1. Introduction

Quantum states of light can enhance optical imaging beyond the capabilities of classical physics [1,2]. Entangled or correlated photon pairs are readily produced using spontaneous parametric down conversion (SPDC), and have therefore been used to enable a variety of quantum-enhanced imaging methods [3]. Examples include the use of entanglement to increase the signal-to-noise ratio (SNR) in phase and intensity imaging, and spatial correlations to improve imaging resolution or robustness to stray light [4–7]. The unique capabilities of these imaging methods have attracted wide attention from the biomedical and industrial sectors [8,9]. For example, biomedical analysis often requires imaging sensitive biological samples, including live cells and organisms, which can be altered or even damaged if the illumination brightness is too high [10–13]. However, such detrimental effects can be avoided with quantum techniques, which are able to provide precision measurements using fewer photons compared to classical imaging [1,14]. Industrial applications of imaging entangled photon pairs include enhanced sensitivity in pattern recognition and process control, as well as materials spectroscopy [15–17].

Two key aims in developing quantum imaging systems are speed and practicality, both for real-world applications, as well as proof-of-principle advances. For practicality, complementary metal–oxide–semiconductor (CMOS) compatible single photon avalanche diode (SPAD) image sensor array (ISA) cameras represent the most important recent advance, as they enable wide-field (i.e. without need for pixel-scanning) low-noise photon pair imaging in a mass-producible compact form factor, without requiring active cooling [18]. On the other hand, the speed of quantum imaging with SPDC photon pairs is at present far lower than in classical counterparts, limiting many quantum-enabled improvements to academic interest. In Ref. [4] we identified two main factors as the cause of current low imaging speeds: low photon detection efficiency (PDE) in SPAD-ISAs for photon pairs at the common near-infrared (NIR) SPDC emission wavelength (typically ${\sim }$800 nm), and low detector duty cycle.

Here, we address the first of the two aforementioned issues, and show that short-wavelength SPDC is an enabling technology for fast and practical quantum imaging. Fabrication of mass-scalable SPAD-ISAs must adhere to standard CMOS processes, resulting in very few customizable design parameters. In particular, a limited thickness of SPAD photon absorption regions presents a fundamental barrier to achieving high PDE at NIR wavelengths [19]. On the other hand, CMOS SPAD-ISA efficiencies peak in the green visible wavelength range, and can be even further optimized to approach the values of other image sensor technologies [20,21]. In this work, we take advantage of this, and demonstrate a quantum imaging system using a recently developed green visible-wavelength (532 nm) entangled photon pair source (EPS), generating hyperentanglement in polarization and space [22]. This visible-wavelength EPS (VEPS) is combined with a compact and stable, large field-of-view (${\sim }4\times 4 \mathrm {mm}^2$) phase imager to perform supersensitive phase imaging [4]. We show that our VEPS-enabled quantum imaging scheme is able to accurately retrieve the features of two test samples – an electron-beam evaporated silica pattern on glass, and a protein microarray. These measurements illustrate our technique’s potential applicability to real-world uses, as imaging nanometer-scale height steps has important applications in semiconductor metrology [23], while protein microarrays represent a widely used biomedical diagnostic tool [24]. Introducing a phase sensitivity calculation independent of sample spatial features, we show the supersensitivity of our quantum imaging scheme which yields an increase in SNR by a factor of $1.351 \pm 0.004$. This is close to the theoretically predicted $\sqrt {2}\approx 1.414$ enhancement. Compared to imaging with the widely used ${\sim }$800 nm EPS, for our two samples, our VEPS enabled speedups by a factor of 39, and 60, respectively. This is consistent with our SPAD-ISA’s ${\sim }5.3{-}9.5$-fold PDE increase from the NIR to 532 nm, that is, corresponding to a ${\sim }28{-}90$ times higher coincidence efficiency [20].

2. Entanglement-enhanced imager

Our wide-field quantum imaging platform is optimized for the measurement of large area transparent samples. Similarly to our previous work Ref. [4], we perform wide-field quantum-enhanced imaging by using space-polarization hyper-entangled photon pairs, which probe a sample held in a large field-of-view (FoV) interferometric microscope (LIM). Photons are detected by a commercially available SPAD-ISA from Micro Photon Devices, which uses the SPAD array from Ref. [20]. This camera has pixel pitch ${150}\;\mathrm{\mu}\textrm {m}$, features a micro-lens array to enhance its pixel fill factor to 78%, and has PDE of ${\sim }35{\pm }3\%$ at 532 nm, compared to ${\sim }5{\pm }1\%$ at 810 nm. Phase information about samples is retrieved through the use of digital holography methods, which, in contrast to conventional interferometry, allows calculating phases without requiring a priori knowledge about sample absorbance and illumination brightness [25–27].

2.1 Visible-wavelength hyper-entanglement illumination

As can be seen in Fig. 1(a), hyper-entangled photon pairs are generated in our setup by spontaneous parametric down conversion, using a recently developed crossed-crystal geometry VEPS [22]. The collimated pump laser at 266 nm (Toptica TopWave, CW, linewidth ${<1}\;\textrm {MHz}$) is prepared in the diagonal polarization $|{D}\rangle \equiv (|{H}\rangle + |{V}\rangle )/\sqrt {2}$, where $H$($V$) is the horizontal (vertical) polarization, and then passes through four barium borate (BBO) crystals sequentially. In the first (second) BBO crystal, 532 nm wavelength photon pairs are generated by SPDC with $H$($V$) polarization. The third and fourth BBO crystals compensate spatial walk-off between the two SPDC processes, a band-pass filter (BPF) then removes the pump, and an yttrium vanadate (YVO4) crystal is used for temporal compensation. This leaves the polarization-entangled state $(|{HH}\rangle +|{VV}\rangle )/\sqrt {2}$, that is, a two-photon N00N state in polarization modes.

 

Fig. 1. (a) Entanglement-enhanced imaging setup, 266 nm pump in violet, and entangled photon pair emission centered at 532 nm in green shading. HWP, half-wave plate; BBO, barium borate crystal (first pair for SPDC, second pair for compensation); BPF, band-pass filter; YVO4, yttrium vanadate crystal; L, lenses with focal lengths $f_1 = {100}\;\textrm {mm}$ for $\mathrm {L}_1$, $f_2 = {1000}\;\textrm {mm}$ for $\mathrm {L}_2$, $f_3 = f_4 = {200}\;\textrm {mm}$ for $\mathrm {L}_3$, $\mathrm {L}_4$; SP, Savart plate; dPBS, lateral displacement polarizing beam splitter. (b) Detecting nonbirefringent sample height steps with the LIM. Example trajectories through the LIM: dashed lines, $H$; dotted lines, $V$. (c) N00N state interference integrating across whole camera. (d) N00N state interference with a single fixed pixel. For (c) and (d): red crosses, $\langle {DA}|$; blue circles, $\langle {DD}|$; green diamonds, $\langle {AA}|$ projections. Solid lines are fitting curves. Note that projections $DA$ and $AD$ are identical and indistinguishable from each other ($|\langle {DA|\Psi }\rangle |^2 = |\langle {AD|\Psi }\rangle |^2$; i.e., one photon on each SPAD-ISA half) and are together represented by $DA$. $AA$ and $DD$ may contain two photons on the same pixel, which cannot be resolved as coincidence. Thus, the maximum of $DA$ is larger than twice the maximum of $AA$ and $DD$.

Download Full Size | PDF

The SPDC near-field is imaged onto the sample in the LIM, and then re-imaged onto the SPAD camera sensor, using two pairs of lenses in 4f configuration (see Fig. 1(a)). Because the VEPS is based on bulk crystal SPDC, photon pairs in the near-field plane are spatially correlated (approximately in the same position) [28,29]. This property, combined with the polarization entanglement, therefore provides a hyper-entangled state at the sample and detection planes, which can be expressed as $|{\Psi }\rangle (\mathbf {r}) \approx \sum _{\mathbf {r} , \mathbf {r'}} (|{HH}\rangle _{\mathbf {r,r'}}+\mathrm {exp}(i 2\Theta (\mathbf {r}))|{VV}\rangle _{\mathbf {r,r'}} )$. Here, we neglect normalisation coefficients for clarity, $\Theta$ represents the spatially dependent phase difference between $H$ and $V$ induced by the LIM and sample in each photon, and $\mathbf {r}$ and $\mathbf {r'}$ are the transverse coordinates of the two spatially correlated photons. The two photons are close in space ($\mathbf {r} \approx \mathbf {r'}$) and thus acquire approximately the same phase ($\Theta (\mathbf {r}) \approx \Theta (\mathbf {r'})$), that is, the two-photon entangled state $|{\Psi }\rangle$ acquires a total phase factor of $2\Theta (\mathbf {r}) \approx \Theta (\mathbf {r}) + \Theta (\mathbf {r'})$.

A half-wave plate (HWP) and a lateral displacement polarizing beam-splitter (dPBS) project the state $|{\Psi }\rangle$ into the diagonal polarization measurement bases $|{DD}\rangle$, $|{AA}\rangle$, and $|{DA}\rangle$ before the SPAD-ISA. Here, $|{A}\rangle \equiv (|{H}\rangle -|{V}\rangle )/\sqrt {2}$ denotes the anti-diagonal polarization. Note also that light is spatially filtered in the far-field after the VEPS with a ${2.5}\;\textrm {mm}$ aperture. This reduces the photon pairs’ momentum distribution in order to minimize k-vector-dependent phase distortion inherent in crossed-crystal EPS designs [30].

2.2 Interferometric microscope

The LIM can be used to inspect ultra-small height steps in large area material and biological samples such as microarrays of proteins or micro-organisms for diagnostic applications [31,32]. As illustrated in Fig. 1(b), the LIM is composed of two Savart plates (SPs; $SP_{1}$ and $SP_{2}$), where a non-birefringent target sample is placed between them. For an input beam, $SP_{1}$ laterally displaces the $H$ and $V$ components of $|{\Psi }\rangle$, introducing a shear ($\mathbf {S}$) between the two polarizations. This shear is then reverted by the oppositely oriented $SP_{2}$, effectively forming a Mach-Zehnder interferometer (MZI) for each lateral spatial location, with displacement $\mathbf {S}$ between the MZI modes. Motorized pitch tilting on $SP_{1}$ induces a controllable offset phase $\alpha$ between $H$ and $V$, while the spatially dependent variations of the sample height induce an additional optical path difference (OPD). The combined effect of the LIM on every photon is therefore to introduce the following phase between $H$ and $V$:

2.3 Imaging entanglement with SPAD-ISA

We can extract spatially resolved two-photon coincidences, $\mathrm {cc}$ between any two arbitrary pixels $i$ and $j$, using a large number ($>10^7$) of intensity image frames acquired by a SPAD-ISA [33,34]. The coincidences calculated from the $p^{\mathrm {th}}$ to the $q^{\mathrm {th}}$ intensity frame of an acquisition are given by:

As in Ref. [4], we use position-correlation based filtering to remove spatially uncorrelated noise in the measured quantity $\mathrm {cc}(i,j,p,q)$ given by Eq. (2). This processing step involves fitting a Gaussian model to $\mathrm {cc}(i,j,p,q)$ for every $i^{\mathrm {th}}$ pixel, characterising the maximum probable distance between real photon pair detection locations, and discarding all coincidences between more separated pixel pairs. We trace out the detection coordinates of one of the two photons to convert the filtered four-dimensional coincidence count quantity into a two-dimensional coincidence image $\mathrm {ci}_{pq}(x,y)$, according to

In order to quantify the entanglement of our probe state $|{\Psi }\rangle$, we measured the coincidence interference visibility by monitoring Eq. (3) for different phase offsets $\alpha$. Figure 1(c) shows the coincidences integrated across the whole SPAD-ISA, that is, $\sum _{x,y}\mathrm {ci}_{pq}(x,y)$ for each $\alpha$. On the other hand, Fig. 1(d) plots the coincidences for one fixed pixel, that is, a single coincidence image pixel as calculated by Eq. (3). Both results show two interference periods as the applied phase increases to the SPDC photon’s wavelength, rather than a single period as in classical optics, manifesting therefore the expected phase superresolution effect characteristic of N00N states [14,35]. However, while the fitted visibility of the single pixel coincidence curve (Fig. 1(d)) is $\mathcal {V_{\mathrm {local}}} = 0.96\pm 0.03$, indicating high local fidelity with the ideal theoretical state $|{\Psi }\rangle$, the integrated coincidence curve (Fig. 1(c)) shows a lower visibility of $\mathcal {V_{\mathrm {overall}}} = 0.75\pm 0.02$. This discrepancy in visibilities is evidence of a spatially dependent phase background across the N00N state wavefront, which we measure and remove when imaging samples.

We can take advantage of the LIM’s controllable offset $\alpha$ to retrieve the phase induced by the sample, through the use of phase-shifting digital holography (PSDH). For a N00N state with $N$ entangled photons, this involves acquiring four $N$-photon coincidence images $\mathrm {ci}_{pq}(\mathbf {r}, \alpha )$ at respective offset phases $\alpha = \{0, \pi /(2N), \pi /N, 3\pi /(2N)\}$. The phase is then calculated according to [26]

3. Accurate phase imaging of test samples

To demonstrate the fast and accurate quantum-enhanced imaging capability of our system, we measured two test samples representative of possible use cases. First, we acquired a phase image of a silica test sample, and confirmed the accuracy of our quantum-enhanced step height estimation using an atomic force microscope (AFM) scan. Second, we demonstrated the potential applicability of our platform in the biomedical field, by imaging a protein microarray sample. Samples were illuminated with our VEPS, and coincidence images detected with the SPAD camera, to calculate sample phase according to Eq. (4).

3.1 Silica test sample

A silica test sample was fabricated in-house, by electron-beam evaporating silica steps of controlled height onto a borosilicate glass substrate, in the shape of the word “ICFO” as shown in Fig. 2(c). The phase image of this silica test sample, retrieved from N00N state interference, can be seen in Fig. 2(a), where the letters “ICFO” can readily be made out. As illustrated in Fig. 1(b), when using the LIM to measure a non-birefringent sample, the retrieved phase contains a positive and negative double-image, which is clearly visible in Fig. 2(a). In Fig. 2(b) we plot the $x$ cross-sections along all rows in the area defined by the black rectangle in Fig. 2(a), where again the positive and negative steps in phase measured are clearly visible.

 

Fig. 2. Quantum-enhanced phase imaging using visible-wavelength EPS. (a) Entanglement-enhanced phase image of silica sample. (b) Cross-sections in $x$ direction of the area defined by black rectangle in (a). For the blue and orange shaded regions respectively, subtracting the mean of the right from the left regions, yields the experimental estimate of the phase induced by the sample. (c) AFM image of sub-section of test sample, showing jump in height from substrate to step. (d) Average cross-section of AFM image in (c). (e) Entanglement-enhanced phase image of protein microarray sample. (f) and (g) $x$ cross-sections along upper and lower dashed black lines in (e), respectively. (h) Bright classical illumination reference phase image of protein microarray sample. Colour scale the same as in (e). (i) and (j) $x$ cross-sections along upper and lower dashed black lines in (h), respectively. Scale bars in (a), (e), (h), 1 mm both at sample and camera sensor plane.

Download Full Size | PDF

Figure 2(a) shows the phase induced by the sample $\hat {\phi } = \mathrm {OPD}_{\mathrm {exp}}/(\lambda /2\pi )$, expressed in radians. For Fig. 2(b), we used Eq. (1) to convert $\hat {\phi }$ to the height difference $\Delta \text {Height} = h(\mathbf {r} + \mathbf {S}/2)- h(\mathbf {r} - \mathbf {S}/2)$, in terms of nanometers. This required the refractive indices of silica and air at 532 nm, $n_{\mathrm {Sample}} = 1.46$ and $n_{\mathrm {Air}} = 1.00$ [36]. Taking the difference between, respectively, the mean of the $\Delta \text {Height}$ values in the upper blue and orange shaded regions with the average of the $\Delta \text {Height}$ values in the lower blue and orange shaded regions in Fig. 2(b), gives an experimental estimate the sample feature step height of $h_{\mathrm {exp}} = 44 \pm {8}\;\textrm {nm}$. We confirmed the sample step height with a reference AFM measurement, as shown in Fig. 2(c) and (d), where Fig. 2(c) illustrates the region on our sample scanned by the AFM as well as the AFM, and Fig. 2(d) the cross-section showing clearly the jump in sample height at the feature step. Taking the difference between the mean heights of the two grey shaded regions in Fig. 2(d), we obtain the reference AFM measurement of the silica sample step height $h_{\mathrm {ref}} = 44.7 \pm {0.4}\;\textrm {nm}$. Our quantum-enhanced imaging system was therefore able to retrieve the sample feature height with a high degree of accuracy, thereby confirming its suitability for material science inspection tasks of transparent samples involving nanometer-scale variations in structure height.

The acquisition time for obtaining the image in Fig. 2(a) was ${1200}\;\textrm {s}$, and with a total number of detected coincidences of $7.2\times 10^5$ this corresponds to a coincidence detection rate of $6.0\times 10^2$ $\mathrm {s}^{-1}$. In contrast, the fastest acquisition in Ref. [4] counted $1.55\times 10^6$ coincidences over a total measurement time of 28 hours, corresponding to a coincidence detection rate of $1.5\times 10^1$ $\mathrm {s}^{-1}$. Therefore, our VEPS enabled a 39-fold increase in quantum-enhanced imaging speed compared to Ref. [4].

3.2 Protein microarray test sample

The second sample measured was a microarray of protein spots, similar to clinical microarray assays, in which different capture antibodies are spotted onto a substrate, where each spot binds with a specific disease biomarker or microrganism [24,37]. Therefore, optically detecting changes in signal for all the microarray spots enables biomedical applications such as disease detection. Phase imaging, which does not require sample labelling as in fluorescence imaging, has only recently begun to be used in microarray evaluation [31,32,37], and it has not been systematically studied which illumination intensities can adversely affect measurement accuracy. That is, minimizing the number of photons probing a sample may become a requirement in evaluating microarrays. Therefore, accurate quantum-enhanced imaging in this case demonstrates our system’s potential applicability to biomedical use cases. The microarray test sample was fabricated in-house,spotting Recombinant Protein A/G (Thermo Fisher Scientific, 21186, used for preparing a variety of microarray probes) solution diluted to ${250}\;\mathrm{\mu}\textrm {g}/\textrm {mL}$ onto glass slide. A phase image of this sample, retrieved from N00N state interference, can be seen in Fig. 2(e), where several protein spots can readily be made out. Cross-sections of the phase image along dashed lines in Fig. 2(e), shown in Fig. 2(f) and (g), also confirm the detection of individual protein spots. Unlike for the silica test sample, it was not possible to confirm phase measurements of the mechanically fragile microarray using an AFM. We therefore acquired a reference image with bright classical illumination (i.e., using many more photons than for Fig. 2(e)), which is shown in Fig. 2(h). Comparing Fig. 2(h), and cross-sections in Fig. 2(i) and (j), with the corresponding entanglement-enabled images Figs. 2(e)-(g) clearly confirm the accuracy of our quantum-enhanced imaging system.

The image in Fig. 2(e) was obtained over a total acquisition time of ${3600}\;\textrm {s}$, and is made up of $3.3 \times 10^6$ detected coincidences, corresponding to a coincidence detection rate of $9.2\times 10^2$ $\mathrm {s}^{-1}$. Therefore, compared to the coincidence detection rate of $1.5\times 10^1$ $\mathrm {s}^{-1}$ in Ref. [4], our VEPS-illuminated imager again enabled a huge improvement in quantum-enhanced imaging speed, by a factor of 60.

4. Supersensitivity of phase imaging

In order to prove super-sensitivity of our entanglement-enhanced phase imaging results, we extend the method from Ref. [38] to the imaging domain. This yields an empirical measure of phase uncertainty for every pixel, which can be compared to the theoretically expected noise of an ideal classical measurement with an equal number of photons.

The PSDH formula Eq. (4) ($N=2$) retrieves the phase from coincidence images calculated using the $p^{\mathrm {th}}$ to the $q^{\mathrm {th}}$ intensity frame of a SPAD-ISA acquisition. Therefore, a total $M$-frame acquisition can be subdivided into $Q$ sub-acquisitions, by setting $(p,q) = [(1,M/Q), (M/Q+1,2M/Q),\ldots,((Q-1)M/Q+1,M)]$. This yields $Q$ different $\hat {\phi }_{pq}$ phase estimates, each calculated from $M/Q$ camera frames. We then compute the standard deviation over these sub-acquisition retrieved phase images, to obtain $\mathrm {sd}(\hat {\phi }(\mathbf {r}, Q))$, which is an empirical measure of the uncertainty in retrieved phase for each pixel.

In order to prove that our visible-wavelength entanglement-enhanced method enables supersensitive phase imaging, we show that $\mathrm {sd}(\hat {\phi }(\mathbf {r}, Q))$ is lower than the retrieved phase uncertainty of a perfect classical measurement acquired using the same number of photon detections. For a given $Q$, the mean number of photons used per sub-acquisition on a given pixel is $I_{\mathrm {tot}}(\mathbf {r},Q) = (2/Q)\sum _{j=0}^3 \mathrm {ci}_{pq}(\mathbf {r}, \alpha = j\pi /4)$, that is, summing over all four offset-phase settings, and multiplying by two as as each coincidence consists of two single photons. To calculate the uncertainty of an ideal classical PSDH phase measurement, we assume shot noise limited intensity detection and perfect interference visibility, and use the error propagation formula $\mathrm {sd}(f) = \sqrt {\sum _j ( (\partial f/\partial x_j)^2 \mathrm {sd}(x_j)^2 )}$ [39]. In the case of ideal classical imaging with the LIM, $D$-polarized classical light is used for illumination, projected into $|{D}\rangle$ and $|{A}\rangle$ bases before the camera, resulting in detected intensities of $I_D = (\cos (\Theta (\mathbf {r}))+1)I_0/2$ and $I_A = (-\cos (\Theta (\mathbf {r}))+1)I_0/2$, respectively [4,31]. Here $I_0$ is the input intensity, $\Theta$ is defined by Eq. (1), and the uncertainties in these measurements are simply $\sqrt {I_D}$ and $\sqrt {I_A}$ due to shot noise. The retrieved phase is calculated using Eq. (4) with $N=1$, and the error propagation formula is used to numerically compute $\mathrm {sd}(\hat {\phi }_{\mathrm {class}})$, the theoretical phase uncertainty of an ideal classical measurement. We compare to the quantum enhanced measurement’s experimental uncertainty value, for a given pixel and number of sub-acquisitions $Q$, by setting $4I_0 = I_{\mathrm {tot}}(\mathbf {r},Q)$.

We performed this analysis, dividing into $Q = \{16, 32, 64, 128\}$ equally sized sub-acquisitions. Figure 3(a) shows $\mathrm {sd}(\hat {\phi }(\mathbf {r}, Q))$ for three example pixels, where the x-axis value for each data point is $M(\mathbf {r}, Q)$, the number of photons used. The dashed line represents the phase uncertainty from an ideal classical measurement ($\mathrm {sd}(\hat {\phi }_{\mathrm {class}})$), while the solid line represents the theoretical uncertainty from a perfect 2-photon N00N state PSDH measurement, both as a function of the number of photons used. Clearly the empirically derived uncertainties, as shown in Fig. 3(a), are lower than the classical bound, therefore indicating supersensitivity of the phase measurement. Error bars in Fig. 3(a) represent the statistical standard error, due to calculating standard deviation from a finite sample size. In Fig. 3(b) we show the spatially resolved enhancement in phase imaging afforded by our entanglement-enabled method. That is, using $Q=64$ sub-acquisitions, for every single pixel, Fig. 3(b) plots the experimental phase uncertainty $\mathrm {sd}(\hat {\phi }(\mathbf {r}, Q))$ divided by the theoretical noise of an equivalent perfect classical measurement. A value below 1 in this noise reduction is therefore evidence of phase supersensitivity, which in Fig. 3(b) is represented by a blue pixel colour, showing that our system achieved supersensitivity over practically the entire FoV. We attribute the region of higher experimental noise in the bottom right corner to the presence of stray light hitting the sensor there. Figure 3(c) shows a cross-section along the yellow dashed line in Fig. 3(b), where the shaded area represents the statistical standard error, again due to calculating standard deviation from a finite sample size. Figure 3(c) clearly shows again the reduction in phase measurement noise of our system with respect to an ideal classical measurement, with a reduction close to the theoretically expected value of $1/\sqrt {2}$. By taking the mean over the area defined by the rectangle in Fig. 3(b), we calculated the average noise reduction afforded by our method to be $0.740 \pm 0.002$. Taking the inverse therefore yields an average increase in sensitivity over the entire FoV of $1.351 \pm 0.004$, which is close to the theoretically expected ideal sensitivity enhancement of $\sqrt {2}\approx 1.414$.

 

Fig. 3. (a) Number of detected photons vs empirically measured phase uncertainty, for three example pixels. Blue shaded region, phase uncertainty lower than for ideal classical measurement. Grey shaded region, phase uncertainty lower than for ideal 2-photon N00N state measurement. (b) Reduction in noise enabled by quantum-enhanced method for all individual pixels. "X" show the location of pixels used for (a). Rectangle, FoV used for calculating average sensitivity enhancement. Scale bar, 1 mm both at sample and camera sensor plane. (c) Cross-section along dashed line in (b).

Download Full Size | PDF

5. Discussion

In this work we showed how the use of visible-wavelength entangled photon pairs results in dramatically higher detection efficiency, thereby addressing one of the two prominent issues that thus far prevented fast quantum imaging [4]. Indeed, for mass-producible CMOS SPAD-ISAs, our method using VEPS illumination likely represents the only path towards high PDE quantum imaging, as standard CMOS fabrication processes place constraints on the thickness of a silicon SPAD pixel’s photon absorption region, which fundamentally limits PDE at longer wavelengths [19]. The other issue discussed in Ref. [4] is camera duty cycle, which in the present work remains a limiting factor. This is due to the use of a general purpose SPAD camera, which reads out and transfers information for every pixel in every frame regardless of whether a detection occurred or not. The shortest possible frame readout time with the camera used here is ${10.4}\;\mathrm{\mu}\textrm {s}$, which is obtained simply by multiplying the pixel readout by the number of pixels [20]. As the frame exposure time is ${10}\;\textrm {ns}$, we operate at a duty cycle of ${\sim }0.1\%$. However, this problem will be addressed in the near future through the use of a new generation of SPAD cameras, optimized for sparse coincidence imaging [18]. For example, the camera described in Ref. [40] can image coincidences at a rate of hundreds of kilohertz, with a duty cycle close to $100\%$, and has a modular design that can easily be scaled to large numbers of pixels. We anticipate therefore that, while using visible-wavelength entanglement here reduced measurement times from hours to minutes, the addition of sparse detection optimized SPAD array cameras will result in further speed improvements, to achieve real-time entanglement-enhanced quantum imaging at high spatial resolution.

We emphasize that with the present general purpose frame-based SPAD camera it would not be possible to simply use a longer frame exposure time in order to obtain a higher duty cycle, and thereby increase coincidence imaging speed. This is because the SPAD camera used here does not provide any timing information about photon detections within a frame [20]. Therefore, a longer exposure time results in lower SNR due to greater uncertainty about whether coincident photodetections originated from real SPDC photon pairs [41]. Increasing duty cycle without negatively affecting SNR therefore requires faster frame readout times and/or photodetection timing information (for example detection time-stamping), both of which are provided by the next-generation SPAD array described by Ref. [40]. When using a SPDC EPS with SPAD detectors it is generally also not possible to increase the generation rate (e.g. by increasing pump power) without incurring a penalty in SNR [41,42]. Our technique is therefore not limited by currently achievable entangled photon emission rates.

In this work the supersensitivity of our quantum-enhanced imaging method was calculated using postselection for coincidence counting, without considering photon losses in detection. This is standard practice in almost all entanglement-enabled phase measurement experiments to date (with the notable exception of Ref. [38]), and does not affect the validity of quantum imaging proof-of-principle demonstrations [3,4,43,44]. However, with currently available detection efficiencies, SPAD-ISAs can detect at much higher intensity (i.e., single photon) count rates than coincidence rates. Therefore, the sensitivity that can be achieved in practice using classical light remains, at present, higher than for the quantum case (e.g., as seen comparing Fig. 2(e) and (h)). Indeed, to achieve an actual quantum-enabled sensitivity advantage in real-world applications, detector efficiencies higher than $1/\sqrt {2}\approx 0.707$ are required when using 2-photon N00N states [38]. State-of-the art CMOS SPAD arrays are approaching this efficiency for the visible wavelength range; for example, Ref. [45] showed a PDE of 70% at 490 nm, while Ref. [21] demonstrated a PDE of 69.4% at 510 nm. Moreover, custom SPAD technologies are close to reaching these efficiencies in the red visible wavelength range, and may eventually become viable options for cameras [46]. Nevertheless, in the NIR, the critical threshold PDE $1/\sqrt {2}$ remains far out of reach for SPAD arrays [18], further emphasizing the need for visible-wavelength EPSs in useful quantum imaging. We note that recent research has identified entangled states that are more tolerant to loss in phase measurements than the N00N states used here, which may in future lower the required detection efficiency [47].

Sensitivity enhancements beyond the theoretical $\sqrt {2}$ factor in this work are enabled by states with $N>2$ entangled photons [1,14]. However, these are extremely challenging to experimentally realize with passive SPDC setups, in which photon generation is probabilistic and thus scales poorly for large $N$ [14]. On the other hand, while currently lacking the required technological maturity to be used in practical quantum imaging, alternative platforms capable of generating entanglement between many photons have shown promising developments. These include semiconductor quantum dots, high harmonic generation, trapped atoms, and SPDC combined with active feed-forward [48–51]. Lastly, multipass methods represent a different approach that may yield practical supersensitive imaging, without requiring the generation of exotic large entangled states [52,53].

An important feature of our imaging platform is its large FoV. We note that the AFM image in Fig. 2(c) only covers a very small area out of the entire test sample, which has dimensions ${5}\;\textrm {mm} \times {5}\;\textrm {mm}$. The reason for this is that AFMs are not able to image the height of areas larger than a few $({100}\;\mathrm{\mu}\textrm {m})^2$, without complicated and labour-intensive scanning and image-stitching operations. Our quantum-enhanced phase imager on the other hand is able to image nanometer-height material samples of large areas in a single shot, representing an important advantage with respect to AFMs.

In conclusion, in this work we have demonstrated a fast and practical quantum-enabled supersensitive imaging platform. Through the use of a visible-wavelength (532 nm) EPS we optimized photon detection efficiency on our SPAD array camera. When imaging a silica and protein microarray test sample, this allowed us to increase imaging speed by factors of 39 and 60, respectively, compared to equivalent measurements with the commonly used standard NIR ($\sim$ 800 nm) EPS [4]. We showed accurate imaging of sample phase features, with a sensitivity enhancement of $1.351 \pm 0.004$ over an equivalent ideal classical measurement. Our technique represents an important stepping stone towards the real-world application of quantum-enhanced imaging.