Nondegenerate Levels Research Articles

Equidistribution of phase shifts in trapped scattering

We consider semiclassical scattering for compactly supported perturbations of the Laplacian and show equidistribution of eigenvalues of the scattering matrix at (classically) non-degenerate energy levels. The only requirement is that sets of fixed points of certain natural scattering relations have measure zero. This extends the result of [16], where the authors proved the equidistribution result under a similar assumption on fixed points but with the condition that there is no trapping.

The influence of higher spatial harmonics of atomic polarization on the saturated absorption resonance upon excitation of open dipole transitions by a field of counterpropagating waves

The effect of a double structure of saturated absorption resonance in the field of counterpropagating light waves interacting with an atomic gas is studied. The experimental observation of this effect was first reported in 2011 in a work by our colleagues at the P.N. Lebedev Physical Institute of the Russian Academy of Sciences (Laboratory of Frequency Standards). The essence of the effect lies in the fact that, on exciting an open dipole transition, another, narrower, resonance of an opposite sign can be observed at the center of the ordinary saturated absorption resonance. A theoretical analysis of this effect has also been performed in this work in terms of a simple spectroscopic model of an atom with two nondegenerate energy levels without taking into account higher spatial harmonics of atomic polarization and polarizations of light waves (scalar model). The present work is devoted to the development of a theory of the formation of a central narrow resonance for the example of a real Fg = 1 → Fe = 1 atomic transition and to the study of its main characteristics (amplitude, width, contrast, and amplitude-to-width ratio). In addition, the theoretical results obtained without taking into account the influence of higher spatial harmonics and with inclusion of the influence of first higher harmonics are compared. This comparison shows that their influence on the parameters of the new nonlinear resonance is strong even in moderately intense light fields (R ~ γ, where R is the Rabi frequency). The results of this study can be of interest for quantum metrology, as well as for many experiments in which the laser-radiation frequency is stabilized by the saturated absorption resonance on open dipole transitions in atoms and molecules.

General form of the boson-fermion interaction in the interacting boson-fermion model-2

The boson-fermion interaction in the interacting boson-fermion model-2 (IBFM-2) is derived in a systematic and general form from a quadrupole-quadrupole force using several nondegenerate levels. The boson-fermion quadrupole operator employed is obtained from the boson-fermion image of the one nucleon transfer operator which in turn can be calculated following two alternative schemes: the Otsuka-Arima-Iachello and generalized Holstein-Primakoff schemes. Four different terms (two quadrupole and two exchange) were obtained. Application of the new expressions to a single-$j$ model is studied and analyzed.

Residual degeneracy from non-degenerate Landau levels of ultracold atoms in light-induced gauge potentials

We study non-degenerate Landau levels of ultracold trapped atoms in two dimensions, subject to an U(1)×U(1) Abelian gauge field and a lateral confining potential along a specific direction. The Landau-level degeneracy is removed due to the presence of the lateral confining potential that makes the single-particle energy spectrum explicitly dependent on the transverse momentum. The effect of the finite size of the atomic cloud on the energy spectrum is to split each Landau level into a set of sub-levels, once the transverse momentum becomes quantized. We show that under appropriate conditions some energy sub-levels overlap leading to a residual degeneracy of the system. Through numerical calculations, we map the residual degeneracy as a function of the effective magnetic field strength. Finally, we briefly discuss future studies on the transport properties of this atomic system that can be considered an optically induced atomic waveguide.

Dielectric and electrical properties of SbSI and SbSeI single crystals in the region of antiferroelectric phase transition

Experimental results have shown that the capacitance (dielectric permittivity) and electrical conductivity of SbSI and SbSeI crystals along the c(z)-axis change significantly in the region of the antiferroelectric phase transition when DC voltage is applied. An electric field changes the form of B1u (A1) soft mode potential in sites of Sb atoms, which turns the antiferroelectric phase into an induced ferroelectric phase. Degenerate energy levels then split into non-degenerate levels due to electron–phonon interaction (pseudo Jahn–Teller effect), while a narrowed band gap simultaneously creates strong and abrupt changes in C(T) and σ(T).

Mixed Rabi Jaynes–Cummings model of a three-level atom interacting with two quantized fields

The quantum Rabi model describes the ultrastrong interaction of a two-level atom coupled to a single quantized bosonic mode. As compared to the Jaynes–Cummings model, in the Rabi model the absorption and emission processes do not need to satisfy energy conservation and the usual rotating wave approximation (RWA) breaks down. As a result, the atom-field dynamics in the Hilbert space splits into two independent parity chains, exhibiting a collapse-revival pattern and exact periodic dynamics in the limit of degenerate atomic levels. Here we introduce a mixed Rabi Jaynes–Cummings model by considering a three-level atom interacting with two quantized bosonic fields, in which the RWA is made for one transition (with a weak atom-field coupling) but not for the other one (with an ultrastrong atom-field coupling). As a result, we show that the field in the weak coupled atomic transition can be used as a tool to control the atom-field dynamics of the other (strong coupled) transition, thus realizing an effective two-level quantum Rabi model with a controllable field. In particular, a periodic temporal dynamics of the atom-field state can be realized by appropriate tuning of the weak control field, even for non-degenerate atomic levels. A photonic simulator of the mixed Rabi Jaynes–Cummings model, based on light transport in evanescently coupled optical waveguide lattices, is also briefly discussed.

Numerical algorithm for the standard pairing problem based on the Heine–Stieltjes correspondence and the polynomial approach

We present a detailed study of the computational complexity of a numerical algorithm based on the Heine–Stieltjes correspondence following the new approach we proposed recently for solving the Bethe ansatz (Gaudin–Richardson) equations of the standard pairing problem. For k pairs of valence nucleons in n non-degenerate single-particle energy levels, the approach utilizes that solutions of the Bethe ansatz equations can be obtained from two matrices of dimensions (k+1)×(k+1) and (n−1)×(k+1), which are associated with the extended Heine–Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach provides an efficient and systematic way to solve the problem. The method reduces to solving a system of k polynomial equations, which can be efficiently implemented by the fast Newton–Raphson algorithm with a Monte Carlo sampling procedure for the initial guesses. By extension, the present algorithm can also be used to solve a large class of Gaudin-type quantum many-body problems, including an efficient angular momentum projection method for multi-particle systems. Program summaryProgram title: exactPairingHSCatalogue identifier: AETD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5411No. of bytes in distributed program, including test data, etc.: 39758Distribution format: tar.gzProgramming language: Mathematica.Computer: Laptop, workstation.Operating system: Tested with MATHEMATICA version 9.0 on Mac OS X and Windows 7.RAM: Less than 10 MBClassification: 17.15.Nature of problem:The program calculates exact pairing energies based on the Heine–Stieltjes polynomial approach. Existing conventional exact-pairing approaches require solving systems of highly nonlinear equations, which are difficult and often impossible to solve beyond the simplest of the quantum-mechanical many-particle systems. In this study, the Heine–Stieltjes polynomial approach is employed to provide solutions for more than one or two pairs of particles residing in many energy levels.Solution method:The new Heine–Stieltjes polynomial approach transforms the pairing problem to one that involves the handling of only two matrix equations. This, combined with an efficient numerical algorithm implemented by the fast Newton–Raphson method with a Monte Carlo sampling procedure for the initial guesses, makes exact pairing solutions feasible even when more energy levels or heavy nuclei (many pairs) are considered.Running time:Less than a hundred seconds using a 2.80 GHz processor. The notebook takes approximately 23 min to complete.

Spectroscopic manifestations of random lattice deformations in rare-earth doped crystals

The inhomogeneous broadening of a zero-phonon line of an optical transition between nondegenerate and degenerate levels of a rare-earth impurity center in a crystal that is caused by random lattice deformations has been considered. Spectra of non-Kramers and Kramers rare-earth ions located at tetragonal and cubic sites have been investigated. Lines of a characteristic shape with a deep dip in the center have been detected.

Roles of Doping, Temperature, and Electric Field on Spin Transport Through Semiconducting Channels in Spin Valves

Manipulation of spin information in semiconductors has been the topic of both experimental and theoretical studies. In this paper, the theoretical compact models for the spin-relaxation length (SRL) in nondegenerately doped silicon and gallium arsenide are presented. These models account for the impact of impurity doping and phonons on mediating spin relaxation. In addition, the models are exhaustively calibrated with the published experimental data. It is shown that the SRL at room temperature in Si drops from 5 to 1 μm as the doping increases from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . However, the SRL in GaAs is independent of doping for nondegenerate doping levels. While the rolloff of the SRL with temperature in Si depends upon the doping concentration, the rolloff of the SRL for nondegenerately doped GaAs is doping independent and proceeds as T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , where T is the operating temperature. The models of the SRL in conjunction with spin drift-diffusion equation are used to study the steady-state spin transport in both the conventional and nonlocal semiconducting spin-valve geometries. The presence of an electric field leads to a clear enhancement of spin injection and transport efficiency in the conventional spin-valve geometry. The degradation in the spin injection and transport efficiency with the channel length is much steeper in nonlocal spin valves as compared to that in the conventional spin valves.

Coherence and decoherence in photon–spin-qubit entanglement

We study the dynamics of spontaneous generation of coherence and photon spin-qubit entanglement or "flying qubits" in a $\Lambda$ system with non-degenerate lower levels. The cases of entanglement in frequency only and frequency and polarization are compared and the reduced density matrix and entanglement entropy are analyzed. We explore in detail how which-path information manifest when the energy difference between the qubit states is larger than the linewidth of the excited state suppresses coherence. A framework is provided to describe the complete dynamics of spontaneous generation of coherence and (ideal) photodetection obtaining the post measurement qubit density matrix. A simple model of photodetection with a quantum eraser to suppress which-path information in the detection measurement is implemented. It is found that such quantum eraser purifies the post measurement qubit density matrix establishing contact with recent experiments.

Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates

In this paper, the Lamb shift in systems with non-degenerate energy levels, put in the electromagnetic environment provided by two infinite parallel conducting plates, is analyzed. An explicit formula giving the relative Lamb shift (as compared to the standard one in a vacuum) is derived for spherical semiconductor quantum dots (QDs), via a careful mathematical treatment of divergences in the calculations using the theory of distributions. This result settles a controversy between two different formulas existing in the current literature. Its sensitive dependence on the plates separation may be viewed as an indirect manifestation of the Lamb shift and may be used for the fine tuning of the QD non-degenerate energy spectrum in some experimental contexts.

Quantum Simulation of the Cooperative Jahn-Teller Transition in 1D Ion Crystals

The Jahn-Teller effect explains distortions and nondegenerate energy levels in molecular and solid-state physics via a coupling of effective spins to collective bosons. Here we propose and theoretically analyze the quantum simulation of a many-body Jahn-Teller model with linear ion crystals subjected to magnetic field gradients. We show that the system undergoes a quantum magnetic structural phase transition which leads to a reordering of particle positions and the formation of a spin-phonon quasicondensate in mesoscopic ion chains.

Spectra, energy levels, and symmetry assignments for Stark components of Eu 3+(4f 6) in gadolinium gallium garnet (Gd 3Ga 5O 12)

Absorption and fluorescence spectra observed between 450 and 750 nm at 85 K and room temperature (300 K) are reported for Eu 3+(4f 6) in single-crystal Czochralski-grown garnet, Gd 3Ga 5O 12 (GGG). The spectra represent transitions between the 2 S+1 L J multiplets of the 4f 6 electronic configuration of Eu 3+ split by the crystal field of the garnet. In absorption, Eu 3+ transitions are observed from the ground state, 7F 0, and the first excited multiplet, 7F 1, to multiplet manifolds 5D 0, 5D 1, and 5D 2. The Stark splitting of the 7F J multiplets ( J=0–6) was determined by analyzing the fluorescence transitions from 5D 0, 5D 1, and 5D 2 to 7F J . The Eu 3+ ions replace Gd 3+ ions in sites of D 2 symmetry in the lattice during crystal growth. Associated with each multiplet manifold are 2 J+1 non-degenerate Stark levels characterized by one of four possible irreducible representations (irreps) assigned by an algorithm based on the selection rules for electric-dipole (ED) and magnetic-dipole (MD) transitions between Stark levels in D 2 symmetry. The quasi-doublet in 5D 1 was characterized by an analysis of the magneto-optical spectra obtained from the transitions observed between 5D 1 and 7F 1. A parameterized Hamiltonian defined to operate within the entire 4f 6 electronic configuration of Eu 3+ was used to model the experimental Stark levels and their irreps. The crystal-field parameters were determined through use of a Monte-Carlo method in which nine independent crystal-field parameters, B q k , were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 57 calculated-to-experimental Stark levels is 5.9 cm −1. The choice of coordinate system, in which the nine B q k are real and the crystal-field z-axis is parallel to the [0 0 1] crystal axis and perpendicular to the xy plane, is identical to the choice we used previously in analyzing the spectra of Er 3+ and Ho 3+ garnets.

Effect of single-particle splitting in the exact wave function of the isovectorial pairing Hamiltonian

The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for $N=Z$ nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.

Exciton Coherence and Energy Transport in the Light-Harvesting Dimers of Allophycocyanin

Femtosecond transient grating and photon echo spectroscopies with a sub-20 fs time resolution are applied to allophycocyanin (APC), a protein located at the base of the phycobilisome antenna of cyanobacteria. Coupling between pairs of phycocyanobilin pigments with nondegenerate energy levels gives rise to the four-level exciton electronic structure of APC. Spectroscopic signals obtained in multiple experiments (e.g., linear absorption, fluorescence, transient grating, 2D Fourier transform photon echo) are used to constrain the parameters of a Frenkel exciton Hamiltonian. Comparison between experiment and theory yields a robust microscopic understanding of the electronic and nuclear relaxation dynamics. In agreement with previous work, transient absorption anisotropy establishes that internal conversion between the exciton states of the dimer occurs with time constants of 35, 220, and 280 fs. The sub-100 fs dynamics are decomposed into three distinct relaxation processes: electronic population transfer, intramolecular vibrational energy redistribution, and the dephasing of electronic and nuclear coherences. Model calculations show that the sub-100 fs red-shift in the transient absorption signal spectrum reflects interference between stimulated emission (ESE) and excited state absorption (ESA) signal components. It is also established that the pigment fluctuations in the dimer are not well-correlated, although further experiments will be required to precisely quantify the amount of correlation. The findings of this paper suggest that the light harvesting function of APC is enhanced by nondegeneracy of the pigments comprising the dimer and strong vibronic coupling of intramolecular modes on the phycocyanobilins. We find that the exciton states are 96% localized to the individual molecular sites within a particular dimer. Localization of the transition densities, in turn, is suggested to promote significant vibronic coupling which serves to both broaden the absorption line shape and open channels for fast internal conversion. The dominant internal conversion channel is assigned to a promoting mode near 800 cm(-1) involving hydrogen out-of-plane (HOOP) wagging motion similar to that observed in phytochrome and retinal. This rate enhancement ensures that all photoexcitations quickly and efficiently relax to the electronic origin of the lower energy exciton state from which energy transfer to the reaction center occurs.

Exotic quantum holonomy in Hamiltonian systems

We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.

Measurement of coherence dynamics based on coherent anti-Stokes Raman scattering

Nanosecond time-resolved evolution of coherence between two nondegenerate ground levels has been investigated in Rb atomic vapor. Using STIRAP and fractional STIRAP, a time-dependent coherence is prepared and indirectly monitored by the generated coherent Raman scattering signal proportional to the coherence. The experimental data fit very well with numerical simulations. This technique have potential applications in nonlinear process based on atomic coherence.

Energy functional for the three-level Lipkin model

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three nondegenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.

Spin waves in cold gases with nondegenerate levels

The existence of spin waves of a new type is predicted for ultracold paramagnetic gases with nondegenerate energy levels. The waves are generated by creating a nonequilibrium population in the absence of external polarization and are damped not only by diffusion, but also by a previously ignored mechanism due to level splitting. Theoretical calculations are in fair agreement with experimental observations of spin waves in magnetically trapped clouds of rubidium atoms.

Elementary-oscillator model for color centers with degenerate levels

Quantum transitions between nondegenerate and degenerate (with respect to angular momentum projection) levels of color centers in crystals are described in terms of classical electric-dipole oscillators. It is shown that, upon absorption of elliptically polarized exciting radiation, the system under study transfers to a definite state and the transition is described in general by an elliptical oscillator. An electric-dipole transition accompanied by the creation of a photon is described by a random vector, i.e., by an arbitrary elliptical oscillator lying in the corresponding plane. For an ensemble of n identically oriented centers undergoing a given transition, the luminescence intensity is described by a set of n/2 right-handed rotators and n/2 left-handed rotators. The results obtained are important for solving problems related to quantum information.