Quantum microscopy

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Quantum microscopy allows microscopic properties of matter and quantum particles to be measured and imaged. Various types of microscopy use quantum principles. The first microscope to do so was the scanning tunneling microscope, which paved the way for development of the photoionization microscope and the quantum entanglement microscope.

Contents

Scanning tunneling

The scanning tunneling microscope (STM) uses the concept of quantum tunneling to directly image atoms. A STM can be used to study the three-dimensional structure of a sample, by scanning the surface with a sharp, metal, conductive tip close to the sample. Such an environment is conducive to quantum tunneling: a quantum mechanical effect that occurs when electrons move through a barrier due to their wave-like properties. Tunneling depends on the thickness of the barrier; the Schrödinger equation gives the probability that a particle will be detected on the far side and, for a sufficiently thin barrier, predicts some electrons will cross it. This creates a current across the tunnel. The number of electrons that tunnel is dependent on the thickness of the barrier, therefore the current through the barrier also depends on this thickness. The distance between the tip and the sample affects the current measured by the tip. The tip is formed by a single atom that slowly moves across the surface at a distance of one atomic diameter. By observing the current, the distance can be kept fairly constant, allowing the tip to move up and down according to the structure of the sample.

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

Photoionization

The wave function is central to quantum mechanics. It contains the maximum information that can be known about a single particle's quantum state. The square of the wave function is the probability of a particle's location at any given moment. Direct imaging of a wave function used to be considered only a gedanken experiment, but became routine. [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 measurements to be made, which are then statistically averaged. The photoionization microscope directly visualizes atomic structure and quantum states. [2]

A photoionization microscope employs photoionization, along with quantum properties and principles, to measure atomic properties. The principle 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. An atom in an electric field is ionized by a focused laser. 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 dimension. [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. An infinite set of trajectory families lead to a complicated interference pattern on the detector. As such, photoionization microscopy relies on the existence of interference between various trajectories by which the electron moves from the atom to the plane of observation, for example, of a hydrogen atom in parallel electric and magnetic fields. [5] [6] [7]

History and development

The idea stemmed from 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 these ideas bore fruit. [1] In 1996 a team of French researchers developed the first photodetachment microscope. It allowed for direct observation of the oscillatory structure of a wave function. [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 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 by a team of Dutch researchers in 2001. [1] The differences between direct and indirect ionization create different trajectories for the outbound electron. 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] These trajectories produce a distinct pattern that can be detected by a two-dimensional flux detector and subsequently imaged. [11] The images exhibit an outer ring that correspond to the indirect ionization process and an inner ring, which correspond to the direct ionization process. This oscillatory pattern can be interpreted as interference 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 quasibound state is 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, Lithium wave function microscopy images are sensitive to the presence of resonances. [8] Therefore, the quasibound states were directly revealed.

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

The same team of researchers that imaged the hydrogen electron's wave function are attempting to image helium. They report considerable differences, since helium has two electrons, which may enable them to 'see' entanglement. [1]

Quantum entanglement

Quantum metrology makes precise measurements that cannot be achieved classically. Typically, entanglement of N particles is used to measure a phase with 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 (SNR) for a given light intensity is limited by SQL, which is critical for measurements where the probe light intensity is limited in order to avoid damaging the sample. The SQL can be tackled using entangled particles.

The microscope first imaged a relief pattern of a glass plate. In one test, the pattern was 17 nanometers higher than the plate. [14] [15]

Quantum entanglement microscopes are a form of confocal-type differential interference contrast microscope. Entangled photon pairs and more generally, NOON states are the illumination source. Two beams of photons are beamed at adjacent spots on a flat 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 regions of different heights. The patterns can be resolved by analysing the interference pattern and phase difference. A standard optical microscope would be unlikely to detect something so small. The image is precise when measured with entangled photons, as each entangled photon gives information about the other. Therefore, they provide more information than independent photons, creating sharper images. [14] [16]

Future directions

Entanglement-enhancement principles can be used to improve the image. Researchers are thereby able to overcome the Rayleigh criterion. This is ideal for studying biological tissues and opaque materials. However, the light intensity must be lowered to avoid damaging the sample. [14] [15]

Entangled-photon 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, image site selection is flexible, which provides enhanced axial and lateral resolution [17]

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

Biological quantum light microscopes

Researchers have developed quantum light microscopes based on squeezed states of light. [18] [19] [20] Squeezed states of light have noise characteristics that are reduced beneath the shot noise level in one quadrature (such as amplitude or phase) at the expense of increased noise in the orthogonal quadrature. This reduced noise can be used to improve signal-to-noise ratio. Squeezed states have been shown to allow a signal-to-noise ratio improvement of as much as a factor of thirty. [20]

The first biological quantum light microscope used squeezed light in an optical tweezer to probe the interior of a living yeast cell. [18] In experiments it was shown that squeezed light allowed more precise tracking[ compared to? ] of lipid granules that naturally occur within the cell, and that this provided a more accurate measurement[ compared to? ] of the local viscosity of the cell. Viscosity is an important property of cells that is connected to their health, structural properties and local function. Later, the same microscope was employed as a photonic force microscope, tracking a granule as it diffused spatially. [19] This allowed quantum enhanced resolution to be demonstrated, and for this to be achieved in a far-sub-diffraction limited microscope.

Squeezed light has also been used to improve nonlinear microscopy. [20] Nonlinear microscopes use intense laser illumination, close to the levels at which biological damage can occur. This damage is a key barrier to improving their performance, preventing the intensity from being increased and therefore putting a hard limit on SNR. By using squeezed light in such a microscope, researchers have shown that this limit can be broken - that SNR beyond that achievable beneath photo-damage limits of regular microscopy can be achieved. [20]

Quantum enhanced fluorescence super-resolution

In a fluorescence microscope, images of objects that contain 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 a fluorescence image provides additional information that can be used to enhance the microscope's resolution beyond the diffraction limit, [21] and was demonstrated for several types of fluorescent particles. [22] [23] [24]

Intuitively, antibunching can be thought of as detection of ‘missing’ events of two photons emitted from every particle that cannot simultaneously emit two photons.[ contradictory ] It is therefore used to produce an image that would have been produced using photons with half the wavelength of the detected photons.[ clarification needed ] 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 ignored, as simultaneous detection of multiple photon emission requires temporal resolution higher than that of most commonly available cameras.[ clarification needed ] However, improved detector technology enabled demonstrations of quantum enhanced super-resolution using fast detector arrays, such as single-photon avalanche diode arrays. [25]

Quantum enhanced Raman microscopy

Quantum correlations offer an SNR beyond the photo-damage limit (the amount of energy that can be delivered without damage to the sample) of conventional microscopy. A coherent Raman microscope offers sub-wavelength resolution and incorporates bright quantum correlated illumination. Molecular bonds within a cell can be imaged with a 35 per cent improved SNR compared with conventional microscopy, corresponding to a 14% concentration sensitivity improvement. [20]

Related Research Articles

<span class="mw-page-title-main">Double-slit experiment</span> Physics experiment, showing light and matter can be modelled by both waves and particles

In modern physics, the double-slit experiment demonstrates that light and matter can satisfy the seemingly-incongruous classical definitions for both waves and particles, which is considered evidence for the fundamentally probabilistic nature of quantum mechanics. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of the wave behavior of visible light. At that time it was thought that light consisted of either waves or particles. With the beginning of modern physics, about a hundred years later, it was realized that light could in fact show both wave and particle characteristics. In 1927, Davisson and Germer and, independently George Paget Thomson and Alexander Reid demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave–particle duality. He believed it demonstrated that Christiaan Huygens' wave theory of light was correct, and his experiment is sometimes referred to as Young's experiment or Young's slits.

<span class="mw-page-title-main">Electron</span> Elementary particle with negative charge

The electron is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, per the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

<span class="mw-page-title-main">Quantum entanglement</span> Correlation between quantum systems

Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.

Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions.

Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.

A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables to explain the behavior of particles like photons and electrons. As of 2015, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.

In particle physics, spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. This property may pertain to the spin, hence to the magnetic moment, of conduction electrons in ferromagnetic metals, such as iron, giving rise to spin-polarized currents. It may refer to (static) spin waves, preferential correlation of spin orientation with ordered lattices.

Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. The desire to resolve inconsistencies between observed phenomena and classical theory led to a revolution in physics, a shift in the original scientific paradigm: the development of quantum mechanics.

In quantum mechanics, a quantum eraser experiment is an interferometer experiment that demonstrates several fundamental aspects of quantum mechanics, including quantum entanglement and complementarity. The quantum eraser experiment is a variation of Thomas Young's classic double-slit experiment. It establishes that when action is taken to determine which of 2 slits a photon has passed through, the photon cannot interfere with itself. When a stream of photons is marked in this way, then the interference fringes characteristic of the Young experiment will not be seen. The experiment also creates situations in which a photon that has been "marked" to reveal through which slit it has passed can later be "unmarked." A photon that has been "unmarked" will interfere with itself once again, restoring the fringes characteristic of Young's experiment.

A delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1998, is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's delayed-choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

Atom optics "refers to techniques to manipulate the trajectories and exploit the wave properties of neutral atoms". Typical experiments employ beams of cold, slowly moving neutral atoms, as a special case of a particle beam. Like an optical beam, the atomic beam may exhibit diffraction and interference, and can be focused with a Fresnel zone plate or a concave atomic mirror.

<span class="mw-page-title-main">Hydrogen anion</span> Negative ion of hydrogen

The hydrogen anion, H−, is a negative ion of hydrogen, that is, a hydrogen atom that has captured an extra electron. The hydrogen anion is an important constituent of the atmosphere of stars, such as the Sun. In chemistry, this ion is called hydride. The ion has two electrons bound by the electromagnetic force to a nucleus containing one proton.

Within quantum technology, a quantum sensor utilizes properties of quantum mechanics, such as quantum entanglement, quantum interference, and quantum state squeezing, which have optimized precision and beat current limits in sensor technology. The field of quantum sensing deals with the design and engineering of quantum sources and quantum measurements that are able to beat the performance of any classical strategy in a number of technological applications. This can be done with photonic systems or solid state systems.

Photofragment ion imaging or, more generally, Product Imaging is an experimental technique for making measurements of the velocity of product molecules or particles following a chemical reaction or the photodissociation of a parent molecule. The method uses a two-dimensional detector, usually a microchannel plate, to record the arrival positions of state-selected ions created by resonantly enhanced multi-photon ionization (REMPI). The first experiment using photofragment ion imaging was performed by David W Chandler and Paul L Houston in 1987 on the phototodissociation dynamics of methyl iodide (iodomethane, CH3I).

Ghost imaging is a technique that produces an image of an object by combining information from two light detectors: a conventional, multi-pixel detector that does not view the object, and a single-pixel (bucket) detector that does view the object. Two techniques have been demonstrated. A quantum method uses a source of pairs of entangled photons, each pair shared between the two detectors, while a classical method uses a pair of correlated coherent beams without exploiting entanglement. Both approaches may be understood within the framework of a single theory.

Hardy's paradox is a thought experiment in quantum mechanics devised by Lucien Hardy in 1992–1993 in which a particle and its antiparticle may interact without annihilating each other.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

Double ionization is a process of formation of doubly charged ions when laser radiation is exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

Aneta Sylwia Stodolna is a Polish physicist known for being the first person to successfully use a quantum microscope to image electrons in a hydrogen atom.

References

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