Bound Quantum States Research Articles

Mass-energy equivalence in gravitationally bound quantum states of the neutron

Gravitationally bound neutrons have become an important tool in the experimental searches for new physics, such as modifications to Newton's force or candidates for dark matter particles. Here we include the relativistic effects of mass-energy equivalence into the model of gravitationally bound neutrons. Specifically, we investigate a correction in a gravitationally bound neutron's Hamiltonian due to the presence of an external magnetic field. We show that the neutron's additional weight due to mass-energy equivalence will cause a small shift in the neutron's eigenenergies and eigenstates, and examine how this relativistic correction would affect experiments with trapped neutrons. We further consider the ultimate precision in estimating the relativistic correction to the precession frequency and find that, at short times, a joint measurement of both the spin and motional degrees of freedom provides a metrological enhancement as compared to a measurement of the spin alone.

Three-body bound states in antiferromagnetic spin ladders

Stable bound quantum states are ubiquitous in nature. Mostly, they result from the interaction of only pairs of particles, so called two-body interactions, even when large complex many-particle structures are formed. We show that three-particle bound states occur in a generic, experimentally accessible solid state system: antiferromagnetic spin ladders, related to high-temperature superconductors. This binding is induced by genuine three-particle interactions; without them there is no bound state. We compute the dynamic exchange structure factor required for the experimental detection of the predicted state by resonant inelastic X-ray scattering for realistic material parameters. Our work enables us to quantify these elusive interactions and unambiguously establishes their effect on the dynamics of the quantum many-particle state.

4D-imaging of drip-line radioactivity by detecting proton emission from 54mNi pictured with ACTAR TPC

Proton radioactivity was discovered exactly 50 years ago. First, this nuclear decay mode sets the limit of existence on the nuclear landscape on the neutron-deficient side. Second, it comprises fundamental aspects of both quantum tunnelling as well as the coupling of (quasi)bound quantum states with the continuum in mesoscopic systems such as the atomic nucleus. Theoretical approaches can start either from bound-state nuclear shell-model theory or from resonance scattering. Thus, proton-radioactivity guides merging these types of theoretical approaches, which is of broader relevance for any few-body quantum system. Here, we report experimental measurements of proton-emission branches from an isomeric state in 54mNi, which were visualized in four dimensions in a newly developed detector. We show that these decays, which carry an unusually high angular momentum, ℓ = 5 and ℓ = 7, respectively, can be approximated theoretically with a potential model for the proton barrier penetration and a shell-model calculation for the overlap of the initial and final wave functions.

Efimov States in an Ultracold Gas: How it Happened in the Laboratory

In the year 2005, we obtained first evidence for the existence of weakly bound quantum states of three resonantly interacting particles, as predicted 35 years earlier by Vitaly Efimov. In our laboratory, the striking signature of an Efimov state was a giant three-body loss resonance observed in a gas of cesium atoms that was evaporatively cooled to temperatures of about 10 nanokelvin. Here, I will give a short personal account on what prepared the ground for this observation, on how things finally happened in our laboratory, and on how our experiments then developed further.

Yukawa model of screening in low-dimensional excitons: diagonalization, perturbation, variation, and resummation analysis

The Yukawa interaction describes Coulomb screening in several physical systems. We investigate bound quantum states of the Yukawa potential in low-dimensional structures as a model of e.g. excitons in semiconductor nanostructures. Diagonalization, perturbation, variation, and resummation methods are all applied to the problem and their accuracy is compared. For moderate positive screening, all methods are found to be applicable and, in particular, the variational approach is highly accurate except near the threshold for bound states. In contrast, only hypergeometric resummation captures the correct behaviour in the negative (antiscreened) regime. We also determine the dimensional dependence of the critical screening, above which bound states cease to exist. As an application, the critical screening is used to compute critical doping levels for the existence of bound excitons in quantum wells.

Inelastic Neutron Scattering As an Indication of a New Type of Gapped Surface Excitations in Liquid He

We analyze the experimental data on inelastic neutron scattering by a thin ~5-atomic-layer film of liquid helium at three different temperatures: T=0.4K, 0.98K and 1.3K. These data were partially published previously, but here we present them in a better quality and at various temperatures. The neutron scattering intensity plots, in addition to the previously know dispersion of phonons and ripplons, suggest a branch of gapped surface excitations with activation energy $\sim 4.5$K and the dispersion similar to that expected for surfons - the bound quantum states of helium atoms above liquid helium surface, proposed and investigated theoretically. These data, probably, provide the first direct experimental confirmation of surfons. Before these surface excitations received only indirect experimental substantiation, based on the temperature dependence of surface tension coefficient and on their interaction with surface electrons. The existence of surfons as an additional type of surface excitations, although being debated yet, is very important for various physical properties of He surface. We also analyze previous numerical results on excitations in liquid helium and argue that surface excitations similar to surfons have been previously obtained by numerical calculations and called resonance interface states.

Proof of principle for Ramsey-type gravity resonance spectroscopy with qBounce

Ultracold neutrons (UCNs) are formidable probes in precision tests of gravity. With their negligible electric charge, dielectric moment, and polarizability they naturally evade some of the problems plaguing gravity experiments with atomic or macroscopic test bodies. Taking advantage of this fact, the qBounce collaboration has developed a technique – gravity resonance spectroscopy (GRS) – to study bound quantum states of UCN in the gravity field of the Earth. This technique is used as a high-precision tool to search for hypothetical Non-Newtonian gravity on the micrometer scale. In the present article, we describe the recently commissioned Ramsey-type GRS setup, give an unambiguous proof of principle, and discuss possible measurements that will be performed.

Testing gravity at short distances: Gravity Resonance Spectroscopy with qBounce

Neutrons are the ideal probes to test gravity at short distances – electrically neutral and only hardly polarizable. Furthermore, very slow, so-called ultracold neutrons form bound quantum states in the gravity potential of the Earth. This allows combining gravity experiments at short distances with powerful resonance spectroscopy techniques, as well as tests of the interplay between gravity and quantum mechanics. In the last decade, the qBounce collaboration has been performing several measurement campaigns at the ultracold and very cold neutron facility PF2 at the Institut Laue-Langevin. A new spectroscopy technique, Gravity Resonance Spectroscopy, was developed. The results were applied to test various Dark Energy and Dark Matter scenarios in the lab, like Axions, Chameleons and Symmetrons. This article reviews Gravity Resonance Spectroscopy, explains its key technology and summarizes the results obtained during the past decade.

Nonlinear Raman Scattering of Photons by Channeled Particles

The channeled particles are characterized by the bound quantum states of its transversal motion. Photon interactions with the channeled particles in a single crystal may be accompanied by the energy transitions between the transverse motion levels of channeling particles. The photon combination (Raman) scattering by the quasi-bound channeled particles leads to the occurrence of a frequency combination of the incident photon frequency ▪ and the shift frequency ▪, i.e. ▪ where ▪; ▪ is the transition energy between “i” and “f” transversal motion quantum states; ▪ is the channeled positrons Lorentz-factor, Kalashnikov and Krokhin (2014). A “violet” satellite (“anti-Stokes” lines ω) analysis in the Raman combination scattering spectrum is suggested. Three photons Raman type transition is examined, i.e. the process of the simultaneous absorption of two photons with the frequency ▪ and the photon emission with the frequency ▪ Resonance conditions for the third harmonics observation (▪) are discussed.

All-optical approach to determine the spatial shape of nanoscale electron wave functions using intraband spectroscopy

A spectroscopic pump-probe method to determine the spatial shape of bound quantum states in semiconductor quantum dots is proposed. The method uses intraband transitions between the bound states and unbound continuum states in the host medium. The developed theoretical scheme is applicable to quantum dots embedded in bulk material and with some modification also for other nanostructures. In particular, the analyzed pump-probe spectra exhibit specific spectral signatures for different spatial extensions of the quantum dot confinement potential.

Observation of the Spatial Distribution of Gravitationally Bound Quantum States of Ultracold Neutrons and Its Derivation Using the Wigner Function

Ultracold neutrons (UCNs) can be bound by the potential of terrestrial gravity and a reflecting mirror. The wave function of the bound state has characteristic modulations. We carried out an experiment to observe the vertical distribution of the UCNs above such a mirror at the Institut Laue-Langevin in 2011. The observed modulation is in good agreement with that prediction by quantum mechanics using the Wigner function. The spatial resolution of the detector system is estimated to be 0.7 μm. This is the first observation of gravitationally bound states of UCNs with submicron spatial resolution.

Black Hole Atom as a Dark Matter Particle Candidate

We propose the new dark matter particle candidate—the “black hole atom,” which is an atom with the charged black hole as an atomic nucleus and electrons in the bound internal quantum states. As a simplified model we consider the the central Reissner-Nordström black hole with the electric charge neutralized by the internal electrons in bound quantum states. For the external observers these objects would look like the electrically neutral Schwarzschild black holes. We suppose the prolific production of black hole atoms under specific conditions in the early universe.

Precision Measurement of the Position-Space Wave Functions of Gravitationally Bound Ultracold Neutrons

Gravity is the most familiar force at our natural length scale. However, it is still exotic from the view point of particle physics. The first experimental study of quantum effects under gravity was performed using a cold neutron beam in 1975. Following this, an investigation of gravitationally bound quantum states using ultracold neutrons was started in 2002. This quantum bound system is now well understood, and one can use it as a tunable tool to probe gravity. In this paper, we review a recent measurement of position-space wave functions of such gravitationally bound states and discuss issues related to this analysis, such as neutron loss models in a thin neutron guide, the formulation of phase space quantum mechanics, and UCN position sensitive detectors. The quantum modulation of neutron bound states measured in this experiment shows good agreement with the prediction from quantum mechanics.

Study of theBe14Continuum: Identification and Structure of its Second2+State

The coupling between bound quantum states and those in the continuum is of high theoretical interest. Experimental studies of bound drip-line nuclei provide ideal testing grounds for such investigations since they, due to the feeble binding energy of their valence particles, are easy to excite into the continuum. In this Letter, continuum states in the heaviest particle-stable Be isotope, 14Be, are studied by employing the method of inelastic proton scattering in inverse kinematics. New continuum states are found at excitation energies E*=3.54(16) MeV and E*=5.25(19) MeV. The structure of the earlier known 2(1)+ state at 1.54(13) MeV was confirmed with a predominantly (0d5/2)2 configuration while there is very clear evidence that the 2(2)+ state has a predominant (1s1/2, 0d5/2) structure with a preferential three-body decay mechanism. The region at about 7 MeV excitation shows distinct features of sequential neutron decay via intermediate states in 13Be. This demonstrates that the increasing availability of energetic beams of exotic nuclei opens up new vistas for experiments leading towards a new understanding of the interplay between bound and continuum states.

Influence of the chameleon field potential on transition frequencies of gravitationally bound quantum states of ultracold neutrons

We calculate the chameleon field potential for ultracold neutrons bouncing on top of one, or between two, neutron mirrors in the gravitational field of the Earth. For the resulting nonlinear equations of motion, we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit. The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultracold neutrons bound in the gravitational field of the Earth.

Spectroscopic observation of bound ungerade ion-pair states in molecular hydrogen

Frequency-resolved observations of heavy Rydberg states in molecular hydrogen are reported in the ungerade manifold of states. Double-resonance spectroscopy via the $E,F$ ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$, ${v}^{\ensuremath{'}}=6$ state has been used to probe the energy region above the H($1s$) $+$ H(3$l$) dissociation threshold. Resonances are observed by ionizing H(3$l$) to produce H${}^{+}$, which is then detected by using a time-of-flight mass spectrometer. The kinetic energy of the H${}^{+}$ ion confirms that the observed signal is due to the photoionization of neutral H(3$l$) atoms, indicating that dissociation is a significant decay channel for the ion-pair states. The pattern of energies of the resonances agree well with the predictions of a mass-scaled Rydberg formula for bound quantum states of the H${}^{+}$H${}^{\ensuremath{-}}$ ion pair. Energies and quantum defects have been determined for principal quantum numbers in the range of $n=130$ to 207.

Rayleigh–ritz method for excited quantum states via nonlinear variations without constraints: Role of supersymmetry

AbstractQuantum mechanical variation principle in the form of energy minimization is applicable only to ground states of systems, or, at best, states of lowest energies of given symmetries, provided the symmetry information is embedded in chosen trial functions. Thus, for bound quantum states with specified choices of trial functions involving nonlinear parameters, scope of the principle is severely restricted. A pedagogic way out is to enforce exact orthogonality of the chosen function with all exact lower energy states. In actual practice, this limits one to opt for linear variations where upper bound to each state is obtained in a single run. In this work, the motivation is to explore if there exists at all a way to determine optimized wave functions and energies for excited states via nonlinear variations but without any constraints, even for simple systems. Realizing that the major problem in excited‐state nonlinear variations is concerned with the variations of nodal positions, at least for problems reducible to one dimension, we seek a route via which nodes could be fixed beforehand, so that the information gained may be subsequently utilized to construct a suitable nonlinear trial function and carry out a straightforward optimization. To achieve this end, the idea of supersymmetric quantum mechanics has been used quite profitably, yielding the nodal structure of the excited states. Workability of the strategy for several excited‐state wave functions and their properties is demonstrated by choosing the problems of spherical Stark effect on hydrogen atom and anharmonic oscillator. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Beams of gravitationally bound ultracold neutrons in rough waveguides

We investigate the propagation of ultracold neutrons through a rough waveguide in conjunction with recent experiments in which the ultracold neutrons were beamed between a perfect mirror and a rough scatterer and absorber. The main goal is to find a way to resolve the lowest gravitationally quantized discrete states in the peV range. We compare the neutron count for various types of mirrors with Gaussian, power-law, and exponential correlation functions of surface inhomogeneities. The main conclusion is that all the information about inhomogeneities, including their amplitude, correlation radius, and the rate of decay of the correlation function, enter the exit neutron count via just a single constant $\ensuremath{\Phi}$, which effectively renormalizes the amplitude of roughness. To observe well-defined quantum steps, one should have an experimental setup with $\ensuremath{\Phi}g40$. For a wide variety of correlation functions, the constant $\ensuremath{\Phi}$ is proportional to the square of the amplitude of the surface roughness and is inversely proportional to the square root of the correlation radius. The strong dependence of $\ensuremath{\Phi}$ on roughness parameters and the shape of the correlation function opens a novel way for improving the resolution of gravitationally bound states by optimizing the roughness pattern without reverting to an undesirable strong roughness. We discuss how to optimize the scatterer and absorber by first generating numerically the desired roughness profile and then transferring it to the mirror. We also study the effect of beam preparation on the initial occupancies of gravitational states before the beam enters the waveguide. It turns out that there are simple ways to manipulate the beam in front of the waveguide that can help to resolve the gravitationally bound quantum states. Our results are in good agreement with available experimental data.

CHANNELING EXPERIMENTS WITH ELECTRONS AT THE MAINZ MICROTRON MAMI

The dechanneling process of electrons in silicon single crystals has been studied at the Mainz Microtron MAMI for (110)-planar channeling of electrons at beam energies between 195 and 855 MeV. Dechanneling lengths were derived from a high and a low energy loss signal of the electrons which were recorded as function of the crystal orientation with respect to the beam direction for various crystal thicknesses in the range between 14.7 µm and 467 µm. The high energy loss signal corresponds to an energy loss of about 75 % of the total electron energy by emission of a bremsstrahlung photon, while the low energy signal to an energy loss of 0.7-1.7 % by emission of channelling radiation. While the high energy signal saturates as function of the crystal thickness, the low energy signal does not. The nearly constant dechanneling length of about 35 µm, as extracted from the high energy signal, is interpreted to originate from a small fraction of electron which initially occupy deeply bound quantum states.

Gravitationally bound quantum states of ultracold neutrons and their applications

We will review the discovery and characterization of gravitationally bound quantum states of neutrons. The lowest neutron quantum states in a gravitational potential were distinguished and characterized by a measurement of their spatial extent. The neutron transmission was observed through a slit with an absorbing top surface at a variable height. Second, a position-sensitive detector was used for a direct visualization of the wavefunction. An application is the search for new short-range interactions, which would alter the waveform of the quantum states.