Low-Light Shadow Imaging using Quantum-Noise Detection with a Camera Savannah L. Cuozzo, Nikunjkumar Prajapati, Irina Novikova, and Eugeniy E. Mikhailov∗ Department of Physics, William & Mary, Williamsburg, Virginia 23187, USA Pratik J. Barge, Narayan Bhusal, Hwang Lee, and Lior Cohen Department of Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA (Dated: September 22, 2021) We experimentally demonstrate an imaging technique based on quantum noise modification af- ter interaction with an opaque object. By using a homodyne-like detection scheme, we eliminate the detrimental effect of the camera's dark noise, making this approach particularly attractive for imaging scenarios that require weak illumination. Here, we reconstruct the image of an object il- luminated with a squeezed vacuum using a total of 800 photons, utilizing less than one photon per frame on average. Quantum imaging [1{5] is capable of outperforming classical alternatives since it's able to utilize non-classical correlations in probing optical fields. Several quantum- enhanced imaging methods have been developed and proved useful for biological imaging [6,7] and imaging in the presence of contaminating classical background illu- mination [8,9]. When imaging in the low-photon regime, FIG. 1. A conceptual representation of the proposed quan- it can be difficult to implement direct intensity detection. tum shadow imaging using a "+" as the target. The quantum This is due to the accuracy of such detection being de- shadow method uses the average quantum fluctuations of the termined by the photon statistics and by technical noise. probe and reference fields amplified by a local oscillator and Some examples may include laser intensity fluctuations therefore not susceptible to the camera's dark noise. The quantum shadow probe map is on a linear scale. For com- or the detector dark noise, and normally requires a long parison, we show classical intensity image of the \+" target exposure time to allow for statistical averaging. illuminated with a bright beam on a log scale. The \+" is We experimentally demonstrate an imaging technique about 475 µm in width. based on detecting the quantum noise distribution of the quadrature-squeezed vacuum before and after it inter- acts with an opaque object. Our homodyne-like detec- tion scheme allows elimination of the detrimental effects enhanced or quantum correlated intensity measurements, of the camera's dark noise and, potentially, is immune to our measurements are based on an analysis of quantum the classical background illumination while keeping the quadratures variance. We use a quadrature squeezed vac- probing intensity low. This approach is particularly at- uum field [21{24], containing very few photons on aver- tractive for applications requiring weak illumination since age; when such a field interacts with an opaque object, the squeezed vacuum inherently has very few photons il- its quantum fluctuations in the obstructed zone are re- luminating the object. placed with a regular vacuum. To record the spatial dis- Many recent realizations of quantum imaging use two- tribution of the resulting noise quadrature without being mode optical fields with correlated intensity fluctua- affected by the camera dark noise, we mix the quantum tions generated either through parametric down conver- probe with a classical local oscillator field. This ampli- sion [10{13] or four-wave mixing in an atomic vapor [14{ fies the probe's quantum noise, realizing a camera-based 18]. When an object is placed in one of the optical beams, balanced homodyne detection scheme. Our approach al- lows us to image the fields with as low as one photon per arXiv:2106.00785v2 [quant-ph] 20 Sep 2021 its shape can be imaged with sub-shot-noise accuracy by subtracting the intensity images of the two quantum- frame and yet obtain spatial details of the object with correlated beams [19]. However, the average intensity of significantly less acquisition time, making it attractive to each beam limits the acceptable level of the dark noise. e.g. non-destructive imaging of biological samples [25]. Compared with typical photon-counting detectors, CCD Moreover, in such a method, we can use an anti-squeezed cameras often present a challenge for imaging weak opti- quadrature | increasing the tolerance to optical losses. cal fields due to their relatively slow frame rate, making The concept of the proposed method is illustrated in it harder to mitigate low-frequency technical noises) and Fig.1. A CCD camera detects the number of photons in- their intrinsic dark noise [18, 20]. cident on each pixel, N, on top of its internal dark noise Our approach is different. Instead of using quantum Nd. For a standard intensity measurement, the boundary between a fully illuminated region (the average photo- counts hN + Ndi) and a fully blocked region (the average photocounts hNdi) can be distinguished by the difference ∗ [email protected] between these two photocount values. Moreover, we can 2 R ∗ estimate the signal-to-noise of such traditional measure- where O(~x) = A uLOuSqV dA is the overlap between ments as the spatial modes of the local oscillator, uLO, and the squeezed vacuum mode, u , and A is the pixel at lo- N¯ SqV SNRt = ; (1) cation ~x. For the reference beam, where the object is p 2 N¯ + 2(∆Nd) removed, we assume T = 1 everywhere. For the mode- matched local oscillator and quantum probe, we arrive ¯ where N is an average photon number detected per pixel at the following expression of the transmission map us- (or bin), and ∆N is the standard deviation of the dark d ing measured quadrature noise variance Vp and Vr in the noise counts. probe and reference beams, respectively: We propose instead to measure the normalized vari- ance, V , of the quadrature Xθ = cos(θ)X1 + sin(θ)X2, Vp(~x) − 1 y y y Tq(~x) = : (5) where X1 = a + a , X2 = i(a − a), and a (a) is the cre- Vr(~x) − 1 ation(annihilation) operator for the photon state. In this case a similar boundary between the light and darkness Note that our method of transmission calculation is ag- can be detected via the deviation of the noise variance for nostic to the choice of the squeezed or anti-squeezed the region illuminated by a quantum probe from unity | quadrature. In this experiment, we work with anti- the noise variance of the coherent vacuum (shot noise). squeezed quadrature, since it is more robust to the optical This method does not work for a coherent illuminating losses. state because the quadrature variance is unchanged by The schematics of the experimental realization of the the loss. proposed method is shown in Fig.2a. While the specific For example, if an experiment uses a squeezed vacuum method of the squeezed vacuum generation is not im- with the squeezing parameter r, the expected variance portant, in the presented experiments we use a squeezer value for the squeezed and anti-squeezed quadratures are based on the polarization self-rotation in a 87Rb vapor V = e∓2r, respectively. We can also estimate the noise of cell [21, 22], details of which are reported at Ref. [23, 24]. such measurements by calculating the variance of the cor- The principle difference from the previous experimental responding variance values for such a squeezed vacuum arrangement is the pulsed squeezer operation. To avoid field, yielding the following theoretical signal-to-noise ra- camera over-exposure, the pump field is turned on for tio: only 1 µs during the 544 µs duty cycle using an acousto- optical modulator (AOM). Right after the squeezer, we V − 1 detect 1.5 dB of squeezing and 10 dB of anti-squeezing SNRq = p (2) 2 + 2V 2 and these parameters are not affected by the pulsed op- eration. Due to optical losses, after the imaging system Note, that for this calculation we can neglect the cam- we detect (with homodyning photodiodes) only 0.5 dB era dark noise thanks to the homodyne detection. As a squeezing and 7.5 dB anti-squeezing. result, we can compare the performance of the two ap- After the squeezer, the pump and squeezed vacuum proaches as a ratio of the two signal to noise values for (SqV) fields are physically separated using a polarizing an anti-squeezed vacuum field, and a coherent beam with beam displacer (PBD). SqV alone passes through the ob- similar average number of photons N¯ = sinh2(r) 1: ject and then recombines with an attenuated pump field, which now serves as a local oscillator (LO) in the bal- q anced homodyne scheme for imaging. We image the ob- 2r sinh2(r) + 2(∆N )2 SNRq e − 1 d ject onto the camera using a 4-f system of lenses (see L1 = p 2 (3) SNRt 2 + 2e4r sinh (r) and L2 in Fig.2a. r We obtain quantum-limited statistics from images of 2(∆N )2 d the two beams using a Princeton Pixis 1024 camera that ' 1 + ¯ N has 13µm×13µm pixels, an average standard deviation It is easy to see that in the limit of the small pho- of dark noise counts of 10 per pixel and high quantum ◦ ton number N¯ 1, the two methods perform equally efficiency (above 95%), cooled to -70 C. We illuminate −5 well in the case of vanishing dark noise; however, if the our object with an average of 6 × 10 photons per pixel dark noise becomes comparable with the average pho- per frame, so we are in the regime where the dark noise is ton number, the advantage of the quantum noise-based significantly larger than the photon number. Hence, our measurement becomes more obvious. quantum method has an advantage according to Eq.3. With our method, we can produce a quality trans- This camera can only rapidly capture four frames before mission map from the quantum noise measurements and having to pause for half a second for data transfer.