Quantum microscopy

Quantum microscopy is a novel tool that allows microscopic properties of matter and quantum particles to be measured and directly visualized. There are various types of microscopy that use quantum principles. The first microscope to make use of quantum concepts was the scanning tunneling microscope, which paved the way for development of the photoionization microscope and the quantum entanglement microscope.

Scanning tunnelling microscope

The scanning tunnelling microscope (STM) uses the concept of quantum tunnelling to directly image atoms of a sample. The STM can be used to study the three-dimensional structure of a sample, by scanning the surface with a sharp metal conducting tip at an extremely small distance. Such an environment is conducive to quantum tunnelling: a quantum mechanical effect that occurs when electrons move through a barrier due to their wave-like properties. Tunnelling depends on the thickness of the barrier. If the barrier is reasonably thin, the probability function predicts some electrons will pass to the other side. This will create a current across the tunnel. The number of electrons that will tunnel is dependent on the thickness of the barrier, therefore the current through the barrier will also depend on the thickness. In this case, the distance between the sharp metal tip and the surface of the sample will affect the current measured by the tip. The tip is formed by one single atom, and it slowly scans across the surface at a distance of an atom's diameter. By paying attention to the current, the distance can be kept more or less constant, allowing the tip to move up and down according to the structure of the sample. The STM is able to follow even the smallest details.

The STM works best with conducting materials in order to create a current. However, since its creation, various implementations have been created that allow for a larger variety of samples, such as the spin polarized scanning tunneling microscopy (SPSTM), and the atomic force microscopy (AFM).

Photoionization microscopy

The wave function is central to the theory of Quantum Mechanics. It contains the maximum information that can be known about the quantum state of that particle. The square of the wave function describes the probability of where exactly a particle might be located at any given moment. Direct imaging of a wave function used to be considered only a gedanken experiment- however, due to recent microscopy developments, it is now possible to be accomplished.[1] An image of an atom's exact position or the movement of its electrons is almost impossible to measure because any direct observation of an atom disturbs its quantum coherence. As such, observing an atom's wave function and getting an image of its full quantum state requires many direct measurements to be made over time, which are then statistically averaged. One such tool recently developed to directly visualize atomic structure and quantum states is the photoionization microscope.[2]

A photoionization microscope is an instrument that uses photoionization, along with quantum properties and principles, in order to measure atomic properties. The principle behind photoionization microscopy is to study the spatial distribution of electrons ejected from an atom in a situation in which the De Broglie wavelength becomes large enough to be observed on a macroscopic scale. In photoionization microscopy experiments, an atom in an electric field is ionized by a laser with sharply defined frequency, the electron is drawn toward a position-sensitive detector, and the current is measured as a function of position. The application of an electric field during photoionization allows confining the electron flux along one coordinate.[3][4]

Multiple classical paths lead from the atom to any point in the classically allowed region on the detector, and waves travelling along these paths produce an interference pattern. There is an infinite set of different families of trajectories, leading to an extremely complicated interference pattern on the detector. As such, photoionization microscopy relies on the existence of interferences between various trajectories by which the electron moves from the atom to the plane of observation, for example, photoionization microscopy of the hydrogen atom in parallel electric and magnetic fields.[5][6][7]

History and development

The idea for a photoionization microscope that could image the wave-function of an atom stemmed out of an experiment proposed by Demkov and colleagues in the early 1980s.[8] The researchers suggested that electron waves could be imaged when interacting with a static electric field as long as the de Broglie Wavelength of these electrons was large enough.[8] It was not until 1996 that anything resembling the microscopy images proposed by Demkov and colleagues came to fruition.[1] In 1996 a team of French researchers developed the first photodetachment microscope. The development of this microscope allowed for a direct observation of the oscillatory structure of a wave function to become possible.[1] Photodetachment is the removal of electrons from an atom using interactions with photons or other particles.[9] Photodetachment microscopy made it possible to image the spatial distribution of the ejected electron. The microscope developed in 1996 was the first to image photodetachment rings of a negative Bromine (Br-) ion.[10] These images revealed interference between two electron waves on their way to the detector.

The first attempts to use photoionization microscopy were performed on atoms of Xenon (Xe) by a team of Dutch researchers in 2001.[1] Photoionization in the presence of an electric field allows the quantum nature of the wavefunction of an electron to be observed in the macroscopic world . The differences between direct and indirect ionization create different trajectories for the outgoing electron to follow. Direct ionization corresponds to electrons ejected down-field towards the bottleneck in the Coulomb + dc electric field potential, whereas indirect ionization corresponds to electrons ejected away from the bottleneck in the Coulomb + dc electric field and only ionize upon further Coulomb interactions.[1] The different trajectories caused by direct and indirect ionization give rise to a distinct pattern that can be detected by a two-dimensional flux detector and subsequently imaged.[11] The images exhibited an outer ring, which corresponded to the indirect ionization process and an inner ring, which corresponded to the direct ionization process. This oscillatory pattern can be interpreted as being interferences among the trajectories of the electrons moving from the atom to the detector.[1]

The next group to attempt photoionization microscopy used the excitation of Lithium atoms in the presence of a static electric field.[8] This experiment was the first to reveal evidence of quasibound states.[8] A quasi bound state has been defined as a "state having a connectedness to true bound state through the variation of some physical parameter".[12] This was done by photoionizing the Lithium atoms in the presence of a ≈1 kV/cm static electric field. This experiment was an important precursor to the imaging of the hydrogen wave function because, contrary to the experiments done with Xenon, the Lithium wave function microscopy images are sensitive to the presence of resonances.[8] Therefore, the quasi bound states were directly revealed. The success of this experiment led researchers to attempt to microscopy of the hydrogen atom's wave function.

In 2013, Aneta Stodolna and colleagues imaged the hydrogen atom's wave function by measuring an interference pattern on a 2D detector.[4][13] The electrons are excited to their Rydberg state. In this state, the electron orbital is far from the centre nucleus. The Rydberg electron is in a dc field, which causes it to be above the classical ionization threshold, but below the field-free ionization energy. The electron wave ends up producing an interference pattern because the portion of the wave directed towards the 2D detector interferes with the portion directed away from the detector. This interference pattern shows a number of nodes that is consistent with the nodal structure of the Hydrogen atom orbital[4]

Future directions and applications of photoionization microscopy

The same team of researchers that imaged the Hydrogen electron's wave function are now embarking on imaging the Helium (He) atom. They report that there are considerable differences since Helium has two electrons and that imaging of these electrons may actually enable them to 'see' entanglement.[1]

Further studies that remain to be undertaken include examining to what extent photoionization microscopy allows the construction of an atomic-size interferometer. If accomplished, this would enable the direct observation of the influence of an external source of deviation from the system, such as the presence of a magnetic field or neighbouring ions.[1]

Quantum entanglement microscope (Entanglement-enhanced microscope)

Quantum metrology involves using quantum mechanics to make precise measurement that cannot be achieved classically. Typically, entanglement of N particles are used to measure a phase with a precision ∆φ = 1/N. called the Heisenberg limit. This exceeds the ∆φ = 1/√N precision limit possible with N non-entangled particles, called the standard quantum limit (SQL). The signal-to-noise ratio for a given light intensity is limited by the standard quantum limit, which is critical for measurements where the probe light intensity is limited in order to avoid damaging the sample. The standard quantum limit can be tackled using quantum entangled particles.

Researchers developed a microscope that uses quantum entanglement to increase its sensitivity.[14][15] The experimentation of the microscope involved imaging a pattern carved in relief on the surface of a glass plate. In one of these works, the pattern was only 17 nanometers higher than the plate, which can be difficult to resolve when using typical microscopy apparatuses.

Quantum entanglement microscopes are a form of confocal-type differential interference contrast microscope. Entangled photon pairs and more generally, NOON states are used as the source of illumination. Two beams of photons are beamed at two adjacent spots on the flat-surfaced sample. The interference pattern of the beams are measured after they are reflected. When the two beams hit the flat surface, they both travel the same length and produce a corresponding interference pattern. This interference pattern changes when the beams hit portion on the glass surface that are of a different height. The shape of the patterns can be resolved by analysing the interference pattern and phase difference. A standard optical microscope would be very unlikely to detect something so small. The difference when measured with entangled photons is precise, as one entangled photon gives information about the other. Therefore, they provide more information than independent photons, creating sharper images.[14][16]

Future directions and applications of quantum entangled-enhanced microscopy

Entanglement-enhancement principles can be used to vastly improve the image provided by microscopes. By enhancing with quantum entanglement, researchers are able to overcome the Rayleigh criterion. This is ideal for studying biological tissues and materials that are opaque. However, a limitation is that the light intensity is lowered in order to avoid damaging the sample.[14][15]

Further, the use of entangled microscopy can avoid the phototoxicity and photobleaching that comes with two-photon scanning fluorescence microscopy. In addition, since the interaction region within entangled microscopy is controlled by two beams, the selection of where to image is extremely flexible, which provides enhanced axial and lateral resolution[17]

In addition to the sampling of biological tissues, high-precision optical phase measurements have additional applications such as gravitational wave detection, measurements of material properties, as well as medical and biological sensing.[14][15]

Quantum enhanced super-resolution in fluorescence microscopy

In a fluorescence microscope, images of objects that contains fluorescent particles are recorded. Each such particle can emit not more than one photon at a time, a quantum-mechanical effect known as photon antibunching. Recording anti-bunching in fluorescence image provides additional information that can be used to enhance the microscope's resolution over the diffraction limit,[18] and was demonstrated for several different types of fluorescent particles.[19][20][21]

Intuitively, antibunching can be thought of as detection of ‘missing’ events of two photons emitted from every particle that cannot simultaneously emit two photons. It is therefore used to produce an image like one that would have been produced using photons with half the wavelength of the detected photons. By detecting N-photon events, the resolution can be improved by up to a factor of N over the diffraction limit.

In conventional fluorescence microscopes, antibunching information is often ignored, as simultaneous detection of multiple photon emission requires temporal resolution higher than that of most commonly available cameras. However, recent developments in detector technology has already enabled first demonstrations of quantum enhanced super-resolution using fast detector arrays, such as single-photon avalanche diode arrays.[22]

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gollark: I don't think it was actually due to anything you did but just this sort of thing being really hard in general.
gollark: It probably wouldn't be. I suspect it's because it didn't really have that many people, and there was not that much actual discussion of esolangs available.
gollark: Yes, esoserver didn't work, doesn't mean you're okay.
gollark: Are, I should say.

References
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