Dipole Transition Matrix Elements Research Articles

Radiative transitions between Rydberg states of polar diatomic molecule. Part I: Linearly polarized light

With the help of a simple semi-analytical procedure the dipole matrix elements for Rydberg electron-rotational transitions in the SO molecule are calculated with account for dipole moment of rotating core. It results in non-zero matrix elements even for some transitions which are forbidden in conventional models of molecular Rydberg states.

Effect of pressure and electron–phonon interaction on optical properties of GaN triangular quantum wires

In this work, both the effect of electron–phonon (e–p) interaction and pressure on the optical properties of GaN triangular quantum wires has been studied. In this regard, the electronic transition energy and dipole matrix elements are calculated, by taking the effects of the electron–LO–phonon interaction and the hydrostatic pressure into account. Then, the refractive index (RI) changes and absorption coefficients (ACs) are computed within the framework of the compact density matrix approach and iterative method. It is found that the transition energy and dipole matrix elements decrease under the e–p interaction and the hydrostatic pressure. Obviously, it is shown that the hydrostatic pressure increase the effect of e–p interaction on the transition energy. The ACs and RI changes shift toward lower energies under the e–LO–p interaction and the pressure. RI changes and ACs are increased in the influence of e–p interaction but they are decreased under the hydrostatic pressure. The influence of e–LO–p interaction under the hydrostatic pressure on the RI changes and ACs cannot be neglected for a GaN triangular quantum wire.

Rotational spectroscopy and three-wave mixing of 4-carvomenthenol: A technical guide to measuring chirality in the microwave regime.

We apply chirality sensitive microwave three-wave mixing to 4-carvomenthenol, a molecule previously uncharacterized with rotational spectroscopy. We measure its rotational spectrum in the 2-8.5 GHz range and observe three molecular conformers. We describe our method in detail, from the initial step of spectral acquisition and assignment to the final step of determining absolute configuration and enantiomeric excess. Combining fitted rotational constants with dipole moment components derived from quantum chemical calculations, we identify candidate three-wave mixing cycles which were further tested using a double resonance method. Initial optimization of the three-wave mixing signal is done by varying the duration of the second excitation pulse. With known transition dipole matrix elements, absolute configuration can be directly determined from a single measurement.

Photoelectron angular distributions for states of any mixed character: an experiment-friendly model for atomic, molecular, and cluster anions.

We present a model for laboratory-frame photoelectron angular distributions in direct photodetachment from (in principle) any molecular orbital using linearly polarized light. A transparent mathematical approach is used to generalize the Cooper-Zare central-potential model to anionic states of any mixed character. In the limit of atomic-anion photodetachment, the model reproduces the Cooper-Zare formula. In the case of an initial orbital described as a superposition of s and p-type functions, the model yields the previously obtained s-p mixing formula. The formalism is further advanced using the Hanstorp approximation, whereas the relative scaling of the partial-wave cross-sections is assumed to follow the Wigner threshold law. The resulting model describes the energy dependence of photoelectron anisotropy for any atomic, molecular, or cluster anions, usually without requiring a direct calculation of the transition dipole matrix elements. As a benchmark case, we apply the p-d variant of the model to the experimental results for NO(-) photodetachment and show that the observed anisotropy trend is described well using physically meaningful values of the model parameters. Overall, the presented formalism delivers insight into the photodetachment process and affords a new quantitative strategy for analyzing the photoelectron angular distributions and characterizing mixed-character molecular orbitals using photoelectron imaging spectroscopy of negative ions.

Near-infrared induced optical quenching effects on mid-infrared quantum cascade lasers

In space communications, atmospheric absorption and Rayleigh scattering are the dominant channel impairments. Transmission using mid-infrared (MIR) wavelengths offers the benefits of lower loss and less scintillation effects. In this work, we report the telecom wavelengths (1.55 μm and 1.3 μm) induced optical quenching effects on MIR quantum cascade lasers (QCLs), when QCLs are operated well above their thresholds. The QCL output power can be near 100% quenched using 20 mW of near-infrared (NIR) power, and the quenching effect depends on the input NIR intensity as well as wavelength. Time resolved measurement was conducted to explore the quenching mechanism. The measured recovery time is around 14 ns, which indicates that NIR generated electron-hole pairs may play a key role in the quenching process. The photocarrier created local field and band bending can effectively deteriorate the dipole transition matrix element and quench the QCL. As a result, MIR QCLs can be used as an optical modulator and switch controlled by NIR lasers. They can also be used as “converters” to convert telecom optical signals into MIR optical signals.

The algebraic approach for the derivation of ladder operators and coherent states for the Goldman and Krivchenkov oscillator by the use of supersymmetric quantum mechanics

The ladder operators for the Goldman and Krivchenkov anharmonic poten- tialhavebeenderivedwithinthealgebraicapproach.Themethodisextendedtoinclude the rotating oscillator. The coherent states for the Goldman and Krivchenkov oscilla- tor, which are the eigenstates of the annihilation operator and minimize the general- izedposition-momentumuncertaintyrelation,areconstructedwithintheframeworkof supersymmetric quantum mechanics. The constructed ladder operators can bea useful tool in quantum chemistry computations of non-trivial matrix elements. In particular, they can be employed in molecular vibrational-rotational spectroscopy of diatomic molecules to compute transition energies and dipole matrix elements.

Time delays for attosecond streaking in photoionization of neon

We revisit the time-resolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of $2p$ and $2s$ electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The $B$-spline $R$-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multielectron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking process by solving the time-dependent Schr\"odinger equation on the single-active-electron level. The resulting accurate total relative streaking time shifts between $2s$ and $2p$ emission lie well below the experimental data. We identify the presence of unresolved shake-up satellites in the experiment as a potential source of error in the determination of streaking time shifts.

Using coherent control to extract the phases of electronic transition-dipole matrices: the LiRb case

We show that “bichromatic coherent control” (BCC) enables the determination of the amplitudes (= magnitudes + phases) of individual transition-dipole matrix elements (TDMs) and the amplitude of time-evolving wave packets from time-resolved fluorescence data. In the present use of BCC, one induces quantum interferences using two external laser fields to coherently deplete the population of different pairs of excited energy eigenstates. The BCC-induced depletion is supplemented by the computation of the Fourier integral of the time-resolved fluorescence at the beat frequencies of the two states involved. The combination of BCC and Fourier transform enables the determination of both the expansion coefficients of the wave packet in a basis of vibrational energy eigenstates and the amplitudes of the [Formula: see text] electronic TDMs linking the excited and ground rovibrational states. We illustrate our method by determining the amplitudes of the TDMs linking the vibrational states of the [Formula: see text] spin orbit coupled potentials to both the singlet [Formula: see text] and the triplet [Formula: see text] electronic ground states in LiRb. The approach, which is found to be quite robust against errors in the BCC procedure and experimental data, can be readily generalized to the imaging of wave packets of polyatomic molecules.

Large-scale first principles configuration interaction calculations of optical absorption in aluminum clusters.

We report the linear optical absorption spectra of aluminum clusters Aln (n = 2-5) involving valence transitions, computed using the large-scale all-electron configuration interaction (CI) methodology. Several low-lying isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles-doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different clusters were computed using the multi-reference singles-doubles configuration-interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, and thus their photoabsorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion, was carefully examined. Our results were found to be significantly different as compared to those obtained using time-dependent density functional theory (TDDFT) [Deshpande et al. Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 68, 035428]. When compared to the available experimental data for the isomers of Al2 and Al3, our results are in very good agreement as far as important peak positions are concerned. The contribution of configurations to many body wave functions of various excited states suggests that in most cases optical excitations involved are collective, and plasmonic in nature.

Spontaneous emission from a medium with elliptic and hyperbolic dispersion

We analyze the properties of spontaneous emission of a two-level atom in anisotropic media where the geometry of physical dispersion relations is characterized by an ellipsoid or a hyperboloid. Within the framework of quantum optics the rate of spontaneous emission in the above media is explicitly given with the orientation of the dipole transition matrix element taken into account. It indicates that for the ellipsoid case the intensity of the photons coupled into different modes can be tuned by changing the direction of the matrix element relative to the optical axis. For the hyperboloid case it is found that spontaneous emission in the hyperbolic medium (HM) can be dramatically enhanced compared with the case in the background medium. Moreover, in the HM the spontaneous emission exhibits strong directivity and gets the maximum in the asymptote direction.

Hybrid of superconducting quantum interference device and atomic Bose-Einstein condensate: An architecture for quantum information processing

A hybrid quantum system is proposed by coupling the internal hyperfine transitions of a trapped atomic Bose-Einstein condensate (BEC) and a superconducting quantum interference device (SQUID) via the macroscopic quantum field of the flux qubit. The presence of the condensate leads to a bosonic enhancement of the Rabi frequency over the otherwise small single-particle magnetic dipole transition matrix elements. This enhancement allows for the possibility to rapidly transfer and store qubit states in the BEC that were originally prepared in the SQUID. The fidelity of this transfer for different states is calculated, and a direct experimental protocol to determine the transfer fidelity by quantum tomography of the BEC qubit is presented.

Dissecting biexciton wave functions of self-assembled quantum dots by double-quantum-coherence optical spectroscopy

Biexcitons feature prominently in various scenarios for utilization of quantum dots (QDs) for enhancing the efficiencies of solar cells, and for the generation of entangled photon pairs in single QD sources. Two-dimensional double quantum coherence (2D-DQC) nonlinear optical spectra provide novel spectroscopic signatures of such states beyond global intensity and lifetime characteristics which are available by more conventional techniques. We report the simulation of a prototype 2D-DQC optical experiment of a self-assembled InAs/GaAs dot. The simulations consider the QD in different charged states and are based on a state-of-the-art atomistic many-body pseudopotential method for the calculation of the electronic structure and transition dipole matrix elements. Comparison of the spectra of negatively charged, neutral, and positively charged QD reveals optical signatures of their electronic excitations. This technique directly accesses the biexciton ($XX$) energies as well as the projections of their wave functions on the single-exciton manifold. These signals also provide a unique tool for probing the charged state of the QD and thus the occupation of the quantum state. Signatures of Pauli blockade of the creation of certain single and two excitons due to charges on the particles are observed. For all quantum states of the QD, the spectra reveal a strong multiconfiguration character of the biexciton wave functions. Peak intensities can be explained by interference of the contributing Liouville space pathways.

Probing molecular frame photoelectron angular distributions via high-order harmonic generation from aligned molecules

We analyse the theory of single photoionization (PI) and high-order harmonic generation (HHG) by intense lasers from aligned molecules. We show that molecular-frame photoelectron angular distributions can be extracted from these measurements. We also show that, under favourable conditions, the phase of PI transition dipole matrix elements can be extracted from the HHG spectra. Furthermore, by varying the polarization axis of the HHG generating laser with respect to the polarization axis of the aligning laser, it is possible to extract angle-dependent tunnelling ionization rates for different subshells of the molecules.

Intersubband terahertz transitions in Landau level system of cascade GaAs/AlGaAs quantum well structures in strong tilted magnetic field

The tunable terahertz intersubband Landau level transitions in resonant tunneling cascade quantum well structures are considered. The way of lifting the selection rule forbidding the inter-Landau level terahertz transitions of interest by applying a magnetic field tilted with respect to the structure layers is proposed. The importance of asymmetric structure design to achieve considerable values of transition dipole matrix elements is demonstrated.

Influence of the internal heterostructure on nonlinear refractive index changes for intersubband transitions in spherical quantum dotquantum well nanoparticles

The electronic spectra and optical properties of one electron spherical quantum dot-quantum well structure consisting of a CdSe core surrounded by ZnS and CdSe shells and capped by material with a higher electron potential barrier compared with CdSe is investigated. Eigenfunctions and corresponding energies are calculated using effective mass approximation. For allowed transitions between ground and three excited states (1s, 2p, 3d, and 2s), we have calculated dipole transition matrix elements and linear and third-order nonlinear intersubband refractive index changes for different CdSe core radii and ZnS and CdSe shells thicknesses. Electron wave functions and energy of states are considerably affected by the dimensions of core and shells. The localization regime of electron in 1s, 1p, 1d, and 2s states and hence transition energies and dipole matrix elements of 1s-1p, 1p-1d, and 1p-2s transitions can be controlled by core and shell dimensions.

Parametrization of the Forouhi–Bloomer–Lorentz model for Ta_2O_5 films in the fundamental-absorption region

The complex optical and dielectric functions of the energy of an electromagnetic wave are calculated for a film of tantalum (V) oxide in the short-wavelength region, including the fundamental-absorption region. An additive combination of the Forouhi–Bloomer and Lorentz models is constructed to compute these functions. Versions of the Forouhi–Bloomer model with a dipole-transition matrix element that is independent of the wave energy are considered, along with a modified model. It is established that the modified model has an advantage when describing broad-band dielectric amorphous media. The optical band gap computed from the Forouhi–Bloomer and Lorentz models is compared with the value determined from the Tautz extrapolation.

LARGE-SCALE FIRST PRINCIPLES CONFIGURATION INTERACTION CALCULATIONS OF OPTICAL ABSORPTION IN BORON CLUSTERS

We have performed systematic large-scale all-electron correlated calculations on boron clusters B n(n = 2 - 5), to study their linear optical absorption spectra. Several possible isomers of each cluster were considered, and their geometries were optimized at the coupled-cluster singles doubles (CCSD) level of theory. Using the optimized ground-state geometries, the excited states of different clusters were computed using the multi-reference singles-doubles configuration–interaction (MRSDCI) approach, which includes electron correlation effects at a sophisticated level. These CI wave functions were used to compute the transition dipole matrix elements connecting the ground and various excited states of different clusters, eventually leading to their linear absorption spectra. The convergence of our results with respect to the basis sets, and the size of the CI expansion were carefully examined. The contribution of configurations to many body wave-function of various excited states suggests that the excitations involved are collective, plasmonic type.

Laser ablation of CsI: time-resolved Fourier-transform infrared spectra of atomic cesium in the 800–8000 cm^−1 range

Fourier-transform time-resolved spectroscopy of laser-induced breakdown of Cs vapor in a vacuum has been used for the measurement of atomic Cs emission spectra in the 800–8000 cm−1 range with a resolution of 0.02 cm−1. The 6h and 7h levels of Cs are observed. The dipole transition matrix elements (transition probabilities, oscillator, and line strengths) between the observed levels are calculated using quantum defect theory.

Communication: Convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations

It is shown that the convergence of anharmonic infrared spectral intensities with respect to the basis set size is much enhanced in explicitly correlated calculations as compared to traditional configuration interaction type wave function expansion. Explicitly correlated coupled cluster (CC) calculations using Slater-type geminal correlation factor (CC-F12) yield well-converged dipole derivatives and vibrational intensities for hydrogen fluoride with basis set involving f functions on the heavy atom. Combination of CC-F12 with singles, doubles, and non-iterative triples (CCSD(T)-F12) with small corrections due to quadruple excitations, core-electron correlation, and relativistic effects yields vibrational line positions, dipole moments, and transition dipole matrix elements in good agreement with the best experimental values.

Dipole-dipole broadening of Rbns−npmicrowave transitions

The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$, a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.