Energy Level Spacing Research Articles

Theoretical model and verification of the laser thermal effect on the temperature measurement sensitivity of rare earth

The fluorescence temperature measurement based on rare earth ions has been studied widely. It is quite puzzling that the same thermal coupling energy levels present different relative sensitivities of temperature measurement in reports. Different relative sensitivities indicate that the level spacing of the same thermal coupling energy levels calculated by Boltzmann's formula is different. To solve this problem, a physical model is proposed to explain the influence of the laser thermal effect on the fluorescence temperature measurement. The results show that the additional temperature of the sample imposed by the laser thermal effect has an impact on the relative sensitivity, which is the higher the additional temperature, the lower the relative sensitivity. Furthermore, the source of heat generation from laser irradiation of rare earth is discussed. For Er3+ ions, the laser converted into heat mainly generated by the multiphonon transitions between 2H11/2 and 4S3/2 levels. The results show that the theoretical curve fitted well with the experimental data. It is instructive for the design of new temperature sensors.

Friction-Induced Near-Infrared Emission and Its Mechanism.

Triboluminescence (TL) is an optical phenomenon in which light is emitted from the surface of a material when subjected to pressure or shear forces. Due to its potential applications in non-destructive testing, radiation sources, and spectroscopic probes, TL has garnered increasing attention over the past two decades. However, experimental observations in the infrared spectrum remain limited, and its emission mechanism has not yet been fully understood. In this study, significant emission in the near-infrared spectrum was experimentally observed from the tribo-pairs of Cr/YSZ and quartz/YSZ. The results indicate that the Tribo-Induced Near-Infrared Light Emission consists of three peaks, in which the 780 nm peak is related to the electronic transition between the 3d5/2 and 3d3/2 orbitals of Y3+ ions, while the 880 nm and 990 nm peaks can be attributed to hole centers and T-type centers in the intrinsic defects of YSZ, respectively. Additionally, experiments reveal that the Cr/YSZ tribo-pair exhibits a redshift of 11-18 nm at the 780 nm peak compared to the quartz/YSZ tribo-pair. To explain the cause of the redshift phenomenon, X-ray photoelectron spectroscopy and UV-Vis absorption spectroscopy were used to measure the energy level spacing between the 3d5/2 and 3d3/2 orbitals of Y3+ and the bandgap width of YSZ before and after friction, respectively. We found that the bandgap width of the doped YSZ decreases after friction, which is often accompanied by a reduction in the energy level spacing between the 3d5/2 and 3d3/2 orbitals of Y3+. The extent of the reduction in energy level spacing varies with different dopants, leading to the redshift phenomenon.

Optical simulation of a quantum cooling engine powered by entangled measurements

Traditional refrigeration is driven either by external forces or by the information-feedback mechanism. Surprisingly, quantum measurement and collapse, typically viewed as detrimental, can also power a quantum cooling engine without requiring any feedback mechanism. In this work, we perform a proof-of-principle demonstration of quantum measurement cooling (QMC) powered by entangled measurements using a highly controllable linear optical simulator. The simulator can simulate qubits with different energy-level spacings and their thermalizing processes at different temperatures, and also allows for arbitrary projections of two qubits at different energy levels. We show the effect of changes in energy levels and measurement bases on the cooling process and demonstrate the robustness of QMC. These results reveal the special role of entangled measurements in quantum thermodynamics, indicate that quantum measurement is not always detrimental but can be a valuable thermodynamic resource. Our setup also offers a highly controllable simulation platform for multiqubit quantum engines.

Spectral Analysis of Proton Eigenfunctions in Crystalline Environments

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number Nw, reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal.

Spectroscopic Study of a New Electronic Band System 33Δg-a3Πu of C2.

As one of the most important diatomic molecules in the universe, the spectroscopic characterizations of C2 have attracted wide attention in various fields, such as interstellar chemistry, planetary atmospheric chemistry, and combustion. In recent years, a systematic spectroscopic study of C2 in the vacuum ultraviolet (VUV) region has been carried out in our laboratory by using the (1VUV+1'UV) resonance-enhanced multiphoton ionization method based on the combination of a tunable VUV laser source and a time-of-flight mass spectrometer. Two new electronic transition band systems have been reported, following the pioneering work of Herzberg and co-workers in 1969. In the current study, a total of 18 vibronic transition bands of C2 from the lower a3Πu state are experimentally observed in the VUV photon energy range 72000-81000 cm-1, and 6 new upper vibronic levels of 3Δg symmetry are identified, which are assigned as the v' = 0-5 vibrational levels of the 33Δg state of C2. The term energy Te of the 33Δg state is determined to be in the range of 78425-78475 cm-1 (9.724-9.730 eV) with respect to the ground X1Σg+ state, and the molecular constants such as vibrational and rotational constants are also determined, which are in reasonable agreement with those predicted by high-level ab initio theoretical calculations. Irregular vibrational energy level spacings in the 33Δg state are observed, which is tentatively attributed to the strong perturbations between the 33Δg and 23Δg states, as previously predicted by theory.

On the thermodynamic entropy in the microcanonical ensemble of classical systems

We demonstrate that the surface entropy given by the volume of an energy shell in the phase space can be the thermodynamically consistent entropy in a classical microcanonical ensemble if the thickness of the energy shell is not an arbitrary constant but a non-extensive function satisfying a specific differential equation. A particular form of the energy shell thickness as a possible solution to the differential equation converts the surface entropy into the volume entropy given by the phase-space volume bounded by a constant energy surface. However, such a form bears a problem: The temperature derived accordingly becomes extensive when the density of states is a non-monotonic function of energy. Based on the adiabatic invariance of the degeneracy of a quantum system and the Weyl correspondence, we propose an alternative solution: the energy shell thickness given by the energy level spacing in the quantum counterpart of the classical ensemble considered, which is illustrated by a few simple examples.

Nonlinear wireless energy harvesting based uplink transmission in K-tier heterogeneous networks over Nakagami-m fading channels

With the widespread application of various battery-powered devices, it is very challenging to sustainably meet the tremendous wireless transmission requirements over limited spectrum. We propose a wireless energy harvesting (EH) based uplink transmission scheme for the K-tier heterogeneous cellular network (HCN) with all the channels undergoing Nakagami-m fading. The locations of base stations (BSs) in each tier, mobile users (MUs), and power beacons (PBs) are properly modeled as independent homogeneous Poisson point processes. Each MU can be associated with a BS in any tier that provides the maximum averaged received signal power. MUs can harvest wireless energy from all the PBs in a nonlinear fashion, and then transmit data to the associated BS by using the harvested energy. We properly model the energy statuses of MUs by defining a series of unequally spaced energy levels according to the probability distribution of EH amount. Through properly modeling the aggregate interference, we analyze the outage probability and the area throughput of the multi-tier HCN. Numerical results show that our proposed scheme can greatly outperform the benchmark scheme in terms of outage probability and area throughput. The impacts of key parameters are revealed through extensive simulations, which can guide the network deployment.

Extending the Large Molecule Limit: The Role of Fermi Resonance in Developing a Quantum Functional Group.

Polyatomic molecules equipped with optical cycling centers (OCCs), enabling continuous photon scattering during optical excitation, are exciting candidates for advancing quantum information science. However, as these molecules grow in size and complexity, the interplay of complex vibronic couplings on optical cycling becomes a critical but relatively unexplored consideration. Here, we present an extensive exploration of Fermi resonances in large-scale OCC-containing molecules using high-resolution dispersed laser-induced fluorescence and excitation spectroscopy. These resonances manifest as vibrational coupling leading to intensity borrowing by combination bands near optically active harmonic bands, which require additional repumping lasers for effective optical cycling. To mitigate these effects, we explore altering the vibrational energy level spacing through substitutions on the phenyl ring or changes in the OCC itself. While the complete elimination of vibrational coupling in complex molecules remains challenging, our findings highlight significant mitigation possibilities, opening new avenues for optimizing optical cycling in large polyatomic molecules.

Pseudo-Landau levels of hexagonal lattice quantum antiferromagnets under bending strain

The pseudo-Landau energy levels of a hexagonal lattice quantum antiferromagnet under bending strain are studied by linear spin-wave theory (LSWT) and quantum Monte Carlo method (QMC). Using the linear spin wave theory, the magnetic pseudo-Landau energy level can be found to appear at the high-energy end of the magnon spectrum, and the energy level spacing is proportional to the square root of the energy level index. The linear spin wave theory and the quantum Monte Carlo method both indicate that at the same size, the local magnetization gradually weakens with the gradual increase of the strain strength. Additionally, the antiferromagnetic order continuously weakens in the <i>y</i>-direction under the same strain strength. This occurs because the Heisenberg chain on the upper boundary becomes decoupled into an isolated vertical chain, leading to the destruction of the magnetic order near the upper boundary. The quantum Monte Carlo method provides a more accurate antiferromagnetic sequence evolution, that is, the vertical correlation at the upper boundary is unchanged and the horizontal correlation increases under a specific strain intensity. This affects the magnetization intensity, so that the local magnetization shows an upward trend at the upper boundary. The results contribute to the understanding of the effect of bending strain on spin excitations, and this effect may be observed in two-dimensional quantum magnetic material experiments.

Vacuum-field-induced state mixing

By engineering the electromagnetic vacuum field, the induced Casimir-Polder shift (also known as Lamb shift) and spontaneous emission rates of individual atomic levels can be controlled. When the strength of these effects becomes comparable to the energy difference between two previously uncoupled atomic states, an environment-induced interaction between these states appears after tracing over the environment. This interaction has been previously studied for degenerate levels and simple geometries involving infinite, perfectly conducting half-spaces or free space. Here, we generalize these studies by developing a convenient description that permits the analysis of these non-diagonal perturbations to the atomic Hamiltonian in terms of an accurate non-Hermitian Hamiltonian. Applying this theory to a hydrogen atom close to a dielectric nanoparticle, we show strong vacuum-field-induced state mixing that leads to drastic modifications in both the energies and decay rates compared to conventional diagonal perturbation theory. In particular, contrary to the expected Purcell enhancement, we find a surprising decrease of decay rates within a considerable range of atom-nanoparticle separations. Furthermore, we quantify the large degree of mixing of the unperturbed eigenstates due to the non-diagonal perturbation. Our work opens new quantum state manipulation possibilities in emitters with closely spaced energy levels.

Optical tuning of the terahertz response of black phosphorus quantum dots: effects of weak carrier confinement

Abstract In contrast to few-layer black phosphorus (BP) with a relatively larger area, BP quantum dots (BP-QDs) are expected to have distinctive electromagnetic response and carrier behaviors, especially in low-frequency range such as in the THz regime. Herein, we experimentally investigate the THz properties of BP-QDs as well as the optical control of these properties. It is demonstrated that the effects of weak carrier confinement, which is associated with diffusive restoring current in each BP-QD, contribute significantly to the effective THz conductivity of BP-QDs. Instead, spectral features of discretely spaced energy levels as shown for many kinds of semiconductor QDs in UV-visible range are not observed in the THz regime. This indicates an insignificant contribution of strong quantum confinement here. Based on the modified Drude–Smith formula, we show that the optical excitation/pump of a CW laser can induce photogenerated carriers and enhance the effects of weak carrier confinement in BP-QDs. Thus, a nonlinear enhancement of THz absorption can be observed by increasing the power of the excitation laser. These results not only deepen our understanding of the fundamental physics of BP nanomaterials but also provide an alternative approach to realize active control of BP-based THz devices.

Krylov complexity and chaos in quantum mechanics

Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.

Automated superconducting qubit characterization platform based on a modified 3D printer

Josephson Junctions are important components in superconducting qubits. It introduces anharmonicity to the energy level spacings of the qubit which allow us to identify two unique quantum energy states for computing. It is difficult to fabricate multiple junctions within the same desired parameter range. Characterisation of the junctions is, therefore, a necessary step after fabrication. In particular, the critical current of the junctions is determined by measuring their normal state resistance. This is done via two-point or four-point resistance measurement at a manual probe station which is a time-consuming process, especially for wafer-scale fabrication. This bottleneck can be circumvented by automation with object detection. The base of the automated probe station is a 3D printer modified with multiple Arduino Uno microcontrollers and motorized linear stages. The automation process is achieved via auto-alignment of the probes and an automatic measurement procedure. As a result, the fully automated process will take about 27–29[Formula: see text]s to measure the resistance of one junction which saves 28%–51% of the time compared to the manual probe station and can be unsupervised. Due to the reuse of a commercial 3D printer, the cost of this system is 800 SGD which is much less than comparable commercial solutions.

Quantum heat machines enabled by twisted geometry

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines, with an incompressible sample, can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

Shock excitation of H2 in the James Webb Space Telescope era

Context. Molecular hydrogen, H2, is the most abundant molecule in the Universe. Thanks to its widely spaced energy levels, it predominantly lights up in warm gas, T ≳ 102 K, such as shocked regions externally irradiated or not by interstellar UV photons, and it is one of the prime targets of James Webb Space Telescope (JWST) observations. These may include shocks from protostellar outflows, supernova remnants impinging on molecular clouds, all the way up to starburst galaxies and active galactic nuclei. Aims. Sophisticated shock models are able to simulate H2 emission from such shocked regions. We aim to explore H2 excitation using shock models, and to test over which parameter space distinct signatures are produced in H2 emission. Methods. We here present simulated H2 emission using the Paris-Durham shock code over an extensive grid of ~14 000 plane-parallel stationary shock models, a large subset of which are exposed to a semi-isotropic external UV radiation field. The grid samples six input parameters: the preshock density, shock velocity, transverse magnetic field strength, UV radiation field strength, the cosmic-ray-ionization rate, and the abundance of polycyclic aromatic hydrocarbons, PAHs. Physical quantities resulting from our self-consistent calculations, such as temperature, density, and width, have been extracted along with H2 integrated line intensities. These simulations and results are publicly available on the Interstellar Medium Services platform. Results. The strength of the transverse magnetic field, as quantified by the magnetic scaling factor, b, plays a key role in the excitation of H2. At low values of b (≲0.3, J-type shocks), H2 excitation is dominated by vibrationally excited lines; whereas, at higher values (b ≳ 1, C-type shocks), rotational lines dominate the spectrum for shocks with an external radiation field comparable to (or lower than) the solar neighborhood. Shocks with b ≥ 1 can potentially be spatially resolved with JWST for nearby objects. H2 is typically the dominant coolant at lower densities (≲104 cm−3); at higher densities, other molecules such as CO, OH, and H2O take over at velocities ≲20 km s−1 and atoms, for example, H, O, and S, dominate at higher velocities. Together, the velocity and density set the input kinetic energy flux. When this increases, the excitation and integrated intensity of H2 increases similarly. An external UV field mainly serves to increase the excitation, particularly for shocks where the input radiation energy is comparable to the input kinetic energy flux. These results provide an overview of the energetic reprocessing of input kinetic energy flux and the resulting H2 line emission.

Quantum Otto heat engine with Pöschl–Teller potential in contact with coherent thermal bath

Work and efficiency of quantum Otto heat engines (QOHEs) can increase by using non-thermal baths or by inhomogeneous scaling of energy levels of the working substance. Given these points, at first, we construct the coherent thermal state for a trigonometric Pöschl–Teller (PT) potential. Then using a particle in this potential, which has unequally spaced energy levels, as a working substance, we investigate the work extraction and the efficiency of QOHEs that operates between cold and hot coherent thermal baths. The results show that changing the PT potential parameters in the adiabatic processes of QOHE, which causes an inhomogeneous shift in energy levels or/and make use of the hot coherent thermal bath, improve work extraction and efficiency of QOHE relative to the classical counterpart.

Numerical simulation of non-Abelian anyons

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general Abelian and non-Abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons, and Ising anyons. Additionally, we simulate nonequilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times---indicating thermalization.

Stable interaction-induced Anderson-like localization embedded in standing waves

We uncover the interaction-induced stable self-localization of few bosons in finite-size disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it provides a quasi-random potential to localize the other particles. We derive effective Hamiltonians for self-localized states and find their energy level spacings obeying the Poisson statistics. The spatial distribution of the localized particles decays exponentially, which is refered to Anderson-like localization (ALL). Surprisingly, we find that the correlated self-localization can be solely induced by interaction in the well-studied Bose–Hubbard models, which has been overlooked for a long time. We propose a dynamical scheme to detect self-localization, where long-time quantum walks of a single particle form a superposition of multiple standing waves for trapping the subsequently loaded particles. Our work provides an experimentally feasible way to realize stable ALL in translation-invariant disorder-free few-body systems.

Demonstration and operation of quantum harmonic oscillators in an AlGaAs-GaAs heterostructure

The quantum harmonic oscillator (QHO), one of the most important and ubiquitous model systems in quantum mechanics, features equally spaced energy levels or eigenstates. Here we present a new class of nearly ideal QHOs formed by hydrogenic substitutional dopants in an AlGaAs/GaAs heterostructure. On the basis of model calculations, we demonstrate that, when a δ-doping Si donor substitutes the Ga/Al lattice site close to AlGaAs/GaAs heterointerface, a hydrogenic Si QHO, characterized by a restoring Coulomb force producing square law harmonic potential, is formed. This gives rise to QHO states with energy spacing of ∼8–9 meV. We experimentally confirm this proposal by utilizing gate tuning and measuring QHO states using an aluminum single-electron transistor (SET). A sharp and fast oscillation with period of ∼7–8 mV appears in addition to the regular Coulomb blockade (CB) oscillation with much larger period, for positive gate biases above 0.5 V. The observation of fast oscillation and its behavior is quantitatively consistent with our theoretical result, manifesting the harmonic motion of electrons from the QHO. Our results might establish a general principle to design, construct and manipulate QHOs in semiconductor heterostructures, opening future possibilities for their quantum applications.

Germanate-based oxyfluoride transparent glass-ceramic embedded with Tm3+:Ca2YbF7 nanocrystals for high-performance optical thermometer

Germanate-based oxyfluoride transparent glass-ceramic functionalized by Tm3+:Ca2YbF7 nanocrystals was newly developed. The tremendously enhanced upconversion emission of 3F2,3 energy levels by in situ crystallization was extremely beneficial for constructing optical thermometry involving the indirect thermally coupled energy levels (1G4 and 3F2,3) of Tm3+ ions. Utilizing the fluorescence intensity ratio technique, the thermometry potentials of PG and GC8 were systematically evaluated based on the emissions from 3F2,3 and 1G4 energy levels. The relative and absolute sensitivities, thermometry resolutions, and repeatabilities were superior to many reported materials. This work provides an avenue for precipitating ternary fluoride nanocrystals containing rare earths in germanate-based oxyfluoride glass, and proposes a promising way to achieve high performance optical thermometry based on the emissions from widely spaced energy levels.