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Lateral resolution limits in microscopy with entangled photon pairs

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

Published Nov 5, 2020• 0 citations
OpenAlex

Abstract

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.

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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.
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.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.
Spatial resolution defines the fundamental limit of how precisely optical imaging systems can distinguish details within an object. Recent advances in quantum imaging have surpassed classical resolution limits by exploiting entanglement. However, experimental demonstrations of quantum enhancement above two times using entangled biphotons have thus far been limited to nonimaging experiments that use replication of the object or nonlinearity-both are impractical and inefficient. Here, without resorting to either, we enhance the classical resolution using entangled photon pairs by either two- or fourfold in two system configurations. While the signal photons traverse the object-containing arm only once, the idler photons traverse the symmetric object-free arm either once or thrice. These experiments demonstrate a scalable route toward quantum-correlated super-resolution imaging, motivate theoretical exploration of the underlying mechanisms, and open opportunities for high-precision, low-illumination microscopy.
Abstract Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore, there is a strong focus on improving the practicality of quantum imaging methods, with the goal of finding real-world applications. With this in mind, in this tutorial we describe how the concepts of classical light shaping can be applied to imaging schemes based on entangled photon pairs. We detail two basic experimental configurations in which a spatial light modulator is used to shape the spatial correlations of a photon pair state and highlight the key differences between this and classical shaping. We then showcase two recent examples that expand on these concepts to perform aberration and scattering correction with photon pairs. We include specific details on the key steps of these experiments, with the goal that this can be used as a guide for building photon-pair-based imaging and shaping experiments.
Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore, there is a strong focus on improving the practicality of quantum imaging methods, with the goal of finding real-world applications. With this in mind, in this tutorial we describe how the concepts of classical light shaping can be applied to imaging schemes based on entangled photon pairs. We detail two basic experimental configurations in which a spatial light modulator is used to shape the spatial correlations of a photon pair state and highlight the key differences between this and classical shaping. We then showcase two recent examples that expand on these concepts to perform aberration and scattering correction with photon pairs. We include specific details on the key steps of these experiments, with the goal that this can be used as a guide for building photon-pair-based imaging and shaping experiments.
High Resolution Image Download MS PowerPoint Slide The resolution of a classical imaging system is limited by diffraction. This limit can be overcome, for example, by implementing various forms of localization microscopy in which the center of a fluorescence distribution is estimated to an accuracy scaling with the square root of the number of detected photons, N . In quantum imaging the object can be illuminated using correlated photon-pairs, leading early work to suggest that a 2 improvement could be obtained as a result of averaging the position of N = 2 events. However, similar to quantum lithography, which relies upon quantum illumination using entangled photon-pairs and two-photon absorption, the minimum resolvable feature size is reduced by a factor of 2, not just 2 . Quantum imaging schemes can also lead to a factor of 2 improvement. By using a similar source of correlated photon-pairs to illuminate an object, a single-photon sensitive camera to detect the photon-pairs, and an image processing algorithm to record and sum the bisector positions of the transmitted photon-pairs, we realize a similar factor of ×2 improvement in image resolution, surpassing that of most earlier quantum imaging work.