Observation of squeezed noise, 5 +/- 0.3 dB below the shot noise level, generated with pulses in a fiber ring interferometer is reported. The interferometric geometry is used to separate the pump pulse from the squeezed vacuum radiation. A portion of the pump is reused as the local oscillator in a homodyne detection. The pump fluctuations are successfully subtracted and shot noise limited performance is achieved at low frequencies (35-85 KHz). A possible utilization of the generated squeezed vacuum in improving a fiber gyro's signal to noise ratio is discussed

Bergman, K.

Haus, H. A.

English

NASA Technical Reports Server

N92-22061
SQUEEZED PULSED LIGHT FROM A FIBER RING INTERFEROMETER
K. Bergman and H. A. Haus
Department of Electrical Engineering and Computer Science
and Research Laboratory of Electronics,
Massachusetts Institute of Technology, Cambridge, MA 02139
ABSTRACT
Observation of squeezed noise, 5+0.3 dB below the shot noise level, generated
with pulses in a fiber ring interferometer is reported. The interferometric geometry is used
to separate the pump pulse from the squeezed vacuum radiation. A portion of the pump is
reused as the local oscillator in a homodyne detection. The pump fluctuations are
successfully subtracted and shot noise limited performance is achieved at low frequencies
(35-85 KHz). A possible utilization of the generated squeezed vacuum in improving a fiber
gyro's signal to noise ratio is discussed.
INTRODUCTION
Squeezing in a fiber was first demonstrated by Shelby et al. [1] who showed that
the fiber's E(3) nonlinearity could be used to shape the field's fluctuations through self
phase modulation. The group's experimental results were, however, severely limited by
acoustic and thermal noise processes. First, the low Stimulated Brillouin Scattering (SBS)
threshold in fibers forced the IBM group to separate their CW pump into 25 frequency
components. The second noise source, more difficult to avoid, was the so called GAWBS
(Guided Acoustic Wave BriUouin Scattering) excitations [2]. GAWBS is caused by
thermal fluctuations that modulate the fiber's refractive index at high frequencies
(approximately between 20 MHz and 10 GHz) and thereby scatter acoustic waves which
are guided in the forward direction. Because the experiment was performed in a traveling
wave geometry, it was necessary to detect the squeezing at high frequencies (50-100 MHz)
where the laser noise is negligible. The measurement center frequency was within the
frequency range of GAWBS, and only about 12% of noise reduction was thus observed.
To improve upon these earlier results, we used short pulses in a fiber interferometer
configuration. Large nonlinear phase shifts of the order of several u are easily achieved
with short pulses of high peak power, while the SBS threshold is avoided. The fiber ring
geometry is used to separate the pump from the squeezed vacuum fluctuations. Subsequent
detection with a balanced detector permitted complete cancellation of the pump fluctuations
at frequencies as low as 35-85 KHz. Although the GAWBS noise can be frequency
down-converted into the detection "window" when pulses are used [3], it did not seem to
prevent the noise reduction in our experiment. The investigation of the down-conversion
of GAWBS requires further study.
147
https://ntrs.nasa.gov/search.jsp?R=19920012818 2020-03-17T11:58:37+00:00Z
Theexperimentalresultsreportedin this paperhavebeenrecentlypublished[4].
This paperbeginswith a brief review of the broadbandsqueezingprocessin a fiber.
Following the approachof Shirasakiand Haus [5], we then show how the pump is
separatedfrom the squeezedvacuumwhenthe squeezingis performedwithin a Mach-
Zehnderinterferometer.Thesqueezedvacuumis observedwith theaidof a localoscillator
derivedfrom thepump. We describesomeof thetheoreticallimitationson theobserved
squeezingusing homodynedetection and a gaussianshapedlocal oscillator. The
experimentandresultsarethendescribedin detail.
SQUEEZINGIN THE NONLINEAR MACH-ZEHNDER
We considerthe simplepropagationequationfor the field operator, gt(z), in a
nonlinear Kerr medium. Assuming no dispersion this equation becomes:
dh(z) = irlfi+ (z)h(z)lh(z ) (1)
dz
where _: is the Kerr nonlinearity. The Kerr nonlinearity is calculated as follows,
2n: Pp (2)
tc = T n2 Aeff
where Z is the wavelength, n2 the nonlinear index, Pfl the peak power, and Aeff the
effective coupling area. Equation (1) may be integrated dxrectly, yielding a solution for the
field operator, fi(z), after a propagation distance, L:
fi(L) = e irdA+ (°)fi(°)h(O) (3)
The effect of the Kerr medium is to add a nonlinear phase shift proportional to the photon
number, propagation distance, and Kerr coefficient. The mean square fluctuations of the
field are shaped by this nonlinear process as shown in figure 1. The Z(3) process couples
the amplitude and the phase fluctuations, causing the phase insensitive mean square
fluctuations of the incoming field, represented by a circle, to stretch into an ellipse along the
amplitude tangents. The area of the resulting squeezed noise ellipse is equal to the area of
the initial circle.
Next, we place two equal lengths of Kerr media symmetrically in the two arms of a
Mach-Zehnder interferometer, as was analyzed in reference [5]. The input field and its
associated fluctuations enter one input port of the interferometer's First beam splitter in
figure 2. Into the second, unexcited port enter the zero point fluctuations of the vacuum
field. The field's amplitude split coherently in two by the 50/50 beam splitter. The
fluctuations add and subtract incoherently.
As each field-half propagates through its Mach-Zehnder arm, it accumulates a
nonlinear phase shift (not shown on the phasors in figure 2) and its fluctuation circles are
stretched into ellipses. At the second beam splitter, the two half-field amplitudes interfere
coherently. Under a linearized first order analysis, the squeezed fluctuations will again add
and subtract incoherently. As illustrated with the phasors in figure 2, the original mean
148
field amplitude emerges from the constructive interference port, and the squeezed vacuum
exits from the destructive interference port. The interferometer has made possible this
isolation of the squeezed vacuum.
The above explanation for a single frequency phasor (CW pump) also holds for the
case of a pulsed pump, as long as dispersion may be neglected. Without dispersion the
pulse may be divided into short time segments and each segment analyzed independently.
At the output the segments are superimposed to reconstruct the pulse.
DETECTION
The function of homodyne detection is to measure one quadrature of the incoming
signal, amplified by the local oscillator. This detection technique is used to observe the
phase sensitive fluctuations of the squeezed vacuum signal. If the local oscillator phase is
properly adjusted, the squeezed (reduced noise) quadrature is measured. The fluctuations
accompanying the pump are completely subtracted by the balanced detection. When the
signal arm is blocked, the homodyne detection measures the vacuum state noise. This is a
part of the experimental shot noise calibration.
In the Mach-Zehnder squeezing geometry, the exiting pump, shown in figure 2,
may be reused as the local oscillator. In this way, the local oscillator pulse shape matches
the squeezed vacuum pulse. However, to detect the full pulsed squeezing magnitude a
finer matching of the local oscillator phase is required since the squeezing direction as well
as magnitude will vary along the pulse duration. Thus, undei" ideal conditions the local
oscillator should be phase shifted in one direction at the pulse center but in a different
direction at the pulse wings. Experimentally the local oscillator is shifted by one constant
phase leading to a nonideal measured noise reduction magnitude. We have plotted the
expected noise reduction for the ideal and single phase adjusted gaussian pulse cases in
figure 3 (a). In figure 3(b) we show that for the gaussian pulse case, the amplified noise
amplitude is larger than the attenuated noise amplitude for the same peak nonlinear phase
level.
EXPERIMENT
The experiment was implemented by replacing the Mach-Zehnder with a fiber ring
interferometer, to take advantage of the ring's stability to vibrational and thermal
disturbances. Figure 4 is a schematic of the experimental arrangement. A mode-locked
1.31.tm Nd:YAG producing 100 psec pulses at a repetition rate of 100 MHz was used as the
pump. This pulse train pump is coupled into the fiber ring reflector composed of 50 m of
PM (polarization maintaining) fiber which is spliced to the two pigtails of a 3 dB PM fiber
coupler. The coupler's splitting ratio was variable, and was carefully adjusted to 50/50
within 1 part in 500. The pump pulses are thus completely reflected from the ring. A
90/10 beam splitter picks off a portion of the reflected pump to be reused as the local
oscillator. The squeezed vacuum signal emerges from the unexcited transmission port of
the ring.
The local oscillator and the squeezed signal are then mixed in a 50/50 beam splitter
(BS2), and detected with a balanced dual detector receiver. The output difference current is
directly fed into a spectrum analyzer. The Power Spectral Density (PSD) reading
149
correspondsto a measureof the fluctuations magnitudealong one quadratureof the
squeezedvacuum.Theamplifiedandreducednoisequadraturesmaynow bemeasuredby
adjustingtherelativephaseof thelocaloscillatorandsqueezedsignal.
The reducednoisewill increasewith thepulsepeaknonlinearphaseshift, which
canbeestimatedfrom thefollowingCW equation,
(4)
wheren2 is the nonlinear index, L the fiber length, Pp the pulse peak power, and Aeff the
effective coupling area. In this experiment, a peak nonlinear phase shift of 1.4 radians
corresponds to approximately 100 mW of average power in each ring direction. The PSD
measurements were performed at a narrow low frequency window between 39 and 41
KHz. Data was taken with an integration time of 400 msec and a frequency resolution of
2.5 Hz. Before discussing the results, we describe the methods used to calibrate the shot
noise level.
IV SHOT NOISE CALIBRATION
The shot noise level was calibrated in order to confirm that the reduced quadrature
fluctuations of the squeezed vacuum dropped below the zero point fluctuations level. Two
methods were used. First, direct excitation from the laser was sent through the homodyne
detection system and the detector current along with a corresponding PSD level were
recorded for a range of input power levels. To cross check this calibration, two white light
sources were used to generate detector current levels similar to those obtained with the laser
excitation. Again, the PSD levels were recorded along with the current readings for the
same range of power levels. The spectrum analyzer's noise floor was measured at -155
dBm/Hz and typical shot noise levels ranged from -120 to -125 dBm/Hz, so that electrical
noise was not a factor. The two curves plotted on a dB scale in figure 5 overlapped well
with a 45 degree slope. Thus, the laser noise has been successfully subtracted and the
detection's response has been shown linear within the measurement current range.
V EXPERIMENTAL RESULTS
Having accurately established a shot noise level, we proceed with the squeezing
measurement. The local oscillator pulse and the squeezed vacuum pulse are aligned to
overlap spatially and temporally at the detection beam splitter (BS2). For alignment
purposes only, the signal magnitude may be temporarily increased by changing the
coupler's splitting ratio. The coupler is adjusted back to 50/50 and the relative phase
between the local oscillator and squeezed signal is allowed to drift. While the phase is
drifting, PSD measurements are taken continuously with an automated data acquisition
system.
150
The PSD level, a measurementof the squeezednoise will vary from some
maximumvalueto someminimum value corresponding to the amplified and attenuated
quadratures of the squeezed vacuum. The resulting histograms from these measurements
taken at three separate pump power levels: 60, 85, and 110 mW (in each fiber ring
direction) are shown in figure 6 (a), (b), and (c) respectively. In the figure, the black bars
are PSD readings taken with the squeezed vacuum arm blocked, and are thus the shot noise
calibration for the specific power level. The white bars are a collection of PSD readings
taken after the mixing of the local oscillator and squeezed vacuum. The reduced noise level
or squeezing magnitude is defined as the distance between the black bars distribution center
and the left edge of the white bars distribution. We note that as previously predicted for the
case of a gaussian local oscillator, the amplified quadrature noise is larger than the reduced
quadrature for the same power level.
In figure 7 we plot the experimental maximum and minimum PSD readings (in dot
scatter format) obtained for a collection of power levels, on top of the theoretically
predicted limits for the gaussian local oscillator case. The experimental point plot was
adjusted horizontally, along the peak nonlinear phase axis for a best fit. This fitting
compensates for coupling losses, detector quantum efficiencies, and nonlinear phase
estimation.
VI SQUEEZED VACUUM IN A FIBER GYRO
It has been shown both theoretically [6,7,8], and experimentally [9,10], that the
sensitivity of a phase measurement device can be improved with the injection of squeezed
vacuum into the unexcited port. Normally, zero point fluctuations enter this unexcited port.
We briefly consider the circumstances of utilizing the squeezed vacuum generated by the
interferometric fiber ring to improve the performance of a second fiber ring functioning as a
fiber gyro. In principle, all of the pump power reflected from the ring may be reused in the
gyro.
If the same power levels and fiber lengths that are used in the squeezer ring are also
used in the gyro, nonlinear effects in the gyro must be considered. We have explored this
issue in detail in a separate paper [ 11 ]. Here we shall merely point out that the nonlinearity
in the fiber gyro will cause additional squeezing but in an opposite direction. The
squeezing that occurs in the gyro will undo some of the squeezing initially injected.
The analysis is shown diagrammatically in figure 8, using a Mach-Zehnder
configuration. If the gyro is linear (figure 8(a)), it is clear that the squeezed vacuum should
be oriented along the horizontal direction. In this way, at the gyro's output signal port, the
reduced quadrature is along the signal direction.
For a nonlinear gyro, the effect of the X(3) nonlinearity will be to pull the elliptical
locus of fluctuations toward a circular shape, thereby destroying the squeezing. As shown
in the inset of figure 8(b), one must prepare the squeezed vacuum to counterbalance some
of the effect of the gyro nonlinearity. The gyro's signal to noise ratio improvement will
then be diminished, but not destroyed completely. In fact, much of the noise reduction
advantages may be regained by properly designing the relative nonlinearity of the gyro and
squeezer rings. For example, if we set the squeezer's nonlinear phase at n the ideal noise
reduction will be approximately -15 dB. If the gyro's nonlinearity is then half of the
squeezer's, the noise improvement will reduce to -6 dB.
151
VII CONCLUSIONS
We describedthe successfulobservationof squeezedpulsedvacuum,5+0.3 dB
below the shotnoise level, generatedfrom a fiber ring interferometer. Noisegenerated
from GAWBSexcitationsdid not appearto damagethesqueezingmeasurementsat low
frequencies.FurtherstudyshoulddeterminetheexactGAWBSspectraandmagnitudefor
ourexperimentalconfiguration.If thesqueezedvacuum,properlyoriented,is injectedinto
a losslesslinearinterferometer,theinterferometer'signalto noiseratiowill improveby the
noise reduction factor. We consideredthe utilization of squeezedvacuum in the
improvementof the sensitivityof a shotnoiselimited fiber gyro. In this casethegyro's
nonlinearitymustbereducedin proportionto thesqueezer'snonlinearity.
VIII ACKNOWLEDGEMENTS
TheauthorsthankLincoln Laboratoriesfor providingthebalancedreceivercrucial
to thisexperiment.Oneof theauthors[KB] gratefullyacknowledgesupportfrom Kevin
ChampagneandRobertDahlgrenof DraperLaboratories,andthegeneroushelpof Steve
Alexanderof Lincoln Laboratoriesrenderedthroughthecourseof this experiment.The
supportof DrapergrantDL-H-404179,of NSFEET 8700474,andJSEPcontractnumber
DAAL03-89-C-001aregratefullyacknowledged.
152
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REFERENCES
R. M. Shelby, M. D. Levenson, S. H. Pedmutter, R. G. De Voe, and D. F. Walls,
Phys. Rev. Lett., 57, 691, (1986).
R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. B, 31, 5244,
(1985).
R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A, 42, 2966,
(1990).
K. Bergman and H. A. Haus, Opt. Lett., 16, 663, (1991).
M. Shirasaki and H. A. Haus, J. Opt. Soc. Am. B, 7, 30, (1990).
C. M. Caves, Phys. Rev. D, 23, 1693, (1981).
R. S. Boudurant and H. J. Shapiro, Phys. Rev. D, 30, 2548, (1984).
M. Shirasaki and H. A. Haus, J. Opt. Soc. Am. B, 8, 681, (1991).
M. Xiao, L. Wu, and H. J. Kimble, Phys. Rev. Lett., 55, 2520, (1986).
P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, Phys. Rev. Lett., 59,
2153, (1987).
H. A. Haus, K. Bergman, and Y. Lai, "Fiber Gyro with Squeezed Radiation,"
accepted for publication in J. Opt. Soc. Am. B, (1991).
153
drawn with the nonlinear
phase shi btracted
Figure I The field's phase insensitive quantum fluctuations are elongated into an ellipse of
squeezed noise by the self phase modulation process.
154
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attenuated quadrature noise
I I I I I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Pulse Peak Nonlinear Phase Shift (tad)
(b)
Figure 3 (a) Expected noise reduction for the ideal and single phase adjusted gaussian pulse
cases. (b) Predicted maximum and minimum noise amplitudes for the gaussian
local oscillator case, plotted on a dB scale.
156
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Figure 5 Shot noise calibration using both white light and direct laser excitation.
158
100
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(c)
I
-105
Figure Histograms of PSD readings taken at three separate power levels (a) 60, (b) 85, and
(c) 110 mW in each ring direction. The black bars are counts taken with the
squeezed signal arm blocked. The white bars are the squeezing PSD
measurements.
159
N
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i
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0.2 0.4 o.s o.e 1.o 1.2 1.4
nonlinearphase (rad)
Figure Maximum and minimum values of the PSD readings obtained experimentally (black
dots) overlaid on the theoretically predicted curves for the case of a gaussian local
oscillator.
160
(a)
I kerr _1_
gyro )
I squeezed
vacuum
I _ _ lOCUSof motion of
_ ellipse due tononlinearity in gyro
Co)
Figure 8 (a) The linear gyro with squeezed vacuum injected. (b) The nonlinear gyro with
phase compensated squeezed vacuum.
161


Squeezed pulsed light from a fiber ring interferometer

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