Moreau, P.-A., Toninelli, E., Gregory, T. and Padgett, M. J. (2019) Imaging with
quantum states of light. Nature Reviews Physics, 1(6), pp. 367-380.
There may be differences between this version and the published version. You are
advised to consult the publisher’s version if you wish to cite from it.
http://eprints.gla.ac.uk/188342/
Deposited on: 31 October 2019
Enlighten – Research publications by members of the University of Glasgow
http://eprints.gla.ac.uk
Imaging with quantum states of light
P.-A. Moreau
∗
, E. Toninelli, T. Gregory and M. J. Padgett
∗
SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK
∗
e-mail: paul-antoine.moreau@glasgow.ac.uk; miles.padgett@glasgow.ac.uk
August 9, 2019
Abstract
The production of pairs of entangled photons simply by focusing a laser beam onto a
crystal with a non-linear optical response was used to test quantum mechanics and to open
new approaches in imaging. The development of the latter was enabled by the emergence of
single photon sensitive cameras able to characterize spatial correlations and high-dimensional
entanglement. Thereby new techniques emerged such as the ghost imaging of objects —
where the quantum correlations between photons reveal the image from photons that have
never interacted with the object — or the imaging with undetected photons by using non-
linear interferometers. Additionally, quantum approaches in imaging can also lead to an
improvement in the performance of conventional imaging systems. These improvements can
be obtained by means of image contrast, resolution enhancement that exceed the classical
limit and acquisition of sub-shot noise phase or amplitude images. In this review we discuss
the application of quantum states of light for advanced imaging techniques.
Introduction
With the emergence of modern non-linear optics in the second half of the 20th century [1, 2, 3],
physicists found the source of choice to conduct the desired tests of quantum mechanics. Light,
unlike other physical systems, remains well isolated from its environment and is, therefore, by its
nature not very sensitive to the effects of quantum decoherence. This good insulation of photons
from their environment and from each other is highly desirable in order to study or harness the
quantum properties of a system; however, it is also a drawback when it comes to the production
of entangled particles because it is difficult to make two photons interact with each other to create
entanglement. In early tests of quantum mechanics principles, the photons were generated through
a cascaded two photon emission process from single atoms [4, 5, 6]. Such techniques are rather
difficult to implement. They were quickly superseded by the use of non-linear optics that allows the
creation of twin photons within a medium with a non-linear response such as a non-linear crystal.
It was shown theoretically [7, 8, 9] and experimentally [10, 11, 12] that it is possible to generate
photon pairs through the interaction of a single pump photon with a non-linear medium. Such a
three wave interaction process between a pump photon and two lower frequency – signal and idler
– photons is called spontaneous parametric down-conversion (SPDC). It was shown that SPDC
allows the generation of quantum states of light [13, 14]. In particular, it is possible to generate
entanglement in polarisation [15] using such a non-linear process [16, 17]. SPDC has since been
widely used as a source for a variety of fundamental demonstrations of quantum mechanics and
quantum information protocols. Notably, the parametric down conversion process has been used
in the demonstration of Hong-Ou-Mandel (HOM) two photon interference [18], implementation of
delayed-choice experiments [19, 20], quantum teleportation [21], elaboration of optical quantum
gates and information protocols [22, 23] as well as in the entanglement based on quantum key dis-
tribution [24]. It was also used in two realisations of the loophole free Bell test experiment [25, 26].
Interestingly, as demonstrated for imaging applications, the light emitted through the SPDC pro-
cess (Fig. 1) exhibits quantum correlations in both position and momentum [27]. The existence
of momentum correlations between the photons created and annihilated in the SPDC process, was
highlighted experimentally as early as 1970 (Ref. [12] together with the first demonstration of the
existence of temporal photon correlations in the light emitted in this process. These correlations
1
arXiv:1908.03034v1 [quant-ph] 8 Aug 2019
were perfectly expected as they are a result of momentum conservation between the annihilated
pump photon and the two photons emitted in the SPDC process. Even more interestingly, it was
recognized that the state produced through the SPDC process is in fact a good approximation of
the original Einstein-Podolsky-Rosen (EPR) state of entanglement [28] because it presents both
position and momentum correlations [29]. The availability of such a state and the simplicity of its
generation – requiring only to pump a non-linear crystal with a laser – initiated the development
of new types of imaging experiments. Through these experiments emerged the field of ’quantum
imaging’. In the following we will give an overview of how the quantum behaviour of light can be
detected through imaging and how it can be harnessed advantageously in imaging protocols. In
particular, we will describe why SPDC sources play an essential role in these realizations.
Figure 1: Generation and detection of quantum correlations in spontaneous parametric
down-conversion (SPDC). a SPDC generation in a non-linear crystal (NL). The process is
depicted here for Type I phase matching (top) and Type II phase matching (bottom), leading
to the emission of one and two SPDC beams respectively. Inside these beams spatial photon
correlations can be detected. b Observation of correlations within a type I SPDC beam in a high
gain regime. The image on the left is reproduced on the right with white arrows highlighting
the correspondence between similar intensity features that are due to intensity correlations within
diametrically opposed portions of the beam. c Observation of correlations between type II SPDC
beams in a high gain regime. The left and right images correspond respectively to the two beams
(signal and idler) imaged on different regions of a camera. One can also observe similar patterns
within the two beams with a 180
◦
rotation, which is a signature of momentum anti-correlations.
Panel b is reproduced from REF. [30], Springer Nature Limited. Panel c is reproduced from
REF. [31], APS.
Cameras to detect quantum behaviour
The widespread use of SPDC as a source of quantum states rapidly generated interest in the study of
correlations and entanglement in the spatial domain. Not only did it promise to develop new types
of imaging, but it also allowed to engineer very high dimensional quantum states. The concurrent
development of new types of camera technologies enabled the detection of single photons with
cameras [32, 33]. The new types of quantum optical demonstrations no longer relied on scanning
point-like avalanche photo-diodes but rather on spatially resolved detectors. This development
in detection techniques enabled highly parallel correlation measurements, and ultimately led to
time efficient detection of quantum signatures that may be exploited in the context of quantum
information protocols. In this section we describe different camera technologies that have led to
quantum imaging demonstrations of fundamental nature; we highlight different regimes in which
these cameras can perform and discuss the respective advantages and disadvantages of the current
technology.
2
Detection of quantum correlations
Following the early detection of spatial photon correlations [12], further work was performed
throughout the 1990’s both to characterize and exploit the quantum correlations emitted through
SPDC [34, 35, 36]. However, these techniques were inherently inefficient because they used
avalanche photo-diodes to detect single photons, and a scanning pinhole to detect the spatial
features of the correlations. Such a pinhole filtering technique leads to the loss of the vast majority
of the photons, and therefore, the experiment requires a long time to measure the spatial form
of the correlation. Since that time researchers have tried to detect spatial correlations between
photon pairs with cameras, thereby removing the necessity to filter at one particular position. The
first attempt of detecting spatial correlations of quantum origin with a camera was performed in
1998 (Ref. [32]) using a photon-counting intensified CCD camera (ICCD). The results of this work
— despite the relatively noisy images of photon detection — inspired many experiments with more
technologically advanced cameras.
However, because of the technological limitations including the dark count, the noise and low quan-
tum efficiencies of available cameras the subsequent tests had to be performed under a different
regime. In 2000 a conventional single-frame camera was used to detect intensity correlations in
the spatial spectrum of SPDC beams [30]. A lithium triborate crystal was used to generate a
down-converted beam in a high-gain regime. To ensure an efficient emission of the signal and idler
waves through parametric fluorescence, the idler and the signal phases must match throughout
the propagation of the waves inside the non-linear material. This phase matching ensures that
the waves emitted at some point of the crystal do not interfere destructively with the upstream
emissions. There are two main types of phase matching that exists in the context of parametric
fluorescence, type I and type II. In type I phase matching both signal and idler waves are emit-
ted with the same polarization and therefore propagate along the same birefringent axis of the
non-linear crystal [37, 38]. In type II, however, the two waves that are emitted have orthogonal
polarizations and propagate along two distinct birefringent axis which permit, under non-collinear
phase matching conditions the generation of two distinct beams propagating in different directions.
Under the conditions used in [30], the relatively bright beam intensity is able to exceed the noise
floor of the camera. In this work, the correlated intensity fluctuations were detected within differ-
ent parts of the beam (Fig. 1 b).
In the aforementioned demonstration the correlations were simply observed and spatially char-
acterized. However, it is also possible to demonstrate sub-shot noise behaviour with such correla-
tions, thus establishing their quantum nature. Within two correlated regions of interest (ROI) of
the beam, the detected intensities are indeed expected to follow the same temporal fluctuations. If
these joint fluctuations are due to the arrival of correlated photons rather than a result of classical
intensity fluctuations, then, for an ideal system, one would expect to detect in both ROIs exactly
the same number of emitted photons. As a consequence, by subtracting the two signal intensities
one may obtain zero and the fluctuation of this intensity difference will also tend to zero. By con-
trast, classically correlated intensities when subtracted cannot go below a certain limit. This limit,
called shot noise, is due to the quantum nature of light and the fact that the number of photons in
a light beam is subject to a fundamental standard deviation which is equal to the square root of the
average number according to Poisson statistics. The shot noise limit corresponds to the intensity
fluctuations of the lowest noise classical state: a coherent state which is that of an ideal laser. If by
subtracting two intensity signals one obtains a quantity that fluctuates less than that of the shot
noise, then the underlying statistics is said to be sub-shot noise and one can conclude that the two
beams exhibit quantum correlations [39, 40]. This was achieved in parametric down-conversion in
the context of correlated single mode beams [41, 42, 43, 44, 45, 46, 47] before being demonstrated
in the context of imaging. Indeed, a few years after the aforementioned demonstration [30], such a
quantum signature of correlations in images was observed under a similar regime [31, 48]. It was
done using parametric fluorescence generated in a barium borate (BBO) crystal with type II phase
matching. By acquiring images of the bright fluorescence beams, the authors showed the sub-shot
noise nature of the detected spatial correlations (see Fig. 1 c).
As mentioned above, although it is true that these results demonstrated genuine photon quan-
tum correlations, they were performed in a high-gain regime of the down-converted emission. This
means that such correlations were not composed of pure twin photon correlations but also of higher
order photon correlations generated through the stimulated emission. Such higher order terms can
introduce excess noise when the imaging system is subject to losses that is in non-ideal conditions.
3
A few years later the sub-shot noise behaviour of SPDC light in images captured with an electron-
multiplying CCD camera (EMCCD) was demonstrated [49]. Moreover, in another work [50], a
scheme was proposed to use photon correlations to achieve sub-shot noise imaging, that is the
acquisition of images in a scheme that outperforms classical imaging schemes in terms of noise.
It was suggested that an optimal regime to use for such a realization is a bright light low gain
regime, which prevents the introduction of excess noise. Following these suggestions, a similar
regime was later used to detect twin photons [51] on the way to realizing sub-shot noise imag-
ing of a low transmission sample [52]. To access this particular regime, a pump laser with pulse
duration much longer than the coherence time of the SPDC was used to ensure that the number
of photons emitted per spatio-temporal mode of fluorescence emission was low enough to make
the stimulated emission negligible. Hence a very low contribution from the higher order photon
number correlations was ensured, thus limiting the impact of the excess noise. This low emission
rate led to a demonstration of sub-shot-noise spatial correlations without background subtraction
using a conventional CCD camera [52].
Efficient characterization with cameras
The aforementioned demonstrations were focused on simply detecting a signature of quantum
correlations. As we have seen, this can be done in a bright light regime with conventional scientific
cameras. However, such cameras are not sensitive enough to detect single photons. Indeed the
noise floor of such cameras is typically of several electrons even when the sensor is cooled. Under
such conditions the detection of a single photon leading to a photo-electron trapped in the CCD
well would not be observable in the image, which would be largely dominated by the technical noise
of the camera. This considerably limits the range of quantum behaviour that can be observed with
such cameras. To detect more subtle quantum characteristics that require the detection of single
photons one needs to use different camera, for example, EMCCD. In contrast to conventional
CCDs, EMCCD cameras incorporate on-chip gain placed before the charge reading stage [53]. The
gain register generates a multiplicative avalanche effect that occurs in around 500 stages. At each
stage the electrons contained in accelerated potential wells have a small probability to generate a
secondary electron through impact ionization with the chip substrate. This amplification before
reading has the potential to make single photon events to emerge from the camera readout noise.
With such cameras it is possible to develop photon-counting strategies [33]. As mentioned before,
these strategies led to the detection of sub-shot noise features in SPDC light [54, 49]. It was
followed by several other demonstrations aimed at detecting and using quantum correlations with
EMCCD cameras [55, 56, 57, 58, 59].
With single-photon cameras one can also demonstrate more fundamental quantum phenomena
such as an ERP paradox [28]. Correlations demonstrating the EPR paradox were performed in a
series of experiments [60, 61, 62, 63] (Fig. 2 ).
4
![Figure 2: Experimental test of Einstein-Podolsky-Rosen (EPR) paradox in images. a Experimental setup used to demonstrate a two dimensional EPR paradox with a pair of synchronised electron multiplying CCD cameras (EMCCD1 and EMCCD2). A nonlinear crystal (NL) cut for type II downconversion is pumped with a UV laser, the two spatially separated beams are then sent to two cameras, either by reimaging the crystal plane as shown here (the green planes indicate the crystal plane and the crystal image planes) or by imaging a Fourier plane of the crystal to detect the momenta of the photons. M1 andM2 are mirrors, L1 and L2 are lenses and BD is a beam dump. The pump is represented by a blue beam and the signal and idler are represented by red beams. xi and yi are the transverse positions of detection of photon i = {1, 2} along the horizontal (x) and vertical (y) directions. pxi and pyi are the transverse momenta of photon i = {1, 2} along the horizontal and vertical directions, respectively. b Detected conditional probability distribution of bi-photons in the acquired images. The results exhibit quantum correlations in both momentum (top) and position (bottom). The right column corresponds to the cross-correlations of the images composed of single photon events extracted from the two cameras. The correlation peaks are the signature of two dimensional quantum correlations that can be shown to demonstrate a high dimensional EPR paradox. Panel b is reproduced from REF. [63], APS.](/figures/figure-2-experimental-test-of-einstein-podolsky-rosen-epr-9md2llqq.webp)
![Figure 3: Sub-shot-noise quantum imaging. a Quantum correlated beams are generated in a barium borate non-linear crystal (NL) through type II SPDC. One of the beams probes a low absorptive object (O) before being detected on a camera, the second beam is directly detected on a different part of the same camera. By subtracting the intensities detected within each of the beams it is possible to remove some of the shot noise in the acquired image of the object. BD is a beam dump. b Two examples of images acquired: the images on the left are obtained after subtraction, the ones on the right are the images recorded directly by the camera. One can see that the images on the left appear less noisy, which is due to the sub-shot-noise nature of the correlations between the beams. It was shown that such images themselves exhibit sub-shot-noise qualities. Panel b is reproduced from REF. [52], Springer Nature Limited.](/figures/figure-3-sub-shot-noise-quantum-imaging-a-quantum-correlated-32itkk18.webp)
![Figure 4: Principle of quantum lithography. a Simplified version of a quantum lithography experimental scheme. A NOON state with N=2 is generated at the output of a beam-splitter (BS) through a HOM effect by recombining two photons generated by SPDC. The two photons are then in a superposition state of being both in the upper arm or in the lower arm of the interferometer situated between the BS and the screen. A phase shifter (PS) can be added in one of the paths. And one can displace two adjacent detectors in the plane of the screen to detect two photon coincidences and compute the centroid of such detected bi-photons. M1,2,3,4 are mirrors, NL is a non-linear crystal. b Experimental results evidencing the principle of quantum lithography. The black circles correspond to the single count interference pattern obtained with a classical coherent state. In the bottom panel, the two red curves correspond to single counts detected at the two detectors (right arrow). The green curve correspond to the coincidence count (CC)’ centroid measurements (left arrow). One can observe that the period of the interference fringes on this later figure is approximately half that of the classical interference pattern. Panel b is reproduced from REF. [146], APS.](/figures/figure-4-principle-of-quantum-lithography-a-simplified-230agdy2.webp)
![Figure 6: Quantum imaging with undetected photons. a Model of the experimental setup used to perform imaging without detecting the photons that interact with the object. A non-linear interferometer is built by seeding the idler produced in the first non-linear crystal NL1 into a second one NL2 and recombining the signal waves emitted by the two crystals on a beam splitter (BS). Due to quantum interference between the two photons wave-functions emitted by the crystals, an interference figure appears within the signal intensities outputting the BS. If one adds an object between NL1 and NL2 in the idler beam, one affects the whole wave function and as a consequence, the interference of the signal waves after the BS. One can in such conditions acquire an image of the object without having to detect the photons that have interacted with it. L1, 2, 3, 4, 5, 6 are lenses, D1, 2, 3, 4 are the dichroic mirrors, O is the imaging object and EMCCD is the electronmultiplying CCD camera. b Images of an object obtained by detection of the interference of signal photons that have not interacted with it. The idler photons that have interacted with the object remain undetected. The top row represents the imaging of a phase object, the blue dots on the right plot correspond to a scan of the object etch depth, the bottom row represents the imaging of a transmissive object. The colour bar represents the number of counts. Panel b is reproduced from Ref. [173], Springer Nature Limited.](/figures/figure-6-quantum-imaging-with-undetected-photons-a-model-of-1ecouy25.webp)
![Figure 1: Generation and detection of quantum correlations in spontaneous parametric down-conversion (SPDC). a SPDC generation in a non-linear crystal (NL). The process is depicted here for Type I phase matching (top) and Type II phase matching (bottom), leading to the emission of one and two SPDC beams respectively. Inside these beams spatial photon correlations can be detected. b Observation of correlations within a type I SPDC beam in a high gain regime. The image on the left is reproduced on the right with white arrows highlighting the correspondence between similar intensity features that are due to intensity correlations within diametrically opposed portions of the beam. c Observation of correlations between type II SPDC beams in a high gain regime. The left and right images correspond respectively to the two beams (signal and idler) imaged on different regions of a camera. One can also observe similar patterns within the two beams with a 180◦ rotation, which is a signature of momentum anti-correlations. Panel b is reproduced from REF. [30], Springer Nature Limited. Panel c is reproduced from REF. [31], APS.](/figures/figure-1-generation-and-detection-of-quantum-correlations-in-ge7m4xm0.webp)