
†
(
−
f
)
,
ˆ
b
†
(
−
f
)
,
ˆ
c
†
(
−
f
). In order to compute optical
power at each particular interferometer port, one needs
to calculate these two kinds of fields. The rest of this
section discusses their propagation inside the interferom-
eter.
C. Propagation of the DC fields
The static laser field
A
s
enters the interferometer
through the symmetric port and resonates in the interfer-
ometer. Optical fields in the arm cavities are denoted as
C
x
and
C
y
as shown in Fig. 1. These fields then transmit
to the rear side of the end mirrors (fields
B
x
and
B
y
) and
to the antisymmetric port (field
B
as
). They are given by
the equations
C
=
C
x
=
C
y
=
√
1
2
G
prc
G
arm
A
s
B
=
B
x
=
B
y
=
√
T
e
C
B
as
= 2
πiG
arm
∆
L
λ
√
G
prc
G
src
A
s
,
(5)
where
T
e
= 3
.
6 ppm is the power transmission of the out-
put couplers (end mirrors). The factors
G
prc
,
G
arm
, and
1/2 in the first equation account for the build up in the
power recycling and arm cavities, and attenuation due to
the 50/50 beam splitter. The factor
G
src
appears in the
denominator of the equation for
B
as
since the carrier field
is anti resonant in the signal recycling cavity. Note that
there is a 90
◦
phase shift (expressed by an imaginary
i
)
between the input field
A
s
and anti symmetric port field
B
as
because of the transmission through the Michelson
interferometer.
D. Propagation of the AC fields
Vacuum fields [1, 2] enter the interferometer through
the antisymmetric (ˆ
a
as
), symmetric (ˆ
a
s
), and transmis-
sion ports (ˆ
a
x
and ˆ
a
y
), as shown in Fig. 1. They prop-
agate through the interferometer and reach the output
ports according to the input–output relations [42]. We
denote output fields at the antisymmetric port as
ˆ
b
as
, at
the arm transmission ports as
ˆ
b
x
and
ˆ
b
y
, and at the arm
cavities as ˆ
c
x
and ˆ
c
y
. In the case with no longitudinal off-
sets in the interferometric degrees of freedom (∆
L
= 0),
and ignoring quantum radiation pressure effects, consid-
ered in Sec. IV, we can write up to the first order in
t
e
=
√
T
e
and
t
i
=
√
T
i
ˆ
b
as
ˆ
b
y
−
ˆ
b
x
√
2
ˆ
c
y
−
ˆ
c
x
√
2
'
−
K
−
/K
∗
−
0
√
2
t
e
g
−
√
2
t
e
g
−
0
−
1
√
2
g
−
0
t
e
t
i
√
2
g
−
ˆ
a
as
ˆ
a
s
ˆ
a
y
−
ˆ
a
x
√
2
,
(6)
where
g
−
=
√
G
arm
/
2
G
src
×
K
−
(
f
). This approximation
is valid for small
t
e
and
t
i
; more precisely, energy conser-
vation always gives
|
X
11
|
2
+
|
X
12
|
2
+
|
X
13
|
2
= 1, where
X
11
,
X
12
and
X
13
are matrix elements with correspond-
ing indices.
Eq. 6 shows that the vacuum field from the laser ˆ
a
s
does not couple to the antisymmetric port and differential
transmission signals. While an intentional offset ∆
L
in
the differential arm length is important for accurately
obtaining the DC field at the antisymmetric port (5),
we find that the effect of ∆
L
is rather insignificant in
the propagation matrix for the AC fields for Advanced
LIGO.
III. REMOVING SHOT NOISE AND
CHARACTERIZING CLASSICAL NOISES
In this section, we describe a correlation technique for
estimating the amount of classical noises buried below the
shot noise. The strength of this noise can be quantified
by its spectral density
S
as
(
f
) = 2
P
as
hν
. Using Eq. (1)
we can convert this noise to the units of length. The
shot noise spectrum in the GW channel
S
shot
limits the
sensitivity of Advanced LIGO above 100 Hz [7, 8] and is
given by the equation
√
S
shot
=
√
S
as
1
−
η
1
|
Z
(
f
)
|
= 2
.
33
×
10
−
20
(
107 kW
P
arm
)
1
/
2
1
|
K
−
(
f
)
|
m
√
Hz
(7)
where
η
= 0
.
28 is the power loss from the signal recycling
cavity to the photodetectors at the antisymmetric port.
The outgoing field at the anti–symmetric port is split
into two beams by a 50/50 beam splitter, and a homo-
dyne detection is performed on each of the beams, as
shown in Fig. 1. In this section, we show that shot noise
and photodetector dark noise can be removed, while in-
terferometer classical and radiation pressure noises kept
intact, by performing a correlation measurement between
the two detectors.
5
A. Shot and dark noise removal
Power fluctuations at the two photodetectors at the
antisymmetric port (see Fig. 1) arise from the shot noise
P
shot
as
,j
, QRPN
P
qrpn
as
,j
, classical noises
P
cl
as
,j
and photode-
tector dark noises
P
dark
as
,j
according to the equation
ˆ
P
as
,j
=
ˆ
P
shot
as
,j
+
ˆ
P
qrpn
as
,j
+
ˆ
P
cl
as
,j
+
ˆ
P
dark
as
,j
,
(8)
where
j
= 1
,
2.
Eq. 8 can be written as the beat of the static field
B
as
with classical field
s
as
and vacuum fields
ˆ
b
as
and
ˆ
b
bs
.
The latter field comes in through the open port of the
50/50 beam splitter in front of the photodetectors. Power
fluctuations can be written as
ˆ
P
as
,
1
=
1
√
2
iB
∗
as
(ˆ
ν
as
,
ph
+ ˆ
ν
bs
,
ph
+
ν
cl
,
ph
) +
ˆ
P
dark
as
,
1
ˆ
P
as
,
2
=
1
√
2
iB
∗
as
(ˆ
ν
as
,
ph
−
ˆ
ν
bs
,
ph
+
ν
cl
,
ph
) +
ˆ
P
dark
as
,
2
,
(9)
where ˆ
ν
as
,
ph
, ˆ
ν
bs
,
ph
and
ν
cl
,
ph
are phase quadratures
of the fields
ˆ
b
as
,
ˆ
b
bs
and
s
as
defined as ˆ
ν
x
,
ph
= (ˆ
x
−
x
†
)
/
(
√
2
i
). Note that
ν
cl
,
ph
includes QRPN since this
noise is indistinguishable from classical noises at the an-
tisymmetric port.
Then we compute the cross spectral density
S
12
be-
tween signals
P
as
,
1
and
P
as
,
2
. From Eq. 9 we can write
S
12
=
S
b
,
as
−
S
b
,
bs
+
1
4
(
S
cl
+
S
qrpn
)
,
(10)
where
S
b
,
as
and
S
b
,
bs
are spectra of power fluctuations
due to vacuum fields
ˆ
b
as
and
ˆ
b
bs
,
S
cl
is the spectrum of
classical interferometer noises and
S
qrpn
is the spectrum
of QRPN. Since
S
b
,
as
=
S
b
,
bs
=
B
as
B
∗
as
hν/
2, the cross
spectral density
S
12
removes the shot noise from the GW
spectrum (4
S
12
=
S
cl
+
S
qrpn
). Note that dark noises
of the photodetectors are incoherent and cancel out from
S
12
.
Fig. 3 shows the calibrated cross–correlation amplitude
spectrum, computed using the data from the Livingston
interferometer. The spectrum of the interferometer clas-
sical noises is determined by the equation
S
cl
= 4
S
12
−
S
qrpn
≈
4
S
12
,
(11)
since
S
qrpn
S
cl
in the current configuration (see
Sec. IV). Above 40 Hz this spectrum reveals the level
of the classical noises in the gravitational wave channel.
This result is applied to set the upper limit for the coat-
ing thermal noise [43] (cf. Sec. III B) and verify the level
of the gas phase noise [16] (cf. III C). The estimated
spectrum of classical noises also provides the potential to
predict the sensitivity of the Advanced LIGO detectors
during future science runs (cf. Sec. III D), in which shot
noise will be reduced by increasing the laser power, and
squeezed states of light will be introduced [1, 2].
B. Coating thermal noise
Dielectric coatings used in the LIGO detectors con-
sist of alternative layers of materials with low (SiO
2
) and
high (Ta
2
O
5
) index of refraction. Thermal noise in these
coatings arises from mechanical dissipation in the coat-
ing materials, guided by the fluctuation–dissipation theo-
rem [44]. This noise is theoretically predicted to be one of
the limiting noise sources for the Advanced LIGO design
sensitivity in the frequency range 50 Hz–500 Hz [14, 15],
as well as for the proposed next generation of the grav-
itational wave detectors [45, 46]. For this reason, direct
measurement of the coating thermal noise in Advanced
LIGO is of significant importance.
Theoretical models depend on parameters such as the
mechanical loss angles, Poisson ratio, and Youngs modu-
lus [47]. However, due to uncertainties in the multilayer
parameters, theoretical predictions have limited accuracy
(up to a few tens of percent). The first table top exper-
iment that directly measured the coating thermal noise
of the Advanced LIGO coating sample predicted that the
noise level is a factor of 1.22 above the theoretical pre-
diction [48].
Since the coating thermal noise is coherent between the
two photodetectors at the antisymmetric port, we can re-
veal its spectrum
S
CTN
(
f
) using the quantum correlation
technique and O1 data. The estimated upper limit for
this noise is
√
S
CTN
(
f
)
≤
1
.
6
×
10
−
19
1
√
f
m
√
Hz
.
(12)
This upper limit can be improved if known classical noises
are subtracted from the cross spectrum
√
S
cl
. Above
100 Hz the largest contribution comes from the gas phase
noise, discussed in Sec. III C. Once this noise is incoher-
ently subtracted, the upper limit for the coating thermal
noise is
√
S
CTN
(
f
)
≤
1
.
2
×
10
−
19
1
√
f
m
√
Hz
.
(13)
This upper limit is a factor of
'
1
.
2 larger than the
theoretically predicted Advanced LIGO coating thermal
noise [15].
C. Gas phase noise
The Advanced LIGO core optics are kept under high
vacuum with an average pressure of
p
'
1
μ
Pa. The pres-
ence of residual gas in the 4 km beam tubes causes extra
noise in the differential arm channel. Broadband phase
noise is induced by the stochastic transit of molecules
through the laser beam in the arm cavities [16]. This
noise may limit the ultimate sensitivity that Advanced
LIGO can achieve using the same vacuum infrastructure
between 30 Hz and 10 kHz. For this reason, it is impor-
tant to measure and verify the models of the gas phase
noise.