Self consistent, absolute calibration technique for photon number resolving detectors
A. Avella, G. Brida, I. P. Degiovanni, M. Genovese, M. Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, M. L. Rastello, E. Taralli, P. Traina, M. White
aa r X i v : . [ qu a n t - ph ] N ov Self consistent, absolute calibrationtechnique for photon number resolvingdetectors
A. Avella, , G. Brida, I. P. Degiovanni, M. Genovese, M.Gramegna, L. Lolli, E. Monticone, C. Portesi, M. Rajteri, , ∗ M. L.Rastello, E. Taralli, P. Traina, and M. White , INRIM, Strada delle Cacce 91, Torino 10135, Italy Dipartimento di Fisica Teorica, Universit ` a degli Studi di Torino, Via P. Giuria 1, Torino10125, Italy NPL, National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK ∗ [email protected] Abstract:
Well characterized photon number resolving detectors are arequirement for many applications ranging from quantum information andquantum metrology to the foundations of quantum mechanics. This promptsthe necessity for reliable calibration techniques at the single photon level.In this paper we propose an innovative absolute calibration technique forphoton number resolving detectors, using a pulsed heralded photon sourcebased on parametric down conversion. The technique, being absolute, doesnot require reference standards and is independent upon the performancesof the heralding detector. The method provides the results of quantumefficiency for the heralded detector as a function of detected photonnumbers. Furthermore, we prove its validity by performing the calibrationof a Transition Edge Sensor based detector, a real photon number resolvingdetector that has recently demonstrated its effectiveness in various quantuminformation protocols. © 2018 Optical Society of America
OCIS codes: (270.5570) Quantum detectors; (030.5260) Photon counting; (030.5630) Radiom-etry.
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Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency h it is necessary a careful estimation of the optical transmittance t , accounting for the coupling efficiency in theoptical fiber and the optical losses in the non-linear crystal. According to the results of Ref.s [S.V. Polyakov,A.L. Migdall, Opt. Express , 1390 (2007); J. Y. Cheung et al. , Appl. Opt. ( submitted )], one could provide anestimate of this parameter with a less than 1% uncertainty.
1. Introduction
Photon number resolving (PNR) detectors are a fundamental tool in many different fields ofoptical science and technology [1, 2] such as quantum metrology (redefinition of the SI candelaunit [3]), super-resolution [4], foundations of quantum mechanics [5], quantum imaging [6] andquantum information [7, 8, 9].Unfortunately, most conventional single-photon detectors can only distinguish between zerophotons detected (“no-click”) and one or more photons detected (“click”). Photon number reso-lution can be achieved by spatially [10, 11] or temporally [12, 13] multiplexing these click / no-click detectors. True PNR detection can be achieved only by exploiting detectors intrinsicallyable to produce a pulse proportional to the number of absorbed photons. However, detectorswith this intrinsic PNR ability are few [1, 2], for example photo-multiplier tubes [14, 15, 16]and hybrid photo-detectors [17]. At the moment, because of their high detection efficiency, themost promising PNR detectors are the visible light photon counters [18, 19] and transition edgesensors (TESs) [20].TESs are based on a superconducting thin film working as a very sensitive thermometer. Theyare able to discriminate up to tens of photons per pulse. TESs have recently found important ap-plication to quantum information experiments [21, 22, 23], demonstrating their huge potentialin this field. For practical application of these detectors it is fundamental they are appropriatelycharacterised. In particular, one of the most important figures of merit to be characterised is thedetection efficiency, defined as the overall probability of detecting a single photon impingingn the detector.For measuring detection efficiency in the photon counting regime, where conventional stan-dards are cumbersome, an efficient solution is given by Klyshko’s absolute calibration tech-nique [24, 25, 26], which exploits parametric down conversion (PDC) as a source of heraldedsingle photons. Despite this technique being suggested in the seventies [27, 28], only in re-cent years has it developed from demonstrational experiments to more accurate calibrations[29, 30, 31, 32]. Nowadays, it has been added to the toolbox of primary radiometric techniquesfor detector calibration, even though it has only been deeply studied in the case of single-photonclick / no-click detectors [33, 34, 35, 36, 37].Recently, other techniques for detector calibration, exploiting PDC in the high gain regime,have been proposed both for the case of analog detectors [38, 39] and CCDs [40]. Furthermore,a new technique for the calibration of single photon detectors was proposed exploiting brightPDC light [41]. This technique, strongly based on the assumption of a specific detection model,can in principle be more accurate than the version of Klyshko, but it is important to under-line that the Klyshko’s technique, properly developed by the radiometric community, has beenproven accurate at the level of parts in 10 [36, 37], i.e. one order of magnitude more accuratethan discussed in Ref. [41].We note that the extension of Klyshko’s technique to the PNR detection system is quitestraightforward when considering the PNR as a click / no-click single-photon detector. Never-theless, this simple application of Klyshko’s method is detrimental to the peculiar property ofthe PNR detector, i.e. its PNR ability.By contrast, in this paper we propose and demonstrate an absolute technique for measuringquantum efficiency, based also on a PDC heralded single photon source, but exploiting all theinformation obtained from the output of the PNR detector. As the technique is absolute noreference standards are required.We also note this represents the first quantum efficiency measurement of a TES detectorexploiting an absolute technique. Other researchers [42, 43] have demonstrated a substitutionmethod [44] employing a laser beam, calibrated optical attenuators and calibrated referencestandard detectors.In particular in section 2 we present the theory of our calibration method, while in section 3we present the experimental setup and the results.
2. Our method
We used a pulsed PDC based heralded single photon source to illuminate our TES detector. Thetypical output of a PNR detector is an histogram representing the relative frequency of detectionevents of a certain number of photons. Specifically, we performed two separate measurements,one in the presence of and one in the absence of heralded photons, obtaining two data his-tograms. Starting from these histograms we estimate the probabilities of observing i photonsper heralding count in the presence and in the absence of the heralded photon, P ( i ) and P ( i ) respectively. Furthermore, we account for the presence of false heralding counts due to straylight and dark counts. As x is the probability of having a true heralding count (i.e. not due tostray light and dark counts), the probability of observing no photons on the PNR detector is thesum of the probability of non-detection of the heralded photons multiplied by the probabilityof having no accidental counts in the presence of a true heralding count and the probabilityof having no accidental counts in the presence of a heralding count due to stray light or darkcounts: P ( ) = x [( − g ) P ( )] + ( − x ) P ( ) , (1)hereafter g is the TES “total” quantum efficiency, i.e. g = th where t is the optical and couplinglosses from the crystal to the fibre end ((a) in Fig. 1) , and h is the quantum efficiency of theES detector. According to Fig. 1, we consider the TES detector as the system from the fibreend (b) to the sensitive area, since this represents the real detector for applications. This meansthat h accounts also for the losses of the fibre in the fridge and the geometrical coupling of thelight from the fibre to the TES sensitive area.Analogously, the probability of observing i counts is P ( i ) = x [( − g ) P ( i ) + g P ( i − )] + ( − x ) P ( i ) , (2)with i=1,2,..., i.e. the sum of the joint probability of non-detection of the heralded photonsand the probability of having i accidental counts, and the joint probability of detection of theheralded photons and the probability of having i − i accidental counts in the presence of aheralding count due to stray light or dark counts.From Eq. (1) the efficiency can be estimated as g = P ( ) − P ( ) x P ( ) , (3)while from Eq. (2) g i = P ( i ) − P ( i ) x ( P ( i − ) − P ( i )) . (4)It is noteworthy to observe that the set of hypotheses in the context of this calibration tech-nique is similar to the one in Klyshko’s technique, i.e. multiphoton PDC events in the timeinterval of the order of DET1 temporal resolution (jitter) should be absolutely negligible. Fur-thermore, in our case for each value of i we obtain an estimation for g allowing a test of consis-tency for the estimation model.
3. Method implementation and discussion
The PNR detector for implementing the proposed calibration technique is a TES based detector,suitable for broadband response. The TES sensor consists of a superconducting Ti film prox-imised by an Au layer [45]. Such detectors have been thermally and electrically characterisedby impendence measurements [46]. The transition temperature of the TES is T c =121 mK with D T c =2 mK. It is voltage biased [47] and mounted inside a dilution refrigerator at a bath tempera-ture of 40 mK. The TES active area is 20 m m x 20 m m and is illuminated with a single mode,9.5 m m core, optical fibre. The fibre is aligned on the TES using a stereomicroscope [48]. Thedistance between the fibre tip and the detector is approximately 150 m m. The read out is basedon a dc-SQUID array [49], mounted close to the detector, coupled to a digital oscilloscope forsignal analysis. The obtained energy resolution is D E FWHM = m s [48].The calibration is performed using an heralded single photon source based on pulsed non-collinear degenerate PDC [24, 25, 26] (Fig. 1). The heralding photon at 812 nm, emitted at 3 o with respect to the pump propagation direction, is spectrally selected by means of an interfer-ence filter 1 nm FWHM (IF1) and detected by a single photon detector DET1 (Perkin-ElmerSPCM-AQR-14). The heralding signal from DET1 announces the presence of the conjugatedphoton that is coupled into the single mode optical fibre and sent towards the TES detector(DET2) after spectral filtering (IF2 centered at 812 nm with 10 nm FWHM). As usual in quan-tum efficiency measurement based on heralding single photon source, the spectral selection isdetermined by the trigger detector, while the filter in front of the detector under-test should notreject heralded photons but it is just inserted to reduce the background counts [24–37]. ig. 1. Experimental setup: the heralded single photon sources based on non-collinear de-generate PDC pumped by 406 nm pulsed laser. The heralding signal from DET1 announcesthe presence of the conjugated photon that is coupled in the single mode optical fibre andsent towards the TES based detector (DET2, identified by the dotted line) starting from thefibre end (b). The pulsed PDC is realised by pumping a type I BBO crystal with a 406 nm laser, electricallydriven by a train of 80 ns wide pulses with a repetition rate of 40 kHz. This low repetition rate isrequired to avoid pile up effect in the statistics of the measured counts. In fact it is necessary touse a pulsed heralded single-photon source with a period longer than the pulse duration of thedetector, in order to avoid unwanted photons impinging on the TES surface before the end ofthe pulse. If it does not happen, the end effect would be a pile up of the signal on the tail of theprevious detection event with a subsequent extension of the pulse tail (that can be, somehow,considered the extended dead time of the detector [50]).Despite the pump laser pulse being quite long (80 ns), we note that it is shorter than thetemporal resolution of TESs (time jitter larger than 100 ns). Furthermore, the poor temporalresolution does not allow the use of small coincidence temporal windows such as the ones usedin the typical coincidence experiments exploiting, for example, Time-to-Amplitude-Convertercircuits. One of the advantages of using a pulsed heralded single photon source is the possibilityof evaluating the events counted by the TES in the presence and absence of an heralding signal,providing an estimate of the probabilities P ( i ) and P ( i ) in terms of events C ( i ) and C ( i ) counted by the TES. In particular C ( i ) ( C ( i ) ) is the number of events observed by the TEScounting i photons in the presence (absence) of the heralding photon, where P ( i ) = C ( i ) / (cid:229) i C ( i ) and P ( i ) = C ( i ) / (cid:229) i C ( i ) .In Fig. 2 typical traces of the TES detected events observed by the oscilloscope are shown.The oscilloscope readout is triggered only when both the pump laser trigger and the heraldingdetector DET1 clicks are present. The time base is set in order to record on the trace twosubsequent laser pulses. In such a way we are able to measure, on the same trace of the DET2pulses, the events containing the heralded photon announced by the contemporary two triggersignal, i.e. the one corresponding to the laser pulse and the one from DET1 (left pulses inFig. 2), and the subsequent ones not containing the heralded photon (right pulses in Fig. 2).By measuring the amplitude of the pulses in this trace we could generate an histogram where ig. 2. Experimental data: oscilloscope screen–shot with traces of the TES detected events.The group of traces on the left (right) are obtained in the presence (absence) of heraldingsignals. Insets (a) and (b) present the histogram of the amplitudes of the pulses in thepresence and in the absence of heralding photons, together with their gaussian fits. the peaks identify the different number of detected photons corresponding to the two kind ofpulses of Fig. 2. The insets (a) and (b) are the histograms of the amplitudes of the pulses inthe presence and in the absence of heralding photons, respectively. The histogram is fitted withgaussian curves (cid:229) i = [ A i exp [ − ( x − x i ) / ( s i )] , where the fit parameters are the areas A i , thecentres x i and the widths s i of the Gaussian curves. The agreement between the experimentaldata and the fitting is excellent, as stated from the ratio between the reduced c -square valueand the reduced total sum of square that is lower than 10 − . The integrals of the gaussiancurves fitted to the histogram peaks provide an estimate for the parameters C ( i ) and C ( i ) .The probability of having true heralding counts x = . ± . x = − n OFF / n ON , where n ON and n OFF are the number of events triggered by the laser pulsesand counted by DET1 in the presence and in the absence of PDC emission, respectively. Theycorrespond in one case to true heralded counts, or stray light and dark counts, while in the othercase only to stray light and dark counts and they are obtained by means of pump polarizationrotation. The PDC extinction provided by the pump polarization rotation was almost perfect atour pump regime.The measured value for stray light and dark counts on DET1, are compatiblewith the values measured with the pump laser blocked before the crystal. The uncertainty on x is evaluated by standard uncertainty propagation on the measured counts in the presence and inthe absence of PDC.According to Eq.s (3) and (4), the different estimated values for the “total” quantum efficien-cies are g = ( . ± . ) %, g = ( . ± . ) %, and g = ( . ± . ) %. In Table 1can be found the full analysis of the uncertainty contributions [51]. All the uncertainties aregiven with coverage factor k =
1, obtained from six repeated measurements, each measurementbeing five hours long, corresponding to approximately 11 × heralding counts. The systemwas very stable during this long run of measurements. We note that the large uncertainty (de-rived from standard uncertainty propagation) in the estimation of g is essentially due to thepoor statistics. For the same reason, i.e. negligible amount of counted events, it was impossibleo obtain estimates of g for i >
2. Nevertheless, within its large uncertainty g is compatiblewith g and g estimates, which are themselves within very good agreement. This is consistentwith the fact that g = g = g is expected, since the TES detector has been recently proved to bea linear detector [52], as generally believed [1, 2]. The averaged results for the efficiency is ( . ± . ) %, from a standard weighted mean, where the uncertainty is calculated accord-ingly. Table 1. Uncertainty contributions in the measurement of g , g g
2. The uncertaintycontributions are calculated according to the well known gaussian propagation of uncer-tainty formula [51], where the correlations are accounted for.
Quantity Value Standard Unc. Unc. Unc.Uncertainty Contrib. Contrib. Contrib.to g ( % ) to g ( % ) to g ( % ) C .
069 10 . − . − . − . C .
200 0 .
004 0 . − − C
118 6 2 10 − − − . C .
103 10 . − − . C . − . − . − . C . . − − − − . x . − − − − − − − g ( % ) .
709 0 . g ( % ) .
709 0 . g ( % ) .
65 0 . g i ’s we evaluate the “total” efficiency in the case of the Klyshko’s technique,obtaining g Klyshko = ( . ± . ) %. The result is in perfect agreement with that obtainedfrom the proposed new technique as implemented in the work reported here.The evaluation of the total efficiency g , instead of h , allows us a better comparison betweenthe results obtained from the two techniques, as the additional independent measurement of t is common to the two techniques. For this reason, in the context of the comparison, it onlyprovides an additional and somewhat misleading common uncertainty contribution [53].We notice that the value of the measured efficiency is rather small with respect to resultspresented in the literature, e.g. [42, 43]. However, the measured values are absolutely consistentwithin the context of our experimental setup. Note that the TES sensitive area is not optimisedfor detection efficiency at a specific wavelength. On the basis of the material used the expectedefficiency of the TES is approximately 49%, while the parameter t is estimated to be 10%. Thegeometrical and optical losses inside the refrigerator contribute to lower the value of h to 7%.
4. Conclusions