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arXiv:2011.03056 · Optics Express

Microscopy with heralded Fock states

Maria Gieysztor, Joshua Nepinak, Christopher J. Pugh, Piotr Leszek Kolenderski

Published May 17, 2023• 0 citations
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Abstract

We consider a microscopy setting where quantum light is used for illumination. Spontaneous parametric down conversion (SPDC) is used as a source of a heralded single photon, which is quantum light prepared in a Fock state. We present analytical formulas for the spatial mode tracking along with the heralded and non-heralded mode widths. The obtained analytical results are supported by numerical calculations and the following discussion taking into account realistic setup parameters such as finite-size optics and finite-size single-photon detectors. This allows us to observe that the diffraction limit can be approached with simultaneous alleviation of the photon loss leading to increased signal-to-noise ratio - a factor limiting practical applications of quantum light. Additionally, it is shown that the spatial resolution can be manipulated by carefully preparing the amplitude and phase of the spatial mode profile of the single photon at the input to the microscope objective. Here, the spatial entanglement of the biphoton wavefunction or adaptive optics can be applied for spatial mode shaping. Analytical dependencies between the incident and focused spatial mode profiles parameters are provided.

DOI
10.1364/oe.486439

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We consider a microscopy setting where quantum light is used for illumination. Spontaneous parametric down conversion (SPDC) is used as a source of a heralded single photon, which is quantum light prepared in a Fock state. We present analytical formulas for the spatial mode tracking along with the heralded and non-heralded mode widths. The obtained analytical results are supported by numerical calculations and the following discussion taking into account realistic setup parameters such as finite-size optics and finite-size single-photon detectors. This allows us to observe that the diffraction limit can be approached with simultaneous alleviation of the photon loss leading to increased signal-to-noise ratio - a factor limiting practical applications of quantum light. Additionally, it is shown that the spatial resolution can be manipulated by carefully preparing the amplitude and phase of the spatial mode profile of the single photon at the input to the microscope objective. Here, the spatial entanglement of the biphoton wavefunction or adaptive optics can be applied for spatial mode shaping. Analytical dependencies between the incident and focused spatial mode profiles parameters are provided.
In this work a theoretical analysis of the lateral resolution limits of an optical setup in a microscopy setting with an entangled photons pair source is performed. A correlated biphoton wavefunction of a general Gaussian form, is propagated through a given experimental setup. Next, the signal photon's spatial mode profile width and central position are investigated in the heralding scenario, which means the information about the idler photon is not neglected. The impact of the correlations on the signal photon's spatial mode profile is compared in the heralding and non-heralding scenario. A realistic experimental scheme is considered, taking into account finite size optics and single photon detectors. This method allows us to significantly alleviate the photon loss problem in the optical setup which is a crucial factor limiting practical applications of single photon based techniques. It is achieved by an effect similar to phase shaping introduced by spatial light modulators.
The resolution of optical scanning microscopes is limited by the spot size of the scanning beam. It has been proposed by Boto1 et al. and Nasr2 et al. that momentum entangled photons can be focused more tightly than classical light. Thus they should enable one to break the di ractive resolution limit. We report experiments measuring the spatial distribution of strong focussed momentum entangled photon pairs at a center wavelength of 812 nm from a spontaneous parametric down conversion source. Using a single gold stripe deposited on a glass surface as test object we observe a two-photon spot size as small as 194 nm, thereby beating the di raction limit even for conventional two-photon microscopy.
We use entangled photons as the light source in a normal microscope. Using this quantum illumination improves both the resolution and noise rejection in the image. The resolution of any classical imaging system is limited by the diffraction created by the finite size of the imaging lens. By using a light source that emits pairs of entangled photons and carefully controlling a camera that is capable of detecting single photons it is possible to observe these photons arriving two-by-two. Applying camera analysis software to log only these two-by-two events one can form an image from the mid-point (bisector) of each of these pair events. The image formed from the sum of all these bisectors has an improved resolution that surpasses the classical limit. Another advantage of using a quantum illumination is that it allows the two-by-two events from entangled photon pairs to be distinguished from background (classical) light and sensor noise. When processed in this way the resulting image is free of camera noise and any background light may be eliminated. The use of a quantum illumination protocol such as that used here results in the elimination of background light and therefore allows the development of the optical equivalent of quantum radar – a quantum enhanced LIDAR scheme. Using quantum illumination, combined with commercially available cameras that are sensitive to single photons creates a new approach to super-resolution and low noise microscopy. Imaging through noise with quantum illumination, T Gregory, P-A Moreau, E Toninelli, and M J Padgett, Science Advances 6, eaay2652 (2020) Resolution-enhanced quantum imaging by centroid estimation of biphotons, E Toninelli, P-A Moreau, T Gregory, A Mihalyi, M Edgar, N Radwell, and M J Padgett, Optica 6, 347-353 (2019)
Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the nonseparability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing.
Quantum ghost imaging approaches have been proposed to enhance biological microscopy, for example, using 2D visible detectors to provide IR images or providing additional dimensions of spatial or spectral information. Toward the goal of making such imaging schemes practical, we compare image quality and depth-of-field between traditional images and ghost images at the same excitation levels. We measure how image quality and depth-of-field depend on the parameters of the entangled light produced using type-I spontaneous parametric down-conversion (SPDC). We use a pair of time-synchronized, photon-timing single-photon avalanche diode (SPAD) array detectors to capture two distinct microscope imaging paths simultaneously on a photon-pair-by-photon-pair basis: one in a traditional imaging pathway and the other a quantum ghost imaging pathway. We calculate the depth-of-field, resolution, contrast, and signal-to-noise ratio (SNR) through the parameter space of a β-Barium Borate (BBO) type-I bulk non-linear crystal length and angle. Our results provide a basis for choosing parameters for quantum ghost imaging with type-I SPDC sources.