Real-time shot-noise-limited differential photodetection for atomic quantum control
F. Martin Ciurana, G. Colangelo, Robert J. Sewell, M.W. Mitchell
RReal-time shot-noise-limited differential photodetection for atomic quantum control
F. Martin Ciurana, G. Colangelo, Robert J. Sewell, and M.W. Mitchell
1, 2 ICFO – Institut de Ciencies Fotoniques, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain ICREA – Instituci´o Catalana de Recerca i Estudis Avan¸cats, 08015 Barcelona, Spain (Dated: May 12, 2016)We demonstrate high-efficiency, shot-noise-limited differential photodetection with real-time sig-nal conditioning, suitable for feedback-based quantum control of atomic systems. The detectorsystem has quantum efficiency of 0.92, is shot-noise limited from 7 . × to 3 . × photons perpulse, and provides real-time voltage-encoded output at up to 2 . Feedback control of atomic quantum systems [1] en-ables quantum information protocols including deter-ministic teleportation [2], stabilization of non-classicalstates [3], entanglement generation [4, 5] and quantum-enhanced sensing [6, 7]. Efficient closed-loop controlhas been achieved by combining optical quantum non-demolition (QND) measurement [8, 9] with electromag-netic [10] or optical [11] feedback. Fidelity of theseprotocols requires speed, sensitivity and low distur-bance in the QND measurement [12]. Because advancedQND techniques such as two-color probing [13] and two-polarization probing [14] address specific hyperfine tran-sitions, this also requires small ( ∼ GHz) detunings, andthus low photon numbers to achieve low disturbance.This combination of requirements in the measurementplaces multiple demands on the detectors used in theQND measurement.Here we present a balanced differential photodetector(DPD) suitable for ∼ µ s pulsed Faraday rotation [15]and two-color [13] dispersive probing of atomic ensem-bles with sensitivity and dynamic range comparable tothe best published differential detectors [16, 17]. TheDPD employs >
90% quantum efficiency photodiodesand charged-particle-detection amplifiers. Real time out-put is achieved with low-noise sample and hold amplifiers(SHAs) and a differential amplifier (DA). The system en-ables atomic quantum control in which feedback to anatomic system must be accomplished with a sub- µ s looptime [11, 18].The electronics for the DPD and DA together with thetest setup are shown schematically in Fig. 1. The detec-tor consists of two PIN photo-diodes (PDs) (HamamatsuS3883) connected in series and reverse biased by 5 V toimprove their response time. The differential output cur-rent is DC coupled to the integrator, a very low noisecharge-sensitive pre-amplifier (Cremat CR-110) with acapacitor C i and a discharge resistor R i in the feedbackbranch. Together these determine the relaxation timeconstant τ = R i C i = 290 µ s of the integrator. The 50 nsrise-time of the circuit is limited by the capacitance of thephotodiodes while the CR-100 itself has a nominal risetime of 7 ns. Pulses longer than the rise time but shorterthan the relaxation produce a step in the output voltageproportional to N diff , the difference of photon numbers on the two photodiodes. The output from the DPD iscaptured by a pair of sample and hold amplifiers (SHAs)(Analog Devices AD783), gated with TTL signals. TheSHA1 captures the voltage of the DPD before the opti-cal pulse arrives, and SHA2 captures it after the end ofthe pulse. A differential amplifier (DA) (Analog DevicesAD8274) amplifies the difference of the two voltages heldon the SHAs. � ��� � ��� ���� ����� � � �� � ���� � ���� � � ( ��� ) � � ( ��� ) � � ( ���� ) � � ( ���� ) � ( �� ) τ ���� � ���� � ���� ′ τ � ��� � � �� ���� �� FIG. 1. Top: Schematic of the optics and detector electronics.A laser and acousto-optic modulator (not shown) are used toproduce pulses of desired duration and energy. A first polar-izing beam splitter (PBS) is used to generate a well definedlinear polarization, a half-wave plate (HWP) and second PBSare used to split a constant fraction of the pulse to a referencedetector (RD). A HWP together with a Wollaston prism areused to balance the energies reaching the photodiodes, wiredin series for direct current subtraction. A charge-sensitive pre-amplifier (Cremat CR-110) amplifies the difference current,and a pair of SHAs (Analog Devices AD783) sample the pre-amplifier output shortly before and shortly after the pulse. Adifferential amplifier (DA) (Analog Devices AD8274) outputsthe difference of the two SHA signals. Bottom: Timing dia-gram of optical input, SHA gate voltages and DPD and DAsignals, illustrating a possible response to two pulses of a pulsetrain. P opt : optical power, V DPD : Balanced detector output,gate 1, gate 2: gate voltages causing the respective SHAs tosample (high) and to hold (low), V DA : differential amplifieroutput. Red circles show oscilloscope voltage samples use tocharacterize the DPD and DA noise characteristics. a r X i v : . [ phy s i c s . op ti c s ] M a y To characterize the noise performance of the DPD wesend trains of pulses with a desired photon number N ,pulse duration τ , and pulse repetition period T rep . Weuse a continuous-wave diode laser at 780 nm, chopped byan acousto-optic modulator and balanced by means of ahalf waveplate and Wollaston prism, as shown in Fig. 1.We record the reference detector (RD) and DPD outputvoltages on an 8-bit digital storage oscilloscope (LeCroyWaverunner 64Xi) at a sampling rate of 100 Msps whichacquires samples continuously and asynchronously to thepulse generation. We define a single measurement for theDPD as N diff = C ( V − V ), where V ( V ) is the meanof N samp voltage samples before (after) the optical pulseand C is a calibration factor. The number of photons N phot in a pulse is estimated as N phot = C RD (cid:80) i V RD ( t i )where V RD is the voltage output of RD. The sum is takenover the duration of the pulse and C RD is a calibrationfactor obtained by comparison against a power meter.For a given set of conditions, we adjust the waveplate togive a balanced signal N diff ≈ M pulses ina single pulse train, from which we extract M values for N diff and N phot and compute statistics.When source and detector fluctuations are taken intoconsideration, a linear detector will have an output sig-nal variance given by a second-order polynomial in theaverage optical input energy [19],var N diff = a N + ηN phot + a N . (1)Here a is the “electronic noise” (EN) contribution, a N is the “technical noise” (TN) and the secondterm is the shot noise (SN) contribution with η the quan-tum efficiency of the detector. The different scalings with N phot allow an unambiguous identification of the differ-ent noise contributions.To estimate the coefficients of Eq.1 we collect data ata variety of N phot in each case recording a train of 2500pulses with repetition period T rep = 0 . µ s and pulseduration τ = 200 ns. Our light source is not powerfulenough to measure the turning point from SN-limitedto TN-limited. In order to estimate when the TN be-comes the dominant source of noise we construct “com-posite pulses” containing a larger total number of pho-tons by summing the signals from multiple pulses [20].The measured variances are fitted with Eq. (1) to ob-tain a , η and a . We set t (DPD)1 = 10 ns to ensurethat V is measuring the voltage before the detectionof the optical pulse and t (DPD)2 = 90 ns which is theminimum time to sample >
99% of the DPD signal,with N samp = 10 points. Typical results are shown inFig. 2 (a). The detector is shot-noise limited when a /η < N phot < η/a . From the fit outputs, see Fig. 2 fordetails, we determine that the DPD is SN-limited from(4 . ± . × < N phot < (3 . ± . × pho-tons, i.e., its SN limited behavior extends over 4 ordersof magnitude. (cid:72) a (cid:76) N photons V a r (cid:72) N L d i ff (cid:72) D P D (cid:76) (cid:76) (cid:72) b (cid:76) N photons V a r (cid:72) N L d i ff (cid:72) D A (cid:76) (cid:76) FIG. 2. Variance of the output signal of the DPD (a) and DA(b) as function of the input photon-number in log-log scale.Solid red line fit to Var(NL diff ) using expression Eq.1. Shadedareas depicts the different detection responses: green EN-limited, blue SN-limited and yellow TN-limited. Error barsrepresent ± σ standard error. For both devices T rep = 0 . µ sand τ = 200 ns. (a): var N DPDdiff as function of the N phot . Anal-ysis done with t (DPD)1 = 10 ns, t (DPD)2 = 90 ns and N samp = 10points. The yellow line dot-dashed is the electronic noise level, a = (4 . ± . × , the dotted gray line is the shot-noiseterm, η = 1 . ± .
01, and the dashed green line is the techni-cal noise contribution, a = (2 . ± . × − . (b): var N DAdiff as function of the N phot . The timings for the gates of theSHAs are t (gate)1 = 10 ns, t (gate)2 = 20 ns with analysis param-eters t (DA) = 170 ns and N (cid:48) samp = 10 points. The yellow linedot-dashed is the EN level, a = (7 . ± . × , the dot-ted gray line is the SN term, η = 1 . ± .
01, and the dashedgreen line is the TN contribution, a = (2 . ± . × − . To characterize the noise properties of the DA we re-peat the same procedure as for the DPD: we record onthe oscilloscope the RD and DA output voltages. TheSHA1 captures V DPD ( t (gate)1 ) before the optical pulse ar-rives, and the SHA2 captures V DPD ( t (gate)2 ) after the endof the pulse, analogous to V and V , respectively. Wedefine a single measurement as N diff = C (cid:48) V DA , where V DA is the mean of N (cid:48) samp voltage samples a time t (DA) after the end of the SHA2 and C (cid:48) is a calibration fac-tor obtained by comparison against a power meter. Un-der the same experimental conditions, T rep = 0 . µ s and τ = 200 ns, we record a train of 2500 pulses for each valueof N phot and fit var N (DA)diff with Eq. (1) we obtain a , η and a . As before, we construct “composite pulses” todetermine a . The SHAs are gated for τ gate = 100 ns attimes t (gate)1 = 10 ns and t (gate)2 = 20 ns. The analysisparameters are t (DA) = 170 ns and N (cid:48) samp = 10 points.Typical results are shown in Fig. 2 (b). From the fit out-puts we determine that the DA is shot-noise limited from(7 . ± . × < N phot < (3 . ± . × photons,i.e., over almost 3 orders of magnitude.From the coefficients a we can deduce the noise-equivalent charge (NEC), the number of photo-electronsnecessary to create a signal equivalent to the electronicnoise q SN = η Q (cid:112) N phot , SN for the DPD and for the DA.The quantum efficiency of the photo-diodes in the detec-tor at 780nm is η Q = 0.92, resulting in NEC DPD = 600electrons and NEC DA = 808 electrons. Since the two cal-ibration experiments were taken under the same exper-imental conditions, i.e., T rep = 0 . µ s and τ = 200 ns,and comparable analysis conditions τ gate = 100 ns and N samp = N (cid:48) samp = 10 points, we see that the capabilityof having the signal available in real time has the cost ofincreasing the electronic noise level by 1.3dB.The electronic noise of DPD contains high-bandwidthnoise, e.g. Johnson noise, that can be reduced by aver-aging the in-principle constant output over a time win-dow, which could be longer than the pulse itself. Onthe other hand, longer windows will be more sensitive todrifts and “1 /f ” noise. We investigate this trade-off bychanging N samp used to obtain V and V and then fitvar N (DPD)diff with Eq.1 to get a , η and a . The experimentis done at T rep = 30 µ s and τ = 200 ns, and the analysiswith t (DPD)1 = 10 ns and t (DPD)2 = 90 ns. For each N phot we record more than 300 pulses in a single pulse train.From these parameters we evaluate the SN limited re-gion of the DPD as a function of the measurement band-width. We fit the EN (TN) limited region a /η < N phot ( N phot > η/a ) with the polynomial α N β samp + α N β samp (Eq.2), where the two terms are for the two noise time-scales.In Fig. 3 we observe a transition from EN ∝ N β samp ,where β < N samp (cid:46)
100 points, describing theeffects of averaging, to a 1 /f regime for N samp (cid:38) ∝ N β samp where β >
0. The fit resultsare β EN DPD1 = − . ± .
02 and β EN DPD2 = 0 . ± . N samp from 1 point to 400 we can reduce the electronic noise ofthe DPD by 10 . N samp to obtain V and V and observethat the a scope0 is negligible relative to a DPD0 . The factthat β EN DPD1 = − .
60 and not − N samp N pho t FIG. 3. DPD SN-limited region (blue area) as function ofmeasurement bandwidth ( N samp ) in log-log plot. EN-limitedregion (green) and TN-limited (yellow), see text for details.Experimental parameters T rep = 30 µ s and τ = 200 ns. Reddot-dashed curve is a fit of TN with Eq. 2 with results α TN1 =(1 . ± . × , α TN2 = (0 . ± . × , β TN1 = 0 . ± . β TN2 = 1 . ± .
31. Purple dashed curve is a fit of ENwith Eq.2 with output values α EN1 = (1 . ± . × , α EN2 = 40 ± β EN1 = − . ± .
02 and β EN2 = 1 . ± . fit (not shown) has values α scope1 = (3 . ± . × , α scope2 = 0 . ± . β scope1 = − . ± .
03 and β scope2 = 0 . ± .
13 and conclude that thescope noise contribution is negligible. Sample rate is 100 Mspsor 10 ns/sample. Error bars represent ± σ standard error. β scope1 ) means that there is some correlated noise in theDPD output signal. This is expected as the 100 MHzsampling frequency exceeds the oscilloscope input band-width at this setting. The measured − N samp > N samp as the reduction of theTN-limited region compensates the increase of the EN.We can observe that the TN is almost flat for N samp (cid:46)
300 but rapidly decreases for N samp > (cid:46)
200 kHz(exact value not reported). Our DPD shows a minimalENC=242 at 125 kHz, representing a noise improvementof 0.63dB (Amptek-based detector) and 1.84dB (Cremat-based detector) while operating at similar measurementbandwidth. Similarly, in [21] the maximum measurementspeed is 200 kHz and SN limited starting from 10 pho-tons/pulse (our DPD is SN limited from 7 × ). Ref[16], working at a repetition rate of 1 MHz reports a NECof 730 electrons, whereas our DPD has a NEC of 600 elec-trons at 1 MHz, a reduction of 0.87 dB. Furthermore, ourDPD has a minimum repetition period of T (DPD)rep = DPDrise time (50 ns) + t (DPD)1 (10 ns) + t (DPD)2 (10 ns) + 2 N samp ( 2 ×
10 ns) = 90 ns, or equivalently, a maximumdetection bandwidth of 11 MHz, which to our knowledgemakes it the fastest quantum-noise limited differentialphotodetector for this energy regime, i.e., for pulses withas few as 6 . × photons. Along with the speed, ourDPD is SN limited over measurements bandwidth run-ning from ∼
10 MHz to kHz.Atomic experiments have coherence times runningfrom µ s to seconds requiring a real time detector with lowlatency and large bandwidth to perform many manipula-tions of the atomic state before decoherence occur. Themaximum measurement speed of our DA is determinedby τ gate , the sampling time of the SHAs to faithfully cap-ture V DPD , and t (DA) , the settling time of the SHA oncethe sampling has been done.We investigate the effect of τ gate by measuring var N DAdiff vs N phot for different values of τ gate and compare the fitoutputs. We obtain the same results for τ gate = 250 ns,the manufacturer recommended value, as for τ gate =100 ns, with fit parameters comparable within the stan-dard error, but not for 50 ns where the DA-output is in-dependent of N phot , i.e., dominated by EN.We study the effect of the settling time of the SHA2by varying the samples used for V DA with t (DA) and fitvar N (DA)diff to obtain the parameters a , η and a . Fromthe fit outputs we determine the EN-limited and TN-limited regions. In Fig. 4 we see that for values of t (DA) where the noise of the SHA has not had time to settlethe EN and the TN contributions are large, dominantover SN. We also observe that once t (DA) is sufficient,the EN region is flat as expected from the output of athe DA. From the fit outputs η we determine that theminimum value to have >
99% of the signal correspondsto t (DA) = 170 ns.The minimum time at which we can measure two con-secutive pulses is given by T (DA)rep = DPD rise time (50 ns)+ 2 τ gate (2 ×
100 ns) + t (DA) (170 ns) + N (cid:48) samp (10 ns)=430 ns, or equivalently, the maximum detection band-width in real time is 2 . N (cid:48) samp used in the analysis. This suggests that the outputof the DA has fast frequency noise components that couldbe filtered to obtain the same noise performance as inFig. 2.In conclusion, we have demonstrated a pulsed differen-tial photodetector (DPD) and a detection system to makethe signal available in real time. The DPD has bandwidthup to ∼
11 MHz which to our knowledge makes it thefastest quantum-noise limited differential photodetectorfor pulses with as few as 6 . × photons per pulse.
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