Matter Waves Research Articles

Constraining the general oscillatory inflaton potential with freeze-indark matter and gravitational waves

The reheating phase after inflation is one of the least observationally constrained epochs in the evolution of the Universe. The forthcoming gravitational wave observatories will enable us to constrain at least some of the non-standard scenarios. For example, models where the radiation bath is produced by the perturbative inflaton decay that oscillates around a minimum of the potential of the form V ∝ ϕ 2n, with n > 2. In such scenarios a part of the inflationary gravitational wave spectrum becomes blue tilted, making it observable, depending on the inflation energy scale and the reheating temperature. The degeneracy between the latter two parameters can be broken if dark matter in the Universe is produced via the freeze-in mechanism. The combination of the independent measurement of dark matter mass with gravitational wave observations makes it possible to constrain the reheating temperature and the energy scale at the end of inflation, at least within some parameter ranges.

Matter waves hang in there

Matter waves hang in there

Linear–quadratic GUP and thermodynamic dimensional reduction

In this paper we investigate the statistical mechanics within the Linear–Quadratic GUP (LQGUP, i.e, GUP with linear and quadratic terms in momentum) models in the semiclassical regime. Then, some thermodynamic properties of a system of 3-dimensional harmonic oscillators are investigated by calculating the deformed partition functions. According to the equipartition theorem, we show that the number of accessible microstates decreases sharply in the very high temperatures regime. When the thermal de Broglie wavelength is of the order of the Planck length, three degrees of freedom are frozen in this setup. In other words, it is observed that there is an effective reduction of the degrees of freedom from 6 to 3 for a system of 3D harmonic oscillators in this framework. The calculations are carried out using both approximate analytical and exact numerical methods. The results of the analytical method are also presented in the form of thermal wavelengths for better understanding. Finally, the case of a 2-dimensional harmonic is treated as another example to comprehend the results, leading to a reduction of the degrees of freedom from 4 to 2.

Final parsec problem of black hole mergers and ultralight dark matter

When two galaxies merge, they often produce a supermassive black hole binary (SMBHB) at their center. Numerical simulations with stars and cold dark matter show that SMBHBs typically stall out at a distance of a few parsecs apart and take billions of years to coalesce. This is known as the final parsec problem. We suggest that ultralight dark matter (ULDM) halos around SMBHBs can generate dark matter waves due to dynamical friction. These waves can effectively carry away orbital energy from the black holes, rapidly driving them together. To test this hypothesis, we performed numerical simulations of black hole binaries inside ULDM halos. Due to gravitational cooling and quasi-normal modes, the loss-cone problem can be avoided. The decay time scale gives lower bounds on masses of the ULDM particles and SMBHBs comparable to observational data. Our results imply that ULDM waves can lead to the rapid orbital decay of black hole binaries.

Optical edge-to-screw singularity state conversions

Optical singularity states, which significantly affect propagation properties of light in free space or optical medium, can be geometrically classified into screw and edge types. These different types of singularity states do not exhibit direct connection, being decoupled from each other in the absence of external perturbations. Here we demonstrate a novel optical process in which a higher-order edge singularity state initially nested in the propagating Gaussian light field gradually involves into a screw singularity with a new-born topological charge determined by order of the edge state. The considered edge state comprises an equal superposition of oppositely charged vortex and antivortex modes. We theoretically and experimentally realize this edge-to-screw conversion process by introducing intrinsic vortex–antivortex interaction. We also present a geometrical representation for mapping this dynamical process, based on the higher-order orbital Poincaré sphere. Within this framework, the edge-to-screw conversion is explained by a mapping of state evolution from the equator to the north or south pole of the Poincaré sphere. Our demonstration provides a novel approach for manipulating singularity state by the intrinsic vortex–antivortex interactions. The presented phenomenon can be also generalized to other wave systems such as matter wave, water wave, and acoustic wave.

Diffraction of polar molecules at nanomasks with low charge density

The wave nature of matter is a cornerstone of modern physics and has been demonstrated for a wide range of fundamental and composite particles. While diffraction at nanomechanical masks is usually regarded to be independent of internal atomic or molecular states, the particles' polarizabilities and dipole moments lead to dispersive interactions with the grating surface. In prior experiments, such forces largely prevented coherent diffraction of polar molecules as they induce dephasing of the matter wave in the presence of randomly distributed charges inside the grating. Here, we show that surface milling using neon ions facilitates the fabrication of lowly charged nanomasks in gold-capped silicon nitride membranes. This allows us to observe diffraction of polar molecules with over four times larger electric dipole moment than in previous experiments, opening a path towards distinction of structural conformers in matter-wave experiments. Published by the American Physical Society 2024

The [formula omitted]-Adic Schrödinger equation and the two-slit experiment in quantum mechanics

p-Adic quantum mechanics is constructed from the Dirac–von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space, QpN. This choice is equivalent to the hypothesis of the discreteness of the space. The time is assumed to be a real variable. The p-adic quantum mechanics is motivated by the question: what happens with the standard quantum mechanics if the space has a discrete nature? The time evolution of a quantum state is controlled by a nonlocal Schrödinger equation obtained from a p-adic heat equation by a temporal Wick rotation. This p-adic heat equation describes a particle performing a random motion in QpN. The Hamiltonian is a nonlocal operator; thus, the Schrödinger equation describes the evolution of a quantum state under nonlocal interactions. In this framework, the Schrödinger equation admits complex-valued plane wave solutions, which we interpret as p-adic de Broglie waves. These mathematical waves have all wavelength p−1. In the p-adic framework, the double-slit experiment cannot be explained using the interference of the de Broglie waves. The wavefunctions can be represented as convergent series in the de Broglie waves, but the p-adic de Broglie waves are just mathematical objects. Only the square of the modulus of a wave function has a physical meaning as a time-dependent probability density. These probability densities exhibit interference patterns similar to the ones produced by ‘quantum waves’. In the p-adic framework, in the double-slit experiment, each particle goes through one slit only. The p-adic quantum mechanics is an analog (or model) of the standard one under the hypothesis of the existence of a Planck length. The precise connection between these two theories is an open problem. Finally, we propose the conjecture that the classical de Broglie wave-particle duality is a manifestation of the discreteness of space–time.

Electric field driven focusing and transport of plasma ion beams by micro-glass capillaries beyond the self-focusing limit

Micro-glass capillaries emerge as an important tool for the lossless guiding and focusing of ion beams (Kojima 2018 J. Phys. B: At. Mol. Opt. Phys. 51 042001). The self-focusing mechanism of the capillaries is primarily governed by charged patches induced on their inner walls by the incident beam (Stolterfoht et al 2002 Phys. Rev. Lett. 88 133201). However, the dominance of space charge forces over self-focusing forces in intense (J ≈ 1 A m−2) ion beams establishes a self-focusing limit (Maurya et al 2019 J. Phys. D: Appl. Phys. 52 055205), posing challenges to beam focusing beyond this limit. In this work, a novel method is introduced, demonstrating electrical control over the charge patch dynamics through an externally applied bias voltage, thereby enabling the focusing of Ar ion beams beyond the self-focusing limit. Experimental results reveal that adjusting the biasing voltage allows overcoming the self-focusing limit, resulting in the generation of a high-intensity ( Jout≈3.05×105 A m−2) nano-beam (∼160 nm). Furthermore, electrical control is shown to enhance the performance of both straight and tapered capillaries (SC/TC), with the TC being more effective for nano-beam generation. A Particle-In-Cell (PIC) simulation code has been developed to explain the experimental results. The implications of high-intensity nano ion beams in advancing nanopatterning, nanoscale material analysis, and matter wave interferometry, underscore significant contributions to research and innovation within electronics, materials science, nanotechnology, and emerging quantum technologies.

Universal acceleration and fuzzy dark matter

Observations of velocity dispersions of galactic structures over a wide range of scales point to the existence of a universal acceleration scale [Formula: see text][Formula: see text]m/s2. Focusing on the fuzzy dark matter paradigm, which proposes ultralight dark matter with mass around [Formula: see text][Formula: see text]eV and de Broglie wavelength [Formula: see text] parsecs, we highlight the emergence of the observed acceleration scale from quantum effects in a fluid-like description of the dark matter dynamics. We then suggest the possibility of a natural connection between the acceleration scale and dark energy within the same paradigm.

Structured electrons with chiral mass and charge.

Chirality is a phenomenon with widespread relevance in fundamental physics, material science, chemistry, optics, and spectroscopy. In this work, we show that a free electron can be converted by the field cycles of laser light into a right-handed or left-handed coil of mass and charge. In contrast to phase-vortex beams, our electrons maintained a flat de Broglie wave but obtained their chirality from the shape of their expectation value in space and time. Measurements of wave function densities by attosecond gating revealed the three-dimensional shape of coils and double coils with left-handed or right-handed pitch. Engineered elementary particles with such or related chiral geometries should be useful for applications in chiral sensing, free-electron quantum optics, particle physics or electron microscopy.

Interference-induced suppression of particle emission from a Bose–Einstein condensate in lattice with time-periodic modulations

Abstract Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications. In this work, we investigate the collective particle emission from a Bose–Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions. We give the regimes for discrete modes, and find that the emission can be distinctly suppressed. The configuration induces a broad band, but few particles are ejected due to the interference of the matter waves. We further qualitatively model the emission process and demonstrate the short-time behaviors. This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices, and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

A theoretical perspective on the almost dark galaxy Nube: exploring the fuzzy dark matter model

In recent astronomical observations, an almost dark galaxy, designated as Nube, has unveiled an intriguing anomaly in its stellar distribution. Specifically, Nube exhibits an exceptionally low central brightness, with the 2D half-light radius of its stars far exceeding the typical values found in dwarf galaxies, and even surpassing those observed in ultra-diffuse galaxies (UDGs). This phenomenon is difficult to explain within the framework of cold dark matter (CDM). Meanwhile, due to its ultralight particle mass, fuzzy dark matter (FDM) exhibits a de Broglie wavelength on the order of kiloparsecs under the typical velocities of galaxies. The interference between different modes of the FDM wave gives rise to fluctuations in the gravitational field, which can lead to the dynamical heating of stars within galaxies, resulting in an expansion of their spatial distribution. In this paper, we aim to interpret the anomalous stellar distribution observed in Nube as a consequence of the dynamical heating effect induced by FDM. Our findings suggest that a FDM particle mass around 1-2 × 10-23 eV can effectively account for this anomaly. And we propose that the FDM dynamical heating effect provides a new insight into understanding the formation of field UDGs.

Controlling dark solitons on the healing length scale

While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose–Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton state can be obtained by selectively driving the impurity atoms. This allows to fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.

No massive black holes in the Milky Way halo.

The gravitational wave detectors have shown a population of massive black holes that do not resemble those observed in the Milky Way1-3 and whose origin is debated4-6. According to a possible explanation, these black holes may have formed from density fluctuations in the early Universe (primordial black holes)7-9, and they should comprise several to 100% of dark matter to explain the observed black hole merger rates10-12. If these black holes existed in the Milky Way dark matter halo, they would cause long-timescale gravitational microlensing events lasting years13. The previous experiments were not sufficiently sensitive to such events14-17. Here we present the results of the search for long-timescale microlensing events among the light curves of nearly 80 million stars located in the Large Magellanic Cloud that were monitored for 20 years by the Optical Gravitational Lensing Experiment survey18. We did not find any events with timescales longer than 1 year, whereas all shorter events detected may be explained by known stellar populations. We find that compact objects in the mass range from 1.8 × 10-4M⊙ to 6.3M⊙ cannot make up more than 1% of dark matter, and those in the mass range from 1.3 × 10-5M⊙ to 860 M⊙ cannot make up more than 10% of dark matter. Thus, primordial black holes in this mass range cannot simultaneously explain a substantial fraction of dark matter and gravitational wave events.

Spin resonance spectroscopy with an electron microscope

Coherent spin resonance methods, such as nuclear magnetic resonance and electron spin resonance spectroscopy, have led to spectrally highly sensitive, non-invasive quantum imaging techniques. Here, we propose a pump-probe spin resonance spectroscopy approach, designed for electron microscopy, based on microwave pump fields and electron probes. We investigate how quantum spin systems couple to electron matter waves through their magnetic moments and how the resulting phase shifts can be utilized to gain information about the states and dynamics of these systems. Notably, state-of-the-art transmission electron microscopy provides the means to detect phase shifts almost as small as that due to a single electron spin. This could enable state-selective observation of spin dynamics on the nanoscale and indirect measurement of the environment of the examined spin systems, providing information, for example, on the atomic structure, local chemical composition and neighboring spins.

Monolithically Structured van der Waals Materials for Volume-Polariton Refraction and Focusing.

Polaritons, hybrid light and matter waves, offer a platform for subwavelength on-chip light manipulation. Recent works on planar refraction and focusing of polaritons all rely on heterogeneous components with different refractive indices. A fundamental question, thus, arises whether it is possible to configure two-dimensional monolithic polariton lenses based on a single medium. Here, we design and fabricate a type of monolithic polariton lens by directly sculpting an individual hyperbolic van der Waals crystal. The in-plane polariton focusing through sculptured step-terraces is triggered by geometry-induced symmetry breaking of momentum matching in polariton refractions. We show that the monolithic polariton lenses can be robustly tuned by the rise of van der Waals terraces and their curvatures, achieving a subwavelength focusing resolution down to 10% of the free-space light wavelength. Fusing with transformation optics, monolithic polariton lenses with gradient effective refractive indices, such as Luneburg lenses and Maxwell's fisheye lenses, are expected by sculpting polaritonic structures with gradually varied depths. Our results bear potential in planar subwavelength lenses, integrated optical circuits, and photonic chips.

Analysis of One-dimensional Double-potential Barrier Structures Resonant Tunnelling Based on Transmission Matrices

The comprehension of the tunnel effect, the passage of matter waves and particles across a high potential barrier, was the most astounding of all discoveries in quantum mechanics. Research on tunnelling in semiconductors and superconductors, as well as the development of scanning tunnelling microscopy, garnered five Nobel prizes in physics. In this study, the resonant tunnelling effect of electron tunnelling through a one-dimensional double-potential barrier was found and verified by solving the time-independent Schrödinger equation and calculating the transmittance rate of the electron tunnelling through the two potential barriers by using the transmission matrix technique performed by MATLAB. According to the analysis, the transmittance rate was one under certain specific conditions (under some specific incident energy values or some specific distance between two potential barriers), which was called as resonant tunnelling. However, in this study, square potential wells were analyzed, which can be considered merely as ideal models in real life, and therefore all results are idealized. For further investigations, researchers can use more realistic parameters to set up potential wells and analyze real-life problems.

Understanding quantum mechanics

Quantum mechanics presently has many unanswered questions, paradoxes, and even outright logical contradictions. To make progress in understanding quantum mechanics, we begin by proposing that relativity be set aside in favor of an absolute aetherial theory. Once that step is taken, we can understand quantum collapse as a description of real wave-packets collapsing in a faster-than-light way. By assuming that a partially observable reality exists, we can then extend our analysis of wave-packets into the subquantum, and the Heisenberg uncertainty principle then follows from the Fourier uncertainty principle coupled with the de Broglie relation. Further progress in understanding quantum mechanics is possible by modifying the de Broglie and Planck relations. Those modifications lead to matter-waves moving at the speed of light rather than superluminally as presently theorized, and they allow the results of matter-wave two-slit experiments to be understood from any reference frame. A modified time-dependent Schrödinger Equation results from our modifications, but the spatial time-independent Schrödinger equation is retained.

Current Oscillations and Resonances in Nanocrystals of Narrow-gap Semiconductors

In single colloidal nanocrystals of narrow-gap semiconductors PbS and InSb, current instability in the form of quasi-periodic spikes and current resonance peaks was studied by measuring on a scanning probe microscope and analyzing Current-Voltage Characteristics (CVC). The observed phenomena are explained in models of the wave de Broglie process and Bloch oscillations. Statistically, the percentages of such samples and the parameters of oscillations on the current-voltage characteristic are higher, the larger the size quantization parameter, determined by the de Broglie wavelength. A possible practical use is the generation and recording of terahertz radiation modulated by ultrashort pulses.

Primordial black holes and induced gravitational waves in non-singular matter bouncing cosmology

We present a novel model-independent generic mechanism for primordial black hole formation within the context of non-singular matter bouncing cosmology. In particular, considering a short transition from the matter contracting phase to the Hot Big Bang expanding Universe, we find naturally enhanced curvature perturbations on very small scales which can collapse and form primordial black holes. Interestingly, the primordial black hole masses that we find can lie within the observationally unconstrained asteroid-mass window, potentially explaining the totality of dark matter. Remarkably, the enhanced curvature perturbations, collapsing to primordial black holes, can induce as well a stochastic gravitational-wave background, being potentially detectable by future experiments, in particular by SKA, PTAs, LISA and ET, hence serving as a new portal to probe the bouncing nature of the initial conditions prevailing in the early Universe.