Pulsed squeezed-light measurement: a new technique
Orhan Aytur and Prem Kumar
Department of Electrical Engineering and Computer Science, The Robert R. McCormick School of Engineering and Applied Science,The Technological Institute, Northwestern University, Evanston, Illinois 60208
Received November 20, 1989; accepted January 26, 1990
A transient noise measurement scheme is described to observe pulsed squeezing generated by means of parametricdownconversion of a Q-switched laser. In the usual implementation of balanced-homodyne detection, the vacuum-state noise level is determined by the average local oscillator power. However, if the local oscillator is derived from apulsed laser, as is the case in our experiments, the associated peak power can easily saturate the detectors along withthe subsequent electronics. To overcome this limitation we have implemented a hybrid frequency-time-domainmeasurement scheme in which the vacuum-state noise level is determined by the peak, instead of the average, localoscillator power, thus avoiding the saturation problem.
In this Letter we report a new technique to measurevacuum-state and squeezed-state noise in pulsed sys-tems. So far, systems that have generated pulsedsqueezed light'"2 have employed the same postdetec-tion processing to measure the vacuum-state orsqueezed-state noise as their cw counterparts. 3 How-ever, the postdetection processing appropriate for cwsystems is not optimal for pulsed systems since it setsconflicting requirements on the local oscillator (LO)power used in homodyne detectioll.2 The hybrid fre-quency-time-domain technique described here relax-es these requirements. We demonstrate this tech-nique by measuring squeezed light generated bymeans of traveling-wave optical parametric downcon-version of a Q-switched laser.
Dual-detector balanced-homodyne detection4 hasbecome a standard method for measuring vacuum-state (shot) and squeezed-state noise. In convention-al homodyne detection the average LO power has to behigh enough for the associated shot noise to dominatethe front-end thermal noise of the detection electron-ics. In cw experiments it is easy to obtain a shot-noiselevel that is 10 dB or more higher than the background(thermal-plus-amplifier) noise. In pulsed experi-ments, however, maintenance of the same shot-noiselevel results in high peak LO powers that are likely tofall outside the dynamic range of the detectors and/orthe subsequent electronics. As a result, it is easy tosaturate the detectors and/or the associated electron-ics, especially if the duty cycle of the LO pulses issmall.
Postdetection electronics is usually composed oflow-noise wideband amplifiers terminated into a rfspectrum analyzer. On a block-diagram level, thespectrum analyzer is made of a rf filter with band-width BR around some center frequency Qc, followedby a rf power detector and a video filter of bandwidthBV, as shown in Fig. 1. Since the input noise in cwexperiments is stationary, there are no constraints onBR. BV is usually of the order 10 Hz to follow thephase-sensitive squeezed-state noise. Therefore, forefficient averaging, BR is chosen to be a few orders of
magnitude larger than Bv. In pulsed experiments,however, the input noise is nonstationary, and BR can-not be chosen to be greater than the inverse pulseperiod, since this would lead to a situation in which thestationary background noise overcomes the shot noiseover the integration period. A rf filter satisfying thisconstraint averages over the shot-noise pulses, whichresults in a stationary process at its output. More-over, the average shot-noise power at the output can-not be increased indefinitely by increasing the averageLO power, because of the limit imposed by the dynam-ic range of the detectors and the duty cycle of thepulses. Thus the maximum shot-noise power usuallyis not high enough to dominate the background noisefor an accurate measurement.
The key idea behind our new technique is to make anoise measurement only during the presence of theshot-noise pulse, thereby minimizing the contributionof the stationary background noise. In order to pre-serve the pulsed nature of the noise process, we use a rffilter whose bandwidth BR is larger than the inversepulse duration. If the bandwidths of the detectorsand the subsequent amplifiers are large, the inputprocess to the filter can be assumed to be delta corre-lated with zero mean. Therefore the noise power atthe output is given by5
Ns(t) = kJ P(t - r)f 2(r)dr, (1)
where P(t) is the short-time-average optical power onthe detectors, f(t) is the filter impulse response, and kis a proportionality constant. If P(t) varies muchslower than f(t), NS(t) n 2BRkP(t). Hence, for a largeenough BR, the noise power at the output follows P(t).
To measure Ns(t) we employ a boxcar that opens agate for the duration of the noise pulse and integratesthe output of the rf detector. This realizes a pulse-by-pulse measurement of the noise energy. To find themean of the noise energy, the averager in the boxcarcomputes an exponential moving average over a num-ber of pulses. Thus the output of the averager asobserved on a sampling oscilloscope is proportional tothe shot noise, and the accuracy with which it is mea-sured depends on the extent of averaging. The num-ber of pulses chosen for averaging is equivalent to thechoice of 1/BV in the conventional technique.
When the boxcar gate width is larger than or equalto the pulse width, a measurement of the shot-noiseenergy is realized for each pulse. If the gate width ischosen to be much smaller than the pulse width, how-ever, a true peak noise-power measurement can bemade. By change in the delay time of the gate withrespect to the pulse, it is also possible to map out thenoise power throughout the pulse.
To demonstrate the usefulness of our new tech-nique, we measured the pulsed squeezed light generat-ed at a wavelength of 1064 nm by means of traveling-wave optical parametric downconversion of a Q-switched laser.2 In our experiment the second-harmonic of a multilongitudinal-mode Q-switchedNd:YAG laser is used to pump a KTP crystal at 532nm. The LO beam for homodyne detection is derivedfrom the fundamental beam of the laser, which has aQ-switch repetition rate of 10.6 kHz and a pulse dura-tion of 390 nsec, resulting in a duty cycle of 1/242.
Figure 1 shows the setups for the conventional andthe new measurement techniques. InGaAs P-I-Nphotodiodes detect the two beams after the homodyn-ing beam splitter. The difference photocurrent ispassed through a low-pass filter (LPF) with a cutofffrequency of 80 MHz in order to suppress the peaks at100 MHz and its harmonics that result from longitudi-nal-mode beating in the Nd:YAG laser. The amplifierchain, which has a total gain (G) of 33.5 dB with a 1.8-dB noise figure, brings the background noise to a levelthat is 8.4 dB higher than the spectrum analyzer noisefloor. The background noise, as observed on the spec-trum analyzer in the absence of any light, is composed
of thermal noise, amplifier noise, and spectrum ana-lyzer noise.
When using the conventional technique (the dashedline in Fig. 1), we set BR at 10 kHz, which is themaximum value without increasing the relative contri-bution of the background noise to the shot-noise pow-er. In Fig. 2 we show the effect of change in BR on theaverage shot-noise power per hertz (Ns/BR) and thebackground noise power per hertz (NB/BR) at Qc = 23MHz. Extensive measurements and calculations in-dicate that the measured noise power indeed corre-sponds to the vacuum-state limit. Clearly, for BRgreater than the Q-switch repetition rate of 10.6 kHz,the average shot-noise power per hertz decreases,whereas the stationary background noise has a con-stant contribution to the measured power per hertz.The ratio BR/BV determines the accuracy with whichthe mean of the noise process is measured. In ourexperiment the minimum BV available on the spec-trum analyzer is 3 Hz, which leads to +0.12 dB ofuncertainty in the noise power measurements.2
Although it is possible to put as high as 800 ,W ofaverage LO power on the detectors without saturatingthem or the electronics, doing so requires a carefulbalancing of the photocurrents. In order to ease thematching requirement and avoid the saturation prob-lem, our new technique allows us to put much lessaverage LO power on the detectors, while maintainingthe shot-noise-limited performance. For a compari-son between the two techniques, we choose to keep theaverage LO power on the detectors at 140 MW. In theconventional technique the presence of the LO beamincreases the measured noise power by 1.3 dB withrespect to the background noise level, as shown in Fig.3(a). When the background noise contribution is sub-tracted, we find that the vacuum-state noise level islower than the background noise by 4.6 dB. There-fore it is not possible to measure accurately the phase-sensitive deviations from the vacuum-state noise level
4.0 -
3.0 -
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tc. 0.0-:0B -1.0-C - -
a- -3.0 -a)0.a) -4.0-U)
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-6.0-
-7.0
BR (Hz)
Fig. 2. Average shot-noise power per hertz NS/BR (filledcircles) and the background noise power per hertz NB/BR
(open circles) as a function of rf filter bandwidth BR. Thevertical scale is relative to NB/BR at BR = 10 kHz.
Fig. 3. Measurement with the conventional technique: (a)the time trace of the background (LO off) and vacuum-state(LO on) noise powers as seen on the spectrum analyzer whenthe pump is off and (b) the time trace of squeezed-state noiseas the LO phase is scanned and the pump is on. The verticalscale is relative to the vacuum-state noise level; the spectrumanalyzer settings are Qc = 23 MHz, BR 10 kHz, and BV = 3Hz.
20.0
210.0 - - _-
zda ~M_ _0 100 200
time (jsec)
1 4 Pump blocked Pump unblocked
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.0 510
time (sec)
Fig. 4. Measurement with the new technique: (a) Shot-noise power pulses as seen on the sampling oscilloscope.The level is due to background noise between the pulses.Averaging is performed by the oscilloscope, which is trig-gered synchronously with the LO pulses. The vertical scaleis relative to the background noise level. (b) The time traceof squeezed-state noise power (pump unblocked) relative tothe vacuum-state noise level (pump blocked) as the LOphase is scanned in time. The spectrum analyzer settingsare Q2c = 23 MHz, BR =3 MHz, and By = 3 MHz; the boxcaraverager settings are gate width of 0.5 gusec, with averagingover 1000 samples.
when squeezing occurs, since this level is veiled by thebackground noise. An attempt to measure squeezingis shown in Fig. 3(b), where we plot a time trace of thenoise power as the phase of the LO beam is scannedwith the help of a mirror mounted on a piezoelectrictransducer. Although the noise level exhibits phasedependence, it is not possible to make an accuratesqueezing measurement.
With our new technique (the solid line in Fig. 1) weset BR to 3 MHz, so that it is larger than the inversepulse duration of 2.6 MHz. Bv is also set to 3 MHzand hence has no effect on the noise process. The
video-out port of the spectrum analyzer provides thenoise power Ns(t) to the boxcar, which is triggeredsynchronously with the LO pulses. Figure 4(a) showsthe mean of Ns(t) as seen on a sampling oscilloscope.The mean is generated, using the averaging facilities ofthe oscilloscope. We see that, for the same averageLO power of 140 MW used in the conventional tech-nique, a peak noise power that is 16 dB higher than thebackground-noise level is obtained. This is 20.6 dBhigher than the -4.6-dB level obtained with the con-ventional technique. The duty cycle, in effect, im-plies a 23.8-dB difference between the average and thepeak noise levels. The measured value falls slightlyshort of this, because BR in our setup is somewhatsmaller than the optimum. This is also reflected inthe noise-pulse duration in Fig. 4(a) of approximately0.5,Msec, which is somewhat larger than the LO pulse.
The boxcar integrates Ns(t) over the entire pulseduration with a gate width of 0.5 Asec, yielding thenoise energy in each pulse. We set the averager to findthe mean of the noise energy per pulse by computingthe exponential moving average over 1000 samples,which corresponds to an equivalent BV of approxi-mately 10 Hz. Figure 4(b) shows squeezing as ob-served on the sampling oscilloscope. The initial flatportion of the trace corresponds to vacuum-state noisewhile the pump to the downconverter is blocked.When the pump is unblocked, deviations in the noiselevel as a function of the LO phase are clearly ob-served. When the LO is in phase with the squeezedvacuum, we see a reduction of 0.5 dB from the vacu-um-state noise level. Similarly, an increase of 1.0 dBis observed when the LO phase is shifted by xr/2. Themeasured values for squeezing are in good agreementwith our calculations based on measured parametricgain and losses.2 If one compares Fig. 4(b) with Fig.3(b), the advantage of our new technique is apparent.The decrease and increase from the vacuum-statenoise level are easily measured with much higher accu-racy.
In conclusion, we have demonstrated a new hybridfrequency-time-domain technique to measure pulsedsqueezing. Since in our technique the vacuum-statenoise level is determined by the peak LO power in-stead of the average power, the detector-amplifier sat-uration problem is easily avoided.
This research was supported in part by the NationalScience Foundation under grant EET-8715275.
References
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2. P. Kumar, 0. Aytdr, and J. Huang, Phys. Rev. Lett. 64,1015 (1990).
3. For references see the feature on squeezed states of theelectromagnetic field, J. Opt. Soc. Am. B 4, 1453-1741(1987).
4. H. P. Yuen and V. W. S. Chan, Opt. Lett. 8, 177, 345(1983); G. L. Abbas, V. W. S. Chan, and T. K. Yee, Opt.Lett. 8, 419 (1983).
5. A. Papoulis, Probability, Random Variables, and Sto-chastic Processes (McGraw-Hill, New York, 1984), p.241.
