We demonstrate the generation of broad-band continuous-wave optical squeezing
down to 200Hz using a below threshold optical parametric oscillator (OPO). The
squeezed state phase was controlled using a noise locking technique. We show
that low frequency noise sources, such as seed noise, pump noise and detuning
fluctuations, present in optical parametric amplifiers have negligible effect
on squeezing produced by a below threshold OPO. This low frequency squeezing is
ideal for improving the sensitivity of audio frequency measuring devices such
as gravitational wave detectors.Comment: 5 pages, 6 figure

A. Rüdiger

B. Abbott

B. Caron

B. C. Buchler

David E. McClelland

Kirk McKenzie

Malcolm B. Gray

Nicolai Grosse

Ping Koy Lam

Stanley E. Whitcomb

T. Corbitt

Warwick P. Bowen

English

arXiv

Crossref

Squeezing in the Audio Gravitational-Wave Detection Band

We demonstrate the generation of broadband continuous-wave optical squeezing from 280 Hz-100 kHz using a below-threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise, and detuning fluctuations, present in optical parametric amplifiers, have negligible effect on squeezing produced by a below-threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational-wave detectors

McKenzie, K.

Grosse, N. B.

Bowen, W. P.

Whitcomb, S. E.

Gray, M. B.

McClelland, D. E.

Lam, P. K.

University of Queensland eSpace

VOLUME 93, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S
week ending
15 OCTOBER 2004Squeezing in the Audio Gravitational-Wave Detection Band
Kirk McKenzie,1 Nicolai Grosse,1,2 Warwick P. Bowen,2 Stanley E. Whitcomb,3 Malcolm B. Gray,1
David E. McClelland,1 and Ping Koy Lam1,2
1Center for Gravitational Physics, Department of Physics, Faculty of Science, The Australian National University,
ACT 0200, Australia
2Quantum Optics Group, Department of Physics, Faculty of Science, The Australian National University, ACT 0200, Australia
3LIGO Laboratory, California Institute of Technology, Pasadena, California, 91125, USA
(Received 21 May 2004; published 15 October 2004)161105-1We demonstrate the generation of broadband continuous-wave optical squeezing from 280 Hz–
100 kHz using a below-threshold optical parametric oscillator (OPO). The squeezed state phase was
controlled using a noise locking technique. We show that low frequency noise sources, such as seed
noise, pump noise, and detuning fluctuations, present in optical parametric amplifiers, have negligible
effect on squeezing produced by a below-threshold OPO. This low frequency squeezing is ideal for
improving the sensitivity of audio frequency measuring devices such as gravitational-wave detectors.
DOI: 10.1103/PhysRevLett.93.161105 PACS numbers: 04.80.Nn, 42.50.Lc, 42.65.Yj, 95.55.YmSqueezed light was proposed for quantum noise reduc-
tion in interferometric gravitational-wave (GW) detec-
tion over two decades ago [1]. Since then, the first
generation of long baseline GW detectors—LIGO [2],
VIRGO [3], GEO 600 [4], and TAMA 300 [5]—have
been built and recently begun operation. The second
generation of detectors, such as Advanced LIGO [6], are
currently in the late planning stages. The prediction that
they will be quantum noise limited (QNL) across most of
the GW signal band (10–104 Hz) has led to further theo-
retical investigations into the use of squeezing [7–9] and
other optical methods [10–12] for quantum noise reduc-
tion. However, to date only one experimental demonstra-
tion of quantum noise reduction in a GW detector
configuration has been reported [13], and that result
was obtained well above the GW signal band.
To be applicable to GW detectors, the requirements on
squeezing include continuous-wave (CW) at 1064 nm,
squeezed at the GW signal frequency, compatible with
readout techniques [14], controllable phase, and a high
level of squeezing. Although squeezed light was first
demonstrated in 1985 [15], a CWsqueezed source at audio
frequencies has not been reported until now. Laser re-
laxation oscillation and other technical noise sources
have typically confined squeezing to the MHz range.
Two of the most successful systems for squeezed state
generation have been the optical parametric oscillator
(OPO) and optical parametric amplifier (OPA), for ex-
ample, see [16,17]. OPA and OPO have the same under-
lying second order nonlinearity, however, they differ in
that the OPA process has a coherent seed field at the
fundamental wavelength, whereas the OPO does not
and is seeded only by vacuum fluctuations. In theory
OPO/OPA systems can produce squeezed states that fulfill
the GW detector requirements outlined above. Experi-
ments to date have been able to demonstrate each require-
ment, except squeezing in the GWsignal band. The lowest
frequency CW squeezing experiments reported so far0031-9007=04=93(16)=161105(4)$22.50 include Bowen et al. [18], Schnabel et al. [19], and
Laurat et al. [20] demonstrating squeezing down to 220,
80, and 50 kHz, respectively. These experiments used
either OPO or OPA, with [18,19] relying on common
mode noise cancellation techniques.
In this Letter we report the generation of high purity
broadband squeezing by a below-threshold OPO at side-
band frequencies from 280 Hz to well above 100 kHz,
covering a large portion of the audio GW detection band.
The phase of the squeezed vacuum relative to the homo-
dyne detector was controlled without a carrier by using a
noise dither locking technique; see for example [20]. The
inferred squeezing level measured at 11.2 kHz (adjusted
for detection efficiency) at the OPO output was 5:5
0:6 dB below the shot noise limit (SNL) with inferred
purity of 1:3 0:1, close to a minimum uncertainty state.
We compare OPO and OPA operation and find that the
presence of a coherent seed field leads to dramatic degra-
dation of the squeezing at low frequency, due to technical
noise coupling. The system operating as an OPO displays
immunity to the same technical noise that degrades OPA
squeezing.
Amplitude () and phase () quadrature variances,
Vsqz  hXsqz2i, at the output of the singly resonant
OPO/OPA on resonance can be modeled using linearized
formalism by
Vsqz! fCsVs !ClVl !Cv !Vv !
	2
CpVp !CV!g=jD!j2; (1)
where Vsqz contains contributions from the seed field, Vs ,
the pump field, Vp , vacuum fluctuations from intracavity
loss, Vl , vacuum fluctuation entering through the output
coupler, Vv , and noise due to detuning fluctuations in the
cavity [21], V, which arise from acoustomechanical
disturbances. Other sources, such as phase matching fluc-
tuations, are not discussed here. The denominator and
coupling coefficients are given by [22,23]2004 The American Physical Society 161105-1
VOLUME 93, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S
week ending
15 OCTOBER 2004D!  i!a

3
1

2	2=2b ;
Cs  4ainaout; Cl  4al aout;
Cv !  j2aoutD!j2; Cp  4aoutbin=b2;
C  8aout

0
1

;
where the intracavity fundamental field, 	  np , with n
the mean intracavity photon number. The parameters aout,
ain, and al are the decay rates of 	 due to the output
coupler, input coupler, and loss, respectively. bin is the
decay rate of the intracavity second harmonic field, ,
due to the input coupler. a and b are the total decay
rates for 	 and .  is the nonlinear coupling parameter
and ! is a small frequency shift relative to the carrier
frequency. The first three terms in Eq. (1) are standard
contributions from the seed noise entering through the
input coupler, vacuum fluctuations due to intracavity loss,
and vacuum fluctuations entering through the output cou-
pler. The last two terms scale with 	2 and show an
important difference between OPO and OPA operation.
That is, the fluctuations of the pump, Vp , and detuning,
V, are coupled into the squeezed field, Vsqz via the beat
with the intracavity fundamental field, 	. Thus, a below-
threshold OPO (	  0) should be immune to these two
noise sources to first order.
A schematic of the experiment setup is in Fig. 1. A
Nd:YAG laser operating at 1064 nm was split into twoOPO/A
PZT2
PZT1
SHG
Signal
Analyser
ED
λ/2
PBS
VA
20kHz
Nd:YAG
FI
DC
LPF BPF
G
SA
LPF
Lock-in
PD1
PD2
ELECTRONICS
OPTICS
FIG. 1 (color online). Schematic of the experiment. The ex-
periment was operated in both OPO and OPA modes. The OPA
seed power was varied using a variable attenuator (VA). The
OPO cavity was isolated from backscatter off the photodetec-
tors using a Faraday isolator (FI). The control electronics for
the homodyne detection phase are indicated by dashed lines.
SA, spectrum analyzer; BPF, band pass filter; ED, envelope
detector; LPF, low pass filter; G gain stage; SHG, second
harmonic generator; OPO/A-optical parametric oscillator/
amplifier; PZT, piezoelectric transducer; PBS, polarizing
beamsplitter; =2-half-wave plate; DC, dichroic mirror;
PD, photodetector.
161105-2beams. One beam is used to pump the second harmonic
generator (SHG). The other was spatially and temporally
filtered by a mode-cleaner cavity [24] and used as the
seed beam for the OPA and as local oscillator (LO) for
the homodyne detector. The OPO/OPA and SHG are
constructed out of type-I phase-matched MgO : LiNbO3
hemilithic crystals. The curved surface of these crystals
were coated for high reflectivity (HR) and the flat surface
coated for antireflectivity (AR) at both 532 and 1064 nm.
In both the SHG and OPO/OPA, standing-wave cavities
were formed at 1064 nm between the HR surface of the
crystal together with an external mirror of reflectivity
RIR  96% at 1064 nm and RGR < 4% at 532 nm. The
OPO/OPA was pumped with 100 mW of 532 nm light
which double passed through the crystal giving a mea-
sured classical gain of 5. Results were taken in the OPO
mode, and in the OPA mode while varying the seed power
from 1 nW–6 W. The squeezed state was detected on
the homodyne detection system which had 96:5% fringe
visibility. While in the OPO operation, a Faraday isolator
was inserted between the OPO cavity and the photode-
tectors to reduce LO backscattered light. The photodetec-
tors were built around ETX 500 photodiodes with 93%
quantum efficiency. The common mode rejection of the
homodyne detector was over 55 dB.
The control electronics for the homodyne detection
phase are indicated by dashed lines in Fig. 1. This error
signal was generated by dithering the LO phase and
demodulating the difference photocurrent noise power.
The noise power was detected using a spectrum ana-
lyzer (Agilent-E4407B, zero span at 2 MHz, resolution
bandwidth RBW300 kHz, video bandwidth VBW
30kHz) then demodulated with a lock-in amplifier
[Stanford Research Systems (SRS)-SR830] and filtered
before being fed back to PZT1. The stability of the homo-
dyne detection phase enabled us to take results without
locking the OPO/OPA cavity, which typically stayed on
resonance for 10 sec. All data, except that in Fig. 3, were
recorded on a dynamic signal analyzer (SRS-SR785).
The OPO squeezing spectrum from 100 Hz–100 kHz is
shown in Fig. 2 [25]. Trace (a) shows the quantum noise
limit of the homodyne detection system. The measure-
ment of the squeezed light is shown in trace (b). Trace (c)
shows the electronics noise of the detection system. The
roll-up in noise power in traces (a) and (b) is attributable
to the imperfect homodyne cancellation at low frequen-
cies. We see that broadband squeezing is obtained from
280 Hz to 100 kHz, with the exception of a locking signal
peak at 20 kHz. Squeezing could not be measured at 150
and 250 Hz due to power supply harmonics in the elec-
tronic noise.
Figure 3 shows the OPO squeezed state at 11.2 kHz as
the homodyne phase was varied. The measured squeezed
state purity is VV  1:6 0:2. The squeezing and
purity at the output of the OPO can be inferred by taking
into account the photodetection and homodyne efficien-161105-2
10
2
10
3
10
4
10
5-10
-8
-6
-4
-2
0
2
4
6
8
10
Po
w
er
 R
el
at
iv
e 
to
 th
e 
SN
L 
[dB
]
Frequency[Hz]
(a)
(b)
(c)
FIG. 2 (color online). Measured noise spectra for (a) the
quantum noise limit, (b) the squeezed light, and (c) the
electronic noise of the homodyne detection system. The traces
are pieced together from three FFT frequency windows:
100 Hz–3.2 kHz, 1.6 kHz–12.8 kHz, and 3.8 kHz–100 kHz.
Each point is the averaged rms value of 500, 1000, and 2000
measurements made in the respective ranges. The RBW of the
three windows was 8, 32, and 128 Hz, respectively. The
electronic noise was 12 dB below the quantum noise from
10–100 kHz. The 20 kHz peak arises from the homodyne
locking signal. Peaks at 50 Hz harmonics are due to electrical
mains supply.
10
2
10
3-5
0
5
10
15
20
]Bd[
 L
NS
 
eht
 
ot
 
evit
al
e
R
 r
e
w
oP
Frequency[Hz]
(a)
(b)
(c)
FIG. 4 (color online). The OPO spectrum 100 Hz–3.2 kHz
without (a) and with (b) the Faraday isolator between the OPO
cavity and homodyne detector. RBW  8 Hz; number of rms
averages for (a) 400 and for (b) and (c) 500. Electronic noise
(not shown) was not subtracted.
40
VOLUME 93, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S
week ending
15 OCTOBER 2004cies and optics loss. The inferred purity is VV  1:3
0:1 and the inferred squeezing is Vsqz  5:5 0:6 dB.
Figure 4 shows a more detailed analysis of the squeez-
ing spectrum at the lowest frequency window of 100 Hz–
3.2 kHz. Trace (a) shows the squeezing spectrum obtained
without an isolator in front of our homodyne detection
system.We observed large peaks between 300 and 700 Hz
due to low frequency noise contamination. This contami-
nation is attributed to light from the LO backscattered
from the photodetectors feeding into the OPO cavity. We0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-6
-4
-2
0
2
4
6
8
Time [S]
Po
w
er
 R
el
at
iv
e 
to
 th
e 
SN
L 
[dB
]
FIG. 3 (color online). The squeezed state at 11.2 kHz as the
phase of the homodyne is varied. RBW  1 kHz, VBW 
30 Hz. Electronic noise (9 dB below SNL) was subtracted
from the data.
161105-3note that even with the photodetectors tilted away from
retroreflection, the scattering from the front face of the
detectors, which is estimated to be of the order of 1 pW, is
sufficient to seed the crystal and causes parametric am-
plification. With the Faraday isolator in place noise cou-
pling via parametric amplification is eliminated, as
shown by trace (b). The squeezed beam experiences an
extra 9% transmission loss through the isolator. Similar
to Fig. 2, electronic noise is still present at 150 and
250 Hz.
The OPA spectrum from 2–100 kHz is shown in Fig. 5
for three different seed powers, 1 nW, 700 nW, and 6 W.
The data were recorded for optimal squeezing at 50 kHz.
The 1 nW seed power spectrum resembles the OPO spec-104 105
-5
0
5
10
15
20
25
30
35
Frequency [Hz]
]Bd[
 L
NS
 
eht
 
ot
 
evit
al
e
R
 r
e
w
oP
6x10-6W
7x10-7W
1x10-9W
FIG. 5 (color online). The OPA spectrum 2–100 kHz with
different OPA seed powers. The variance of the seed beam with
power 6W was less than 4 dB above the SNL across the
spectrum. RBW  128 Hz. Number of rms averages, 1000,
except for 6 W seed power which had 500 rms averages.
Electronic noise (at 12 dB) was subtracted from all traces.
161105-3
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5-5
0
5
10
15
20
Seed Power [W]
]Bd[
 L
NS
 
eht
 
ot
 
evit
al
e
R
 r
e
w
oP
FIG. 6 (color online). The average noise power from 5–6 kHz
as a function of seed power, experimental data indicated by
‘‘x’’, model fit given by line. Electronic noise (at 12 dB) was
subtracted from all data.
VOLUME 93, NUMBER 16 P H Y S I C A L R E V I E W L E T T E R S
week ending
15 OCTOBER 2004trum, with the exception of one added feature at 34 kHz.
The spectrum of the 700 nWseed power shows the feature
at 34 kHz has increased in amplitude with additional
excess noise at other frequencies thereby limiting squeez-
ing to above 10 kHz. The feature at 8 kHz was also present
in the pump intensity noise spectrum and is expected to
have coupled into the squeezed field via the intracavity
fundamental field. As the seed power was increased fur-
ther, the noise floor and features in the spectrum contin-
ued to increase; by seed power 6 W there is no longer
squeezing below 40 kHz. The noise power increase of the
OPA spectrum with seed power is evident in Fig. 6, which
shows the mean noise power between 5–6 kHz as a
function of seed power. The experimental points indicated
by ‘‘x’’ can be compared with a model which has linear
dependence on seed power, given by the solid line.
Although there are large uncertainties expected in the
experimental data, since the OPA cavity was not locked,
the data are not inconsistent with the linear trend pre-
dicted by the theory in Eq. (1).
In summary, we have presented results demonstrating
broadband OPO squeezed vacuum down to 280 Hz. The
phase of squeezed vacuum was controlled using a noise
locking technique. Such squeezed states could already be
of use for reduction of shot noise in first generation GW
detectors. The comparison of the OPO and OPA results
highlights the immunity of OPO and the sensitivity of
OPA to technical noise. The direction of our future re-
search will be to implement an OPO cavity lock, increase
the level of squeezing and probe frequencies lower than
100 Hz for use in second generation GW detectors.
In addition to the possible application to GW detectors,
low frequency squeezed light could potentially be used to161105-4enhance many measurement devices with optical readout.
These include atomic force microscopes [26] and thermo-
optical spectrometers [27]. Many long-standing experi-
mental goals in quantum optics, such as the inhibition of
atomic decay [28] and sub-Doppler cooling of two-level
atoms [29], could also be facilitated using broadband low
frequency squeezing.
We thank Keisuke Goda, Julien Laurat, and Nicolas
Treps for useful discussions. This research was supported
by the Australian Research Council. S.W. was supported
by the United States National Science Foundation under
Cooperative Agreement No. PHY-0107417. This Letter
has been assigned LIGO Laboratory document
No. LIGO-P040018-00-R.[1] C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[2] B. Abbott et al., Nucl. Instrum. Methods 517, 154 (2004).
[3] B. Caron et al., Classical Quantum Gravity 14, 1461
(1997).
[4] H. Lu¨ck et al., Classical Quantum Gravity 14, 1471
(1997).
[5] M. Ando et al., Phys. Rev. Lett. 86, 3950 (2001).
[6] D. Shoemaker, Classical Quantum Gravity 20, S11
(2003).
[7] H. J. Kimble et al., Phys. Rev. D 65, 022002 (2002).
[8] J. Harms et al., Phys. Rev. D 68, 042001 (2003).
[9] T. Corbitt and N. Mavalvala, Proc. SPIE Int. Soc. Opt.
Eng. 5111, 23 (2003).
[10] J.-M. Courty, A. Heidmann, and M. Pinard Phys. Rev.
Lett. 90, 083601 (2003).
[11] A. Buonanno and Y. Chen Phys. Rev. D 64, 042006
(2001).
[12] V. B. Braginsky et al., Phys. Rev. D 61, 044002 (2000).
[13] K. McKenzie et al., Phys. Rev. Lett. 88, 231102 (2002).
[14] A. Buonanno, Y. Chen, and N. Mavalvala, Phys. Rev. D
67, 122005 (2003).
[15] R. E. Slusher et al., Phys. Rev. Lett. 55, 2409 (1985).
[16] P. K. Lam et al., J. Opt. B 1, 469 (1999).
[17] M. Xiao et al., Phys. Rev. Lett. 59, 278 (1987).
[18] W. P. Bowen et al., J. Opt. B, 4, 421 (2002).
[19] R. Schnabel et al., Opt. Commun. 240, 185 (2004).
[20] J. Laurat et al., quant-ph/0403224.
[21] B. C. Buchler et al., Opt. Lett. 24, 259 (1999).
[22] W. P. Bowen, Ph.D. thesis, Australian National
University, Canberra, 2004.
[23] The notation 
31 means multiply by 3 for the amplitude
quadrature or 1 for the phase quadrature.
[24] A. Ru¨diger et al., Opt. Acta 28, 641 (1981).
[25] The squeezing spectrum continues to tens of MHz, as
reported in [22].
[26] N. Treps et al., Science 301, 940 (2003).
[27] A. C. Boccara, D. Fournier, and J. Badoz, Appl. Phys.
Lett. 36, 130 (1980).
[28] C.W. Gardiner, Phys. Rev. Lett. 56, 1917 (1986).
[29] Y. Shevy, Phys. Rev. Lett. 64, 2905 (1990).161105-4


Squeezing in the audio gravitational-wave detection band

http://espace.library.uq.edu.au/view/UQ:152206/UQ152206.pdf

Squeezing in the audio gravitational wave detection band

Squeezing in the audio gravitational wave detection band

Abstract

Similar works

Full text

Available Versions

Crossref

University of Queensland eSpace

Crossref