An effective quantum defect theory for the diamagnetic spectrum of barium Rydberg atom

A theoretical calculation is carried out for the spectrum of barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of barium Rydberg atom at a magnetic field of 2.89 T [J. Phys. B 28 L537 (1995)]. Our calculation employs B-spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s² to 6snp Rydberg states, the spectrum is not influenced by quantum defects of channels ns and nd. The calculation is in agreement with the experimental observation until the energy reaches E=-60 cm^-1. Up beyond in energy, closer to the threshold, the calculated and experimental results do not agree with each other, possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of barium atom can be explained thoroughly using a hydrogen model potential.     

An effective quantum defect theory for the diamagnetic spectrum of a barium Rydberg atom

A theoretical calculation is carried out to investigate the spectrum of a barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of the barium Rydberg atom in a magnetic field of 2.89 T [J. Phys. B 28 L537 (1995)]. Our calculation employs B-spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s2 to 6snp Rydberg states, the spectrum is not influenced by quantum defects of channels ns and nd. The calculation is in agreement with the experimental observations until the energy reaches E = 60 cm-1 . Beyond this energy, closer to the threshold, the calculated and experimental results do not agree with each other. Possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of the barium atom can be explained thoroughly using a hydrogen model potential.     

Energy levels of perturbed 6pnd J = 2 Rydberg states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of atomic lead are analyzed by the multichannel quantum defect theory (MQDT) with previous experimental energy levels. The 6pnd (6≤n ≤ 63) J=2 Rydberg energy levels are calculated and optimal MQDT parameters were obtained. Using these parameters, admixture coefficients for each level are calculated to designate the level denotations. The results show that strong channel mixings exist for the levels near the 6p6d (3/2)[5/2]2° and 6p6d (3/2)[3/2]2° pertubers. The five-channel model different from that in literature is used to predict 21 energy positions of 6pnd (1/2)[3/2]2° levels and to determine the denotations of all the 6pnd J=2 Rydberg states under 59788 cm-1 for Pb I.     

Radiative lifetimes of Rydberg 6pnd J=2 states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of Pb I are analysed by the multichannel quantum defect theory (MQDT) in the frame of a five-channel three-limit calculation model. With optimal MQDT parameters, channel admixture coefficients are obtained and used to calculate the theoretical lifetimes of the levels by comparing to the previously measured lifetimes. The predicted lifetimes for higher-lying Rydberg states are given and discussed. These predicted lifetimes are very different from those obtained by the four-channel two-limit model pl:eviously used, which means that introduction of the additional interacting channel is important for studying the 6pnd J=2 Rydberg states of Pb I.     

Energy level analyses of even-parity J = 1 and 2 Rydberg states of Sn I by multichannel quantum defect theory

This paper analyzes the energy levels along the even-parity J=1 and 2 Rydberg series of Sn I by multichannel quantum defect theory. A good agreement between theoretical and experimental energy levels was achieved. Below 59198 cm-1, a total of 85 and 23 new energy levels, respectively, in the J=1 and J=2 series, which cannot be measured previously by experiments, are predicted in this work. Based on the calculated admixture coefficients of each channel, interchannel interactions were discussed in detail. The results are helpful to understand the characteristics of configuration interaction among even-parity levels in Sn I.     

锡原子奇宇称5pnd和5pns J = 1, 2 Rydberg系列的多通道量子亏损理论研究

利用多通道量子亏损理论（MQDT）,对锡原子奇宇称5pnd和5pns组态的J = 1,2简并受扰Rydberg系列能级进行了理论分析研究. 通过拟合实验能级,得到了MQDT优化参数,所得理论能级值与文献报道的实验结果符合得很好. 由算得的通道混合系数,分析讨论了通道相互作用特性,确定了所有能级的原子态命名. 本文结果有助于人们更好地了解锡原子高激发态的能级结构和组态相互作用特性.     

Non-linear spectral splitting of Rydberg sodium in external fields

We have studied highly excited sodium in various electric fields,parallel electric and magnetic fields,with oneσandπphoton irradiation,and even in a magnetic field with a complex laser polarization configuration.Theσspectra shows a simple linear Stark effect with the applied electric field,while theπspectra exhibits a strong non-linear dependence on the electric field.Theπtransitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field.The diamagnetic spectrum with laser polarization angles between 0 andπ/2 proves that it can be reproduced by simple linear combination ofπandσcomponents,indicating there is no interference between theπandσchannels.A full quantum calculation considering the quantum defects accounts for all the observations.The quantum defects,especially for the channel np,play an important role in the spectral profile.     

Nonrelativistic fermions in magnetic fields: a quantum field theory approach

The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that is compatible with the all reasonable regularization procedures. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.     

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

Measurement of quantum defect of nS and nD states using field ionization spectroscopy in ultracold cesium atoms

<正>This paper reports that ultracold atoms are populated into different nS and nD Rydberg states(n=25~52) by two-photon excitation.The ionization spectrum of an ultracold Rydberg atom is acquired in a cesium magneto-optical trap by using the method of pulse field ionization.This denotes nS and nD states in the ionization spectrum and fits the data of energy levels of different Rydberg states to obtain quantum defects of nS and nD states.     

Optical properties of semiconductor quantum dots in magnetic fields

Optical properties of semiconductor quantum dots in magnetic fields are reviewed. A theory is described based on a multi-band effective-mass approximation with a nonparabolic conduction electron dispersion, the direct Coulomb interaction, and the electron-hole exchange interaction taken into account. The transition from the quantum-confined Zeeman effect for a weak magnetic field to the quantum-confined Paschen-Back effect to a strong magnetic field is discussed in comparison with atomic spectra in magnetic fields. Experimental results of the optical properties of isolated CuCl, CdSSe, and Si quantum dots in magnetic fields are also discussed in conjunction with the theoretical results.     

Time-resolved studies of single quantum dots in magnetic fields

We present time-resolved and time-integrated spectroscopy of single InAs quantum dots grown in a GaAs matrix. We observe a number of interesting features in the spectra, including the zero field splitting of exciton and biexciton lines due to quantum dot asymmetry. By the application of an in-plane magnetic field, the normally optically active and inactive exciton states become mixed, enabling us to optically probe the normally inaccessible ‘dark’ states. Time resolved measurements on the mixed states show decay times several times longer than the exciton lifetime at zero field, which we show to be consistent with a dark exciton lifetime orders of magnitude longer than that for bright exciton.     

各向异性n模耦合谐振子的精确求解

利用量子变换理论,极其简洁地给出了种向异性耦合谐振子的能谱,从而提出了一种普遍的方法。     

A categorical framework for quantum theory

Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear‐sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the “status nascendi” of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non‐sequential time and an extended present which seems to be relevant for a quantum theory of (space)‐time.     

A discrete approach to topological quantum field theories

First, we describe a rather general scheme for constructing three-dimensional euclidean topological quantum field theories, whose basic building blocks are provided by the representation theory of a certain class of (bi-)algebras. Secondly, we discuss in some detail examples, where the algebra is either the function algebra of a finite group, the group algebra of a finite group or a deformation of the enveloping algebra of a classical simple Lie group.     

Nonlinear spectroscopy of barium in parallel electric and magnetic fields

We report on the experimental spectral observations of barium in parallel electric and magnetic fields. The laser pulse is linearly polarized along or perpendicular to the fields, leading to the states m = 0 and the states m = -t-1 populated, respectively, by one photon excitation. By sweeping the electric field, we observe the linear and nonlinear splitting of the diamagnetic spectrum as the electric field increases. The spectral anticrossing is induced by the atomic core effect. The Stark spectrum also shows an obvious nonlinear quadratic behavior when the applied magnetic field varies strongly. All spectra are well explained by the full quantum calculation after taking the quantum defect effects of the channel ns up to nf into account.     

低维量子磁性和量子海森伯反铁磁体之有效场论

文章对低维量子磁性的基本问题和相关研究进展作了简单评述，强调了量子非线性Sigma模型在研究量子海森伯反铁磁体的低能物理方面所起的作用以及理论本身存在的疑难问题，并简单介绍了作者最近提出的克服这些疑难问题的一个新建议．     

含时磁共振系统的精确解和绝热近似解

在瞬时本征态完备基矢下,把一个经典含时磁共振系统的薛定谔方程转化为二阶常系数微分方程,实现了该量子系统的精确求解.利用该系统的精确解,讨论了绝热近似的精确程度,非常清晰地刻画了绝热近似解和精确解在量子态分布概率上的差异.结果表明,若系统初态制备于某个瞬时本征态上,系统保持在该瞬时本征态的概率介于0.888 9～1之间,...