Enhancing LIDAR performance metrics using continuous-wave photon-pair sources
Han Liu, Daniel Giovannini, Haoyu He, Duncan England, Benjamin J. Sussman, Bhashyam Balaji, Amr S. Helmy
EEnhancing LIDAR performance metrics using continuous-wave photon-pair sources
Han Liu, Daniel Giovannini, Haoyu He, Duncan England, Benjamin J. Sussman,
2, 3
Bhashyam Balaji, and Amr S. Helmy ∗ The Edward S. Rogers Department of Electrical and Computer Engineering,University of Toronto, 10 King’s College Road, Toronto, Ontario M5S 3G4, Canada National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6, Canada Department of Physics, University of Ottawa, 598 King Edward, Ottawa, Ontario K1N 6N5, Canada Radar Sensing and Exploitation Section, Defense R&D Canada,Ottawa Research Centre, 3701 Carling Avenue, Ottawa, Ontario, K1A 0Z4, Canada
In order to enhance LIDAR performance metrics such as target detection sensitivity, noise re-silience and ranging accuracy, we exploit the strong temporal correlation within the photon pairs gen-erated in continuous-wave pumped semiconductor waveguides. The enhancement attained throughthe use of such non-classical sources is measured and compared to a corresponding target detectionscheme based on simple photon-counting detection. The performances of both schemes are quanti-fied by the estimation uncertainty and Fisher information of the probe photon transmission, whichis a widely adopted sensing figure of merit. The target detection experiments are conducted withhigh probe channel loss ( (cid:39) − × − ) and formidable environment noise up to 36 dB strongerthan the detected probe power of 1 . × − pW. The experimental result shows significant advan-tages offered by the enhanced scheme with up to 26.3 dB higher performance in terms of estimationuncertainty, which is equivalent to a reduction of target detection time by a factor of 430 or 146(21.6 dB) times more resilience to noise. We also experimentally demonstrated ranging with thesenon-classical photon pairs generated with continuous-wave pump in the presence of strong noise andloss, achieving ≈ I. INTRODUCTION
Non-classical attributes of light have been utilized toextend the sensitivity of several metrology applicationsbeyond the classical limit recently[1][2][3]. One impor-tant sensing technique; namely optical target detection,can benefit greatly from non-classical correlations of pho-tons. Optical target detection has been receiving in-creasing attention due to its pivotal role in emergingapplications such as light based detection and ranging(LIDAR)[4] and non-invasive bio-imaging, among others.Quantum protocols based on quantum illumination haverecently demonstrated that entanglement can be utilizedto beat the best classical target detection schemes[5].The enhancement obtained from such schemes requiresphase-sensitive quantum detection, which entails that theoptical path length of the probe light has to be stabilizedprecisely, on a wavelength scale, while the reference pho-tons have to be stored in a quantum memory[6]. Suchstringent requirements preclude, at this stage, quantumillumination-based schemes from addressing numerouspractical sensing and ranging application. In contrast, aphase-insensitive target detection scheme which utilizesnon-classical primitives, if proven to provide enhance-ment over its classical counterparts, would be a valuableadvance in the quest to improve upon classical limits ofdetection. When developed, such a scheme can be benefi-cial for many practical sensing and ranging applications.The essential idea of nonclassical light enhanced phase-insensitive target detection scheme is to utilize the cor- ∗ [email protected] relation within nonclassical photon pairs to enhance thetarget detection performance. Previous implementationsof such schemes [7][8] are based on the intensity cor-relation within non-classical photon pairs, that is, thecorrelation between the number of probe and referencephotons. However, the quantum enhancement of inten-sity correlation-based schemes diminishes as the outputpower of the probe light increases[8], which limits its ap-plication in practical target detection scenarios. Anothertype of correlation that also exists within non-classicalphoton pairs is the temporal correlation, that is, the cor-relation between the detection time of the probe andreference photons. Compared to the intensity correla-tion, the temporal correlation is not limited by the sourcepower and is therefore much more scalable. As such, itcan be interesting to see whether the temporal correlationcould be utilized to benefit practical phase-insensitivetarget detection schemes.One of the central aspects of practical target detectionsystems is the versatility of the non-classical sourceused. To date, non-classical photon sources for mostquantum-enhanced metrology experiments have beenbased on bulk crystal such as BBO and PPLN with alarge footprint, which inevitably introduces mechanicalinstability and inefficient interaction with the metrologysystem. For practical target detection schemes utilizingnon-classical photon pairs, the sources need to be inspatial single-mode and offer a compact footprint, tocater to the widest range of applications. Integratedphoton-pair sources are therefore ideal candidates forthese applications. In the last decade, there has beenastounding progress in the prowess of non-classicalsources[9][10]. In particular, it has been shown that a r X i v : . [ phy s i c s . op ti c s ] A p r integrated monolithic semiconductor devices based onan active gallium arsenide (GaAs) platform can beused to generate high-quality quantum states of light[11][12]. In addition to its compact footprint as well asefficient coupling into integrated metrology platforms,monolithic semiconductor photon-pair sources could alsooffer great tuning of their spectro-temporal propertieselectro-optically with no moving parts, which is notavailable in bulk photon-pair sources. For example, thespectral bandwidth of the non-classical photon pairscould be tailored from 1 nm to over 450nm throughvarying the waveguide structure with various maskdesigns[13].Another aspect of paramount importance is to choosea suitable criterion, based on which a meaningful andpractical figure of merit (FOM) can be defined to fa-cilitate comparisons between classical and non-classicalschemes. In previous experiments[7][8], the targetdetection performance is quantified by using the opticalsignal to noise ratio (OSNR). The calculation of OSNRnecessitates separate target detection experiments withthe target being present and absent, which may notbe practical in applications where the removal of thetarget is not feasible. Moreover, the definition of OSNRmay vary depending on the implementation, renderingperformance comparisons challenging to standardize.A robust approach to address these issues is to adoptthe estimation theory, which has been widely usedand proven as a reliable figure of merit for varioustarget detection and sensing applications[14][15]. Ifthe estimate of the probe light transmission, which isdefined as the percentage of probe photons that areback-reflected from the target and get detected, isgreater than the uncertainty of estimation, then the probability of the presence of the target object couldbe maximized. The uncertainty of the transmissionestimation, which could be obtained through a singletarget detection experiment, can serve as an effective,and generic, target detection FOM. This is becauseit characterizes the ability to distinguish between thepresence (nonzero probe light transmission) and absence(zero probe light transmission) of the target object.The uncertainty of the transmission estimation is lowerbounded by the Fisher information of the transmissionestimation according to the Cram`er Rao’s Bound[16].In this work, we demonstrate a practical, phase-insensitive target detection scheme which utilizes photonpairs obtained from a continuous-wave (CW) pumpedspontaneous parametric down-conversion (SPDC) sourcerealized using a monolithic semiconductor waveguide.We show that the strong temporal correlation of thenon-classical photon pairs could provide substantial andscalable performance enhancement to phase-insensitivetarget detection schemes. The classical target detectionsystem, which we use as a comparison to the non-classicalsources enhanced scheme, utilizes simple intensity de-tection with the same photon-counting detector thatis used in the enhanced scheme. The performances ofboth schemes are quantified by using the transmissionestimation uncertainty and Fisher information criterion.Furthermore, we demonstrate that temporal correlationenhanced systems are also resilient to active jammingattacks and are capable of effective ranging in a noisyand lossy environment, despite the utilization of CWlight and not pulsed. The experimental results matchwell with the theoretical predictions obtained from theFisher information and the Cram´er-Rao’s Bound.FIG. 1: The schematic of the experimental setup which is divided into two parts. The left part (green background)includes the probe photon source and detectors. Pump laser: Ti-Sapphire CW laser at 783nm. PBS: polarizationbeam-splitter. LPF: long-pass ( > II. PHASE-INSENSITIVE TARGETDETECTION USING NON-CLASSICAL LIGHT
In this section, we theoretically analyze the phase-insensitive target detection scheme using non-classical photon pairs. We compare its performance to a classicaltarget detection scheme with intensity (photon counting)detection. We quantify the performance of both theclassical and non-classical target detection schemesusing transmission estimation uncertainty and Fisherinformation as the FOM. In particular, we show thatthe enhancement obtained using non-classical light isdirectly related to the strong temporal correlation of thesource used.We consider a phase-insensitive target detectionscheme enhanced by non-classical photon pairs (probeand reference photons) that are generated in the semi-conductor waveguide. The scheme will be called classicaltarget detection using non-classical photons, or CDNC inthis article. The SPDC process is pumped by a CW laserto obtain strong temporal correlation between the probeand reference photons. For each generated photon pair,the reference photon is immediately detected on a single-photon detector (the reference detector) and the probephoton is directed towards the unknown object. If theobject is present, a small fraction of probe photons arereflected from the object impinging and detected with afinite efficiency at the second single-photon detector (theprobe detector). A controllable level of background noiseis always coupled onto the probe detector regardless ofthe presence of the object. We assume that the probephotons are indistinguishable from the background noisephotons in terms of their ‘local properties’, e.g., tempo-ral pulse shape and spectral distribution. Therefore it isnot possible to reduce the noise power through any clas-sical filtering technique (i.e. temporal gating, spectralfiltering or mode selection). The photon detection statis-tics from both detectors are recorded for estimating theprobe channel transmission, which is defined as the per-centage of probe photons (not including noise photons)that get back-reflected and detected on the probe detec-tor. If the estimated channel transmission is greater thanthe estimation uncertainty, the likelihood of the presenceof the unknown object increases proportionally. There-fore the uncertainty of the transmission estimation char-acterizes the sensitivity of this target detection system.For comparison, we consider a classical phase-insensitivetarget detection scheme using classical photons, whichwill be called, CDC in this text. CDC utilizes simplephoton counting, with no coincidences, as a means of de-tection. The classical probe photons are sent towardsthe object. The back-reflected photons from the object(none if the object is not present), together with thebackground noise photons are detected and recorded ona single-photon detector. Same as the CDNC scheme,the likelihood of the presence of the unknown object isincreased proportionally to the estimated channel trans-mission increase beyond the estimation uncertainty. Notethat the CDC scheme can be considered as a special caseof the CDNC scheme, where all the reference photonsare blocked. Therefore the same analysis of the CDNCscheme applies. This approach represents a more gen-eral and straight-forward classical phase-insensitive tar- get detection scheme compared to the previous schemesbased on classical intensity correlation of thermal light[7].The SPDC photon pair state generated in the waveguidecould be expressed as: | Ψ (cid:105) = | vac (cid:105) + (cid:90) ∞−∞ (cid:90) ∞−∞ φ ( t p − t r )exp( − iω p, t p − iω r, t r ) a † p ( t p ) a † r ( t r ) dt p dt r | vac (cid:105) (1)where φ ( t p − t r ) exp( − iω p, t p − iω r, t r ) is the joint tem-poral amplitude and ω p, , ω r, are the central frequenciesof the probe and reference photons. The creation opera-tor of the probe (reference) photon at time t is denotedby a † p ( t ) ( a † r ( t )). The intrinsic temporal correlation time∆ t of the SPDC photon pairs are defined as the stan-dard deviation of the detection time difference betweenthe probe and reference photons (assuming infinite de-tection temporal resolution):∆ t = ( (cid:90) + ∞−∞ dt p | φ ( t p − t r ) | (cid:82) + ∞−∞ | φ ( t (cid:48) p − t r ) | dt (cid:48) p ( t p − t r ) ) (2)It could be shown that ∆ t is inversely proportional tothe SPDC photon bandwidth[17]. In our implementa-tion the bandwidth is over 100 nm, which correspondsto ∆ t = 35fs(see Supplement 1 for the characterizationdetails). The output flux ν of the probe photons fromthe source is given by[18]: ν = tr { a † p ( t p ) a p ( t p ) | Ψ (cid:105) (cid:104) Ψ |} = (cid:90) + ∞−∞ | φ ( t p − t r ) | dt r (3)where tr stands for the trace over the joint Hilbertspace of the reference and probe photons. Note that ν is independent of time t p because the SPDC process ispumped using a CW laser. The output flux of the ref-erence photons is also given by ν since the probe andreference photons are always generated in pairs.The total transmission efficiency of the reference pho-tons η r is affected by the optical coupling loss and theinefficiency of the reference detector. The total transmis-sion efficiency of the probe photons η p is also affected bythe reflectivity of the target object and the collection ef-ficiency of the back-reflected probe photons. The flux ofthe noise photons that get detected on the probe detectoris denoted by ν b . Assuming the target detection systemto be time-invariant, i.e. stationary target, the absolutetime of photon detection events carries no informationabout the presence of the object. The only photon de-tection statistics of interest is the photon detection rateupon each detector as well as the coincidence detectionrate across both detectors. A coincidence detection eventis defined as a detection event on the reference detectorat time t r being followed by another detection event onthe probe detector at time t p , such that t p − t r lies withina small coincidence window: t p − t r ∈ [( l p − l r ) /c − T c , ( l p − l r ) /c + T c T c is the temporal width of the coincidence win-dow and l p , l r are the optical path length of the probe andreference photons. To ensure that every probe-referencephoton pair (not including noise-reference photon pairs)that is detected on the detectors could contribute to a co-incidence detection event, the coincidence windows T c istaken to be larger than the effective temporal correlationtime ∆ t eff : T c ≥ ∆ t eff = 2∆ t + 3∆ t (5)where ∆ t is the temporal resolution of both the probeand reference detectors. Then it could be shown thatthe coincidence detection rate is given by (see theSupplement 1 for the detailed derivation): P c = η r η p ν + η r ν b νT c (6)Define the rate of photon detection events on theprobe(reference) detector that do not contribute to co-incidence detection as P p ( P r ), then (see the Supplement1 for the detailed derivation): P r = η r ν − P c P p = ν b + η p ν − P c (7)The uncertainty of transmission estimation in theCDNC scheme and the CDC scheme could be quanti-fied using the classical estimation theory. We first needto model the probabilistic distribution of different pho-ton detection outcomes for an experiment that lasts fora time duration of τ . Let N p ( N r ) denote the numberof photon detection events on the probe (reference) de-tector that does not contribute to coincidence detectionand let N c denote the number of coincidence detectionevents. Because photon detection events at different timeare independent, we assume N p , N r and N c follow Pois-son distributions. Then the joint probability distribution p ( N p , N r , N c ; τ ) could be calculated from (6)(7): p ( N p , N r , N c ; τ ) = f ( N p , P p τ ) f ( N r , P r τ ) f ( N c , P c τ ) (8)where f ( N, λ ) = exp( − λ ) λ N N ! is the Poisson distributionfunction. The overall transmission of the probe photons η p , which parametrize the joint probability distribution p ( N p , N r , N c ; τ ), could be estimated from the actual pho-ton detection statistics N p , N r , N c through maximizingthe probability p ( N p , N r , N c ; τ ) by varying value of η p (the maximal likelihood estimation[16]). The uncertaintyof the transmission estimation is related to the Fisher in-formation I of η p contained in the probability distribu-tion p ( N p , N r , N c ; τ ), which is defined as: I = + ∞ (cid:88) N p ,N r ,N c =0 p ( N p , N r , N c ; τ )( ∂∂η p log p ( N p , N r , N c ; τ )) (9)= ( η r ν P c + (1 − η r ) ν P p + η r ν P r ) τ (10) Note that I has a removable singularity at η r = 0, whichcorresponds to the CDC scheme. Denote the maximallikelihood estimation of probe transmission as ˆ η p . Wechoose to quantify the transmission estimation uncer-tainty as the variance of transmission estimation. Thenthe total Fisher information I is related to the estimationvariance ∆ ˆ η p according to the Cram´er-Rao’s Bound[16]:∆ ˆ η p ≥ I (11)This minimal uncertainty is asymptotically achievablefor maximal likelihood estimation of η p in the limitof a large number of repeated experiments[19]. Sincethe Fisher information I scales linearly with respect toexperiment duration τ , the minimal estimation varianceis inversely proportional to the detection time τ . Thetransmission estimation criterion is a general figure ofmerit for phase-insensitive target detection since it couldbe applied to any target detection scheme and requiresno prior information about the target object.The performance enhancement of the CDNC schemeover the CDC scheme originates from the strong tem-poral correlation of the non-classical photon pairs.This could be seen in the explicit expression of Fisherinformation (10). The first term in the expressionrepresents the contribution of coincidence detection P c to the total Fisher information I and the last two termsrepresent the contribution of P p and P r , as indicated bytheir respective denominators. In the presence of strongbackground noise and a strong loss of the probe photons,the contribution of coincidence detection dominatesin the total Fisher information. This is because noisephotons will significantly increase P p but its influenceon the coincidence detection rate P c is limited by thesmall coincidence window T c . In another word, the noiseresilience of the CDNC scheme (which is defined as themaximal noise power ν b that can be tolerated to achievethe same target detection performance) scales inverselywith respect to T c , as could be seen in (7) and (10).Note that the minimal coincidence window T c , or theeffective temporal correlation time ∆ t eff , is dictated bythe detector temporal resolution ∆ t and the intrinsictemporal correlation time ∆ t .The ability of ranging is another advantage offered bythe CDNC scheme, which utilizes the strong temporalcorrelation of the non-classical photon pairs. This couldbe seen from the fact that the coincidence detectionhistogram( N c versus t p − t r ) that is recorded during theexperiment will peak at the position that corresponds tothe time of flight difference between the probe photonand the reference photon. To be more specific, in theCDNC scheme, the number of coincidence detectionevents N c is a function of l p (the hypothetical targetdistance) as could be seen in (4). Since N c ( l p ) will peakaround the actual value of probe path length, so will theestimated transmission ˆ η p as a function of l p . As a con-sequence, the actual target distance could be estimatedfrom the peak position of ˆ η p ( l p ) during the post dataprocessing. In comparison, ranging is not possible usingCW sources in CDC schemes, since the detected sig-nal N p contains no information about the target distance. III. EXPERIMENT AND RESULT
The experimental setup of the CDNC scheme is shownin Fig. (1). The GaAs waveguide source is based on aBragg-AlGaAs structure [11] which has a ridge widthof 5 µ m and length of 1 mm. The Bragg mode ofthe waveguide is pumped using a CW source with awavelength of 783 nm. It generates photon pairs with1566nm central wavelength through the type II SPDCprocess. The SPDC conversion efficiency is estimatedto be 2.1 × − (photon pairs/pump photon) [11]. Thephoton pair generation rate is around 4MHz for around500 µ W pump power ( (cid:39)
10% pump power is coupledinto the waveguide). The bandwidth of the SPDCphoton pairs is estimated to be at least 100 nm whichcorresponds to the intrinsic temporal correlation time∆ t (cid:39) ≈ ν b and low probe photon flux ν regime. Thevariance ratio between the CDC and CDNC schemesas a function of noise and source power reaches upto 21.36 dB, 26.3 dB respectively, corresponding to ameasurement time reduction by a factor of 137 and 430.At the highest environment noise level (right side of theFig. (2a) ), the CDNC scheme has performance equal to the CDC scheme with 21.6 dB less noise. At theexperiment point of highest variance ratio in Fig. (2b),the background noise flux detected is 36 dB strongerthan the detection rate of the actual probe photons(128 Hz). Each data point in the figure corresponds to99 independent estimation experiments of τ = 300ms.The estimation variance ∆ ˆ η p is given by the varianceof 33 independent estimations (the additional factorof 3 contributes to the error bar in Fig. (2) ). Theresult of every single estimation is obtained through themaximal likelihood estimation using the experimentallyrecorded photon detection statistics. We confirmed thatthe estimation result of the CDNC and the CDC schemeagrees reasonably when averaged over a large numberof independent estimations. The maximal CDNC toCDC discrepancy (the difference between the estimatedtransmission of CDNC and CDC scheme averaged over99 estimations) is less than 15%. The theoretical lowerbound curve of the estimation variance in Fig. (2c) and(2a) is calculated according to the definition of Fisherinformation (9) and the Cram´er-Rao’s Bound, usingthe values of parameters µ, η p , η r extracted from thephoton detection data over a much longer period(30s).The measured points and the theoretical lower boundare in close agreement, suggesting that the maximallikelihood estimation of η p approaches the bound ofthe minimal estimation uncertainty. It is worth notingthat the performance of the CDNC scheme is severelylimited by the inefficient transmission η r <
20% of thereference photons, which is due to the modal mismatchbetween the mode of the waveguide and the fundamentalmode of the fiber. The performance of the experimentalCDNC scheme is also limited by the temporal resolution∆ t (cid:39)
100 ps of the detectors. In Fig. (2a)-(2d) it isalso shown that the performance of the CDNC schemedepends strongly on the temporal coincidence window T c , which is limited by the effective temporal correlation∆ t eff . Since no coincidence detection is involved in theCDC scheme, the temporal resolution of the detector isnot relevant to its performance.We also conduct a ranging experiment based on theCDNC scheme, with the result shown in Fig. (3). Thetarget object is placed at different positions along theoptical axis of the collection optics to simulate differenttarget distance. In order to increase the maximal detec-tion range, we use a piece of aluminum foil that has ahigher reflectivity than paper as the object for the rang-ing experiment. For each position of the target object,the alignment of the collection optics and output colli-mator of the probe photons are fine-tuned to maximizethe collection efficiency of the probe photons. To deter-mine the distance of the target object, the transmissionestimation ˆ η p is calculated for different values of l p . Theestimated probe path length is taken to be the value of l p that maximize the transmission estimation ˆ η p ( l p ). Thedistance of the object is calculated from the estimatedprobe optical path length based on the geometrical lay- (a) noise pho on flux ν b (Hz) -100-95-90-85-80-75-70 e s i m a i o n v a r i a n c e Δ Δ ̂ η p ( d B ) C l a s s i c a l T c ̂ Δ 0 n s T c ̂ Δ n s T c ̂ Δ 0 0 p s T c ̂ Δ0ps (b) noise photon flux b (Hz) q u a n t u m a d v a n t a g e ( d B ) T c = 20ps T c = 200ps T c = 2ns T c = 20ns (c) probe photon flux ν (Hz) -90-80-70-60-50-40 e t i m a t i o n v a r i a n c e Δ ̂ η p ( d ̂ ) T c Δ 20p T c Δ 200p T c Δ 2n T c Δ 20n Cla ical (d) probe photon flux (Hz) q u a n t u m a d v a n t a g e ( d B ) T c = 20ps T c = 200ps T c = 2ns T c = 20ns FIG. 2: (a) Experimentally measured (error bar) and theoretically predicted (solid line) estimation variance ∆ ˆ η p ofthe CDNC (orange) and CDC (black) scheme as a function of the noise flux ν b with η p = 3 . × − and η r = 17 . ν = 3 . ν b . The CW pumppower is around 500 µ W. Theoretical curves that correspond to the CDNC schemes with different coincidencewindow T c is also plotted in different colors. (b) The ratio between the estimation variance ∆ ˆ η p of the CDNC andCDC scheme as a function of noise flux in (a). (c) Experimentally measured (error bar) and theoretically predicted(solid line) estimation variance of CDNC and CDC scheme as a function of source probe flux ν with η p = 8 . × − and η r = 17 .
4% and ν b = 0 . ν . The CW laser power is swept between zero and 1000 µ W. Theoretical curves that correspond tothe CDNC schemes with different coincidence window T c is also plotted in different colors. (d) The ratio between theestimation variance ∆ ˆ η p of the CDNC and CDC schemes in (c). The error bar of the plot (a) and (c) is obtainedby calculating the standard deviation of the averages of the 3 different groups of 33 independent estimations.out of the optical system. The uncertainty of the targetdistance is calculated from the full-width half maximumof the function ˆ η p ( l p ) versus l p . The ˆ η p calculated fromthe data as a function of l p is also shown in Fig. (3).The result shows that even in the presence of dominat-ing background noise, the distance of the target objectcould be determined with reasonable accuracy of ≈ t of the de-tectors. The ranging performance is also closely relatedto the target detection performance that has been dis-cussed above: the maximal ranging distance is limited tothe position where the estimated transmission efficiency ˆ η p is comparable to the estimation uncertainty. IV. DISCUSSIONA. Comparison to intensity correlation-basedschemes
The key difference between the presented CDNCscheme and the previously reported intensity correlation-based schemes[7][8] is utilizing temporal correlation tosubstantially and scalably improve the performance d i s t a n c e ( r a n g i n g ) ( m ) t r a n s m i ss i o n e s t i m a t e ̂ η p probe round-trip path length ̂m) probe round-trip timêns) FIG. 3: Top: estimated object distance (y-axis) versusthe physically measured target distance (x-axis). Rederror bar plot: the estimated object distance and itsuncertainty. The uncertainty of the distance estimationis taken to be the FWHM of the ˆ η p versus l p function.Grey solid curve: the reference curve y = x . In order toincrease the ranging range, aluminum foil is used as theobject for higher reflectivity. When the target is placedaround 0.85 m away, the probe photon detection rate νη p is 26 Hz and the noise photon detection rate ν b is41.6 KHz. Bottom: estimated ˆ η p as a function of proberound-trip path length. The 5-part panel from top tobottom correspond to physical target distance of 13, 32,53, 68, 85 cm, respectively.of phase-insensitive target detection. In intensitycorrelation-based schemes, the reference and probe pho-tons are generated in discrete pairs of pulses and only thecorrelation between the number of the probe and refer-ence photons within each pulse pair is used to enhancethe target detection performance. However, there is afundamental limit in intensity correlation enhancementas the enhancement diminishes as one increases the probepower[8]. As a result, there is a trade-off between correla- tion enhancement and target detection performance. Un-like the intensity correlation-based schemes, the perfor-mance enhancement of the CDNC scheme originates fromthe strong temporal correlation within the non-classicalphoton pairs and is therefore much more scalable. Forthe CDNC scheme, the amount of temporal correlationthat could be utilized for target detection is character-ized by the effective temporal correlation time ∆ t eff . Inthe current implementation, ∆ t eff is severely limited bythe detector temporal resolution ∆ t (cid:39) t (cid:39) not fundamental. First of all, it is possible to achieve abetter detector temporal resolution with improved single-photon detection technology. For example, if the detectortemporal resolution could be improved to ∆ t = 15ps[20],the noise resilience of the CDNC scheme (which is in-versely proportional to the effective temporal correlationtime ∆ t eff ) could be further enhanced by a factor of 7.More importantly, even with commercially available de-tectors (∆ t (cid:39) (cid:39) t , which is the fundamentallimiting factor of the CDNC scheme performance, couldbe improved with different SPDC waveguide structuredesigns [13]. B. Covert operation with the CDNC scheme
The previous sections have shown the significant per-formance advantages of the CDNC scheme over the CDCscheme in a lossy and noisy environment as quantifiedby the transmission estimation/Fisher information crite-rion. However, it is important to note that the perfor-mance enhancement of the CDNC scheme is based on akey assumption we made about the property of the back-ground noise: namely we assumed that the backgroundnoise photons are indistinguishable from the probe pho-tons in terms of their spectral and temporal distribution,i.e., CW and broadband. This assumption is valid for theCDNC scheme for the following reasons. First, it is rea-sonable to assume that the environmental noise is CW,the same as the SPDC probe light. Second, the spectrumof the SPDC probe photons could be tailored to matchthat of the noise photons through different waveguidestructure designs[13]. Third, in some covert detection ap-plication, it may be desirable to deliberately inject noisepower that is indistinguishable from the probe light suchthat the signal to noise ratio for the un-authorized re-ceivers is minimized. However, for the CDC schemes, it ispossible to reduce the in-band noise power through tem-poral or spectral shaping of the probe light. For example,one could utilize pulsed or monochromatic light instead ofCW broadband light to probe the target object, such thatthe spectral-temporal overlap between the probe and thenoise light is minimized. (see Supplement 1 for the de-tailed analysis) Nevertheless, the temporal or spectralconcentration of optical energy will increase the distin-guishability between the probe photon and the noise pho-ton, hence increase the visibility of the target detectionchannel and its vulnerability to active attacks. Althoughclassical scrambling techniques such as frequency scram-bling could help hide the probe light under the disguiseof background noise, such indistinguishability betweenprobe and noise photons is not guaranteed by fundamen-tal principles of physics. The CDNC scheme, on the otherhand, could offer unconditional indistinguishability be-tween the probe and the background noise photon. Thisis because each probe photon in the CDNC scheme is gen-erated at a truly random time and frequency[21]. Fromthis standpoint, the CDNC scheme is an analogue of thequantum noise radar[22] where the probe and the refer-ence signal are completely random but correlated. Covertranging is one example of the stealth operation propertyof the CDNC scheme. Classical optical ranging systemstypically use time-variant optical signal such as pulsedlight to probe the target object. This is because the time-invariant back-reflected signal contains little informationabout the target distance. However, time-variant probelight that is distinguishable from the CW backgroundnoise will make the ranging channel visible, hence vulner-able to active attacks. On the other hand, in the CDNC scheme, the probe light generated is time-invariant andindistinguishable from the background noise for an unau-thorized receiver. Yet the distance of the object to bedetected could still be calculated from detected temporalcorrelation statistics.
V. CONCLUSION
We demonstrated a phase-insensitive target detec-tion scheme enhanced by non-classical light generatedin a semiconductor chip source. We quantified theperformance of both the enhanced and classical targetdetection schemes with the estimation uncertainty andthe Fisher information of the probe photon transmis-sion. We showed that the strong temporal correlation ofnon-classical photon pairs could be utilized to enhancethe target detection performance by up to 26.3 dBin a lossy and noisy environment, which is equivalentto a reduction of target detection time by a factor of430. Such performance enhancement is highly scalablewith improved photon detection temporal resolution orimproved photon detection techniques. We also showedthat this enhanced scheme could be used for rangingwith CW source in a lossy and noisy environment. Dueto the enhanced performance and the phase-insensitivenature, this non-classical source enhanced target detec-tion scheme with semiconductor chip sources could findits application in many real-world sensing scenarios.See Supplement 1 for supporting content. 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