Dipole Transition Matrix Elements Research Articles

Conduction-band nonparabolicity effect on refractive index and phase match in asymmetric quantum wells pumped by two infrared beams

An asymmetric quantum well (AQW) system that is pumped by two infrared beams is designed to generate terahertz (THz) waves. The refractive index and phase mismatch associated with the intersubband transition of the AQW structure are calculated and analyzed for both present and absent conduction band nonparabolicity. The calculated results reveal that, for increasing wavelengths, the refractive index of the AQW for the short-wavelength pump beam varies more than 0.83 and undergoes a 0.204 [Formula: see text]m redshift, when the conduction band nonparabolicity is considered. The variation of the refractive index of the AQW with the long-wavelength pump beam, changes from 0.225 to 0.316 after considering the conduction-band nonparabolicity. In addition, no redshift is observed. Whether the refractive index of one pump beam with its specific wavelength increases is determined mainly by the linear terms. However, for increasing the other pump wavelengths, the refractive index of one pump beam mainly depends on the nonlinear terms. Subband energy-levels and dipole transition matrix elements show noticeable changes due to conduction-band nonparabolicity, which change the refractive index. Phase matching can be achieved by adjusting the wavelength of the two pump beams. However, both phase mismatch and coverage increase when the conduction band nonparabolicity is considered.

Direct measurement of the to lifetime ratio in a single trapped

We present for the first time a direct measurement of the lifetime ratio between the and metastable states in a single trapped 40Ca+. A high-efficiency quantum state detection technique is adopted to monitor the quantum jumps, and a high precision and synchronized measurement sequence is used for laser control to study the rule of spontaneous decay. Our method shows that the lifetime ratio is a constant and is irrelevant to the dwell time; it is only determined by the spontaneous decay probabilities of the two metastable states at one random decay time, independent of the lifetimes of the two metastable states. Systematic errors such as collisions with background gases, heating effects, impurity components, the shelving and pumping rates and the photon counts are analyzed, and the lifetime ratio between the and states is directly measured to be 1.0257(43) with an uncertainty of 0.42%. Our result is in good agreement with the most precise many-body atomic structure calculations. Our method can be used to obtain the lifetime of a state which is usually difficult to measure and can be used to determine the magnetic dipole transition matrix elements in heavy ions such as Ba+ and Ra+, and can also be universally applied to lifetime ratio measurements of other single atoms and ions with a similar structure.

Determinant representations of spin-operator matrix elements in the XX spin chain and their applications

For the one-dimensional spin-1/2 XX model with either periodic or open boundary conditions, it is shown by using a fermionic approach that the matrix element of the spin operator $S^-_j$ ($S^-_{j}S^+_{j'}$) between two eigenstates with numbers of excitations $n$ and $n+1$ ($n$ and $n$) can be expressed as the determinant of an appropriate $(n+1)\times (n+1)$ matrix whose entries involve the coefficients of the canonical transformations diagonalizing the model. In the special case of a homogeneous periodic XX chain, the matrix element of $S^-_j$ reduces to a variant of the Cauchy determinant that can be evaluated analytically to yield a factorized expression. The obtained compact representations of these matrix elements are then applied to two physical scenarios: (i) Nonlinear optical response of molecular aggregates, for which the determinant representation of the transition dipole matrix elements between eigenstates provides a convenient way to calculate the third-order nonlinear responses for aggregates from small to large sizes compared with the optical wavelength, and (ii) real-time dynamics of an interacting Dicke model consisting of a single bosonic mode coupled to a one-dimensional XX spin bath. In this setup, full quantum calculation up to $N\leq 16$ spins for vanishing intrabath coupling shows that the decay of the reduced bosonic occupation number approaches a finite plateau value (in the long-time limit) that depends on the ratio between the number of excitations and the total number of spins. Our results can find useful applications in various "system-bath" systems, with the system part inhomogeneously coupled to an interacting XX chain.

Температурная зависимость порогового тока и выходной мощности квантово-каскадного лазера с частотой генерации 3.3 ТГц

AbstractThe active region of a THz (terahertz) quantum-cascade laser based on three tunnel-coupled GaAs/Al_0.15Ga_0.85As quantum wells with a resonance-phonon depopulation scheme is designed. Energy levels, matrix elements of dipole transitions, and gain spectra are calculated as functions of the applied electric-field strength F and temperature. It is shown that the maximum gain is implemented at a frequency of 3.37 THz and F = 12.3 kV/cm. Based on the proposed design, a quantum-cascade laser emitting at ~3.3 THz with a double metal waveguide and T _max ~ 84 K is fabricated. The activation energy E _ a = 23 meV for longitudinal-optical (LO) phonon emission upon the stimulated recombination of hot electrons from the upper laser level to the lower one is determined from the Arrhenius temperature dependence of the output power.

Measurement of the Na2 51Σg+→A1Σu+ and 61Σg+→A1Σu+ transition dipole moments using optical-optical double resonance and Autler-Townes spectroscopy.

Accurate knowledge of transition dipole moment matrix elements is crucial since important parameters associated with the interaction of light with matter, such as emission and absorption line intensities, lifetimes, and Einstein coefficients, depend on these matrix elements. We report here an experimental study of the Na2 51Σg+↔A1Σu+ and 61Σg+↔A1Σu+ electronic transition dipole moments and their dependence on internuclear distance. We have measured absolute transition dipole matrix elements for ro-vibrational transitions of the Na2 51Σg+↔A1Σu+ and 61Σg+↔A1Σu+ electronic transitions using Autler-Townes and optical-optical double resonance spectroscopy, and we compare the results to ab initio theoretical values [A. Sanli et al., J. Chem. Phys. 143, 104304 (2015)].

Spin-resolved electronic structure of ferroelectric α-GeTe and multiferroic Ge1−xMnxTe

Germanium telluride features special spin-electric effects originating from spin-orbit coupling and symmetry breaking by the ferroelectric lattice polarization, which opens up many prospectives for electrically tunable and switchable spin electronic devices. By Mn doping of the α-GeTe host lattice, the system becomes a multiferroic semiconductor possessing magnetoelectric properties in which the electric polarization, magnetization and spin texture are coupled to each other. Employing spin- and angle-resolved photoemission spectroscopy in bulk- and surface-sensitive energy ranges and by varying dipole transition matrix elements, we disentangle the bulk, surface and surface-resonance states of the electronic structure and determine the spin textures for selected parameters. From our results we derive a comprehensive model of the α-GeTe surface electronic structure which fits to experimental data and first principle theoretical predictions and we discuss the unconventional evolution of the Rashba-type spin splitting upon manipulation by external B- and E-fields.

A new method for accurate retrieval of atomic dipole phase or photoionization group delay in attosecond photoelectron streaking experiments

In recent years, attosecond streaking experiments have been used to extract the phase of photoionization dipole transition matrix element (or the photoionization group delay) in atoms, molecules and condensed materials. The most accurate retrieval method so far is based on the frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG-CRAB). However, the FROG-CRAB employs a number of approximations that would cause errors in the retrieved results. In this article, we applied our recently proposed attosecond pulse characterization method phase retrieval of broadband pulses (PROBP) to the retrieval of photoionization group delay difference between Ne() and Ne() ionization channels, and between Ar() and Ne() channels. Our simulations demonstrate that more accurate results can be retrieved using PROBP than using FROG-CRAB, and cast doubts on group delays reported in previous streaking measurements.

Spin-dependent quantum interference in photoemission process from spin-orbit coupled states

Spin–orbit interaction entangles the orbitals with the different spins. The spin–orbital-entangled states were discovered in surface states of topological insulators. However, the spin–orbital-entanglement is not specialized in the topological surface states. Here, we show the spin–orbital texture in a surface state of Bi(111) by laser-based spin- and angle-resolved photoelectron spectroscopy (laser-SARPES) and describe three-dimensional spin-rotation effect in photoemission resulting from spin-dependent quantum interference. Our model reveals that, in the spin–orbit-coupled systems, the spins pointing to the mutually opposite directions are independently locked to the orbital symmetries. Furthermore, direct detection of coherent spin phenomena by laser-SARPES enables us to clarify the phase of the dipole transition matrix element responsible for the spin direction in photoexcited states. These results permit the tuning of the spin polarization of optically excited electrons in solids with strong spin–orbit interaction.

Bosonic cascades of indirect excitons

Recently, the concept of the terahertz bosonic cascade laser (BCL) based on a parabolic quantum well (PQW) embedded in a microcavity was proposed. We refine this proposal by suggesting transitions between indirect exciton (IX) states as a source of terahertz emission. We explicitly propose a structure containing a narrow-square QW and a wide-parabolic QW for the realisation of a bosonic cascade. Advantages of this type of structures are in large dipole matrix elements for terahertz transitions and in long exciton radiative lifetimes which are crucial for realisation of threshold and quantum efficiency BCLs.

Electronic-state–lifetime interference in the hard-x-ray regime: Argon as a showcase

Electronic-state--lifetime interference is a phenomenon specific for ionization of atoms and molecules in the hard-x-ray regime. Using resonant $K{L}_{2,3}{L}_{2,3}$ Auger decay in argon as a showcase, we present a model that allows extracting the interference terms directly from the cross sections of the final electronic states. The analysis provides fundamental information on the excitation and decay processes such as probabilities of various decay paths and the values of the dipole matrix elements for transitions to the excited states. Our results shed light on the interplay between spectator, shake-down, and shake-up processes in the relaxation of deep core-hole states.

Radiative charge transfer in collisions of C with He+

Radiative charge exchange collisions between a carbon atom and a helium ion , both in their ground state, are investigated theoretically. Detailed quantum chemistry calculations are carried out to obtain potential energy curves and transition dipole matrix elements for doublet and quartet molecular states of the HeC+ cation. Radiative charge transfer cross sections and rate coefficients are calculated and are found at thermal and lower energies to be large compared to those for direct charge transfer. The present results might be applicable to modelling the complex interplay of (or ), , and at the boundaries of interstellar photon dominated regions and in x-ray dominated regions, where the abundance of affects the abundance of .

Twofold diabatization of the KRb(1–2)Π1complex in the framework ofab initioand deperturbation approaches

We performed a diabatization of the mutually perturbed $1^1\Pi$ and $2^1\Pi$ states of KRb based on both electronic structure calculation and direct coupled-channel deperturbation analysis of experimental energies. The potential energy curves (PECs) of the diabatic states and their scalar coupling were constructed from the \textit{ab initio} adiabatic PECs by analytically integrating the radial $\langle \psi_1^{ad}|\partial /\partial R|\psi_2^{ad}\rangle$ matrix element obtained by a finite-difference method. The diabatic potentials and electronic coupling function were refined by the least squares fitting of the rovibronic termvalues of the $1^1\Pi\sim 2^1\Pi$ complex. The empirical PECs combined with the coupling function as well as the diabatized spin-orbit coupling and transition dipole matrix elements are useful for further deperturbation treatment of both singlet and triplet states manifold.

Three-dimensional Dirac cone carrier dynamics inNa3BiandCd3As2

Optical measurements and band structure calculations are reported on three-dimensional Dirac materials. The electronic properties associated with the Dirac cone are identified in the reflectivity spectra of ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ and ${\mathrm{Na}}_{3}\mathrm{Bi}$ single crystals. In ${\mathrm{Na}}_{3}\mathrm{Bi}$, the plasma edge is found to be strongly temperature dependent due to thermally excited free carriers in the Dirac cone. The thermal behavior provides an estimate of the Fermi level ${E}_{F}=25$ meV and the $z$-axis Fermi velocity ${v}_{z}=0.3$ eV \AA{} associated with the heavy bismuth Dirac band. At high energies above the $\mathrm{\ensuremath{\Gamma}}$-point Lifshitz gap energy, a frequency- and temperature-independent ${\ensuremath{\epsilon}}_{2}$ indicative of Dirac cone interband transitions translates into an ab-plane Fermi velocity of 3 eV \AA{}. The observed number of IR phonons rules out the $P{6}_{3}/mmc$ space-group symmetry but is consistent with the $P\overline{3}c1$ candidate symmetry. A plasmaron excitation is discovered near the plasmon energy that persists over a broad range of temperature. The optical signature of the large joint density of states arising from saddle points at $\mathrm{\ensuremath{\Gamma}}$ is strongly suppressed in ${\mathrm{Na}}_{3}\mathrm{Bi}$, consistent with band structure calculations that show the dipole transition-matrix elements to be weak due to the very small $s$-orbital character of the Dirac bands. In ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$, a distinctive peak in reflectivity due to the logarithmic divergence in ${\ensuremath{\epsilon}}_{1}$ expected at the onset of Dirac cone interband transitions is identified. The center frequency of the peak shifts with temperature quantitatively consistent with a linear dispersion and a carrier density of $n=1.3\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{4.pt}{0ex}}{\text{cm}}^{\ensuremath{-}3}$. The peak width gives a measure of the Fermi-velocity anisotropy of $10%$, indicating a nearly spherical Fermi surface. The line shape gives an upper bound estimate of 7 meV for the potential fluctuation energy scale.

Analysis of Polarizability Measurements Made with Atom Interferometry

We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then, we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths fik, Einstein coefficients Aik, state lifetimes τk, transition dipole matrix elements Dik, line strengths Sik, and van der Waals C6 coefficients. Finally, we combine atom interferometer measurements of polarizabilities with independent measurements of lifetimes and C6 values in order to quantify the residual contribution to polarizability due to all atomic transitions other than the principal ns-npJ transitions for alkali metal atoms.

Volkov transform generalized projection algorithm for attosecond pulse characterization

An algorithm for characterizing attosecond extreme ultraviolet pulses that is not bandwidth-limited, requires no interpolation of the experimental data, and makes no approximations beyond the strong-field approximation is introduced. This approach fully incorporates the dipole transition matrix element into the retrieval process. Unlike attosecond retrieval methods such as phase retrieval by omega oscillation filtering (PROOF), or improved PROOF, it simultaneously retrieves both the attosecond and infrared (IR) pulses, without placing fundamental restrictions on the IR pulse duration, intensity or bandwidth. The new algorithm is validated both numerically and experimentally, and is also found to have practical advantages. These include an increased robustness to noise, and relaxed requirements for the size of the experimental dataset and the intensity of the streaking pulse.

Optical properties of spherical quantum dot with on-center hydrogen impurity in magnetic field

This paper studies linear and nonlinear optical properties of the GaAs spherical quantum dot (QD) with impenetrable walls, containing on-center hydrogen impurity, under the presence of the static magnetic field. Transition energy and electric dipole transition matrix element between the impurity electron ground and the first excited state with \(m = 0\) have been computed using the Lagrange mesh method within the effective mass approximation. The linear and the third-order nonlinear optical absorption coefficients (ACs) are obtained using the iterative procedure in the framework of the density matrix approach, and their behavior with respect to the incident photon energy is discussed. In addition, the dependence of these coefficients on the QD radius, magnetic field strength, intensity of the applied laser field and relaxation time is studied. It has been found that for large values of relaxation time, the nonlinear AC prevails over the linear one and the total AC becomes negative.

Strong-field approximation and its extension for high-order harmonic generation with mid-infrared lasers

In recent years intense mid-infrared lasers with wavelength of a few microns have become the standard tools for research in strong field physics laboratories worldwide. These lasers offer the opportunities to extend the traditional study of high-order harmonics generation and attosecond sciences from the extreme ultraviolet to soft x-rays. In this tutorial we revisit the familiar strong field approximation and its simplification—the quantum orbits theory. We draw special emphasis on the factorization of laser induced dipole moment as the product of a returning electron wave packet with the photo-recombination dipole transition matrix element. The former depends on the laser properties only (up to a normalization constant) while the latter is related to laser-free photoionization transition dipole. The factorization leads to the suggested modification beyond the strong field approximation—the quantitative rescattering theory. In applying these theories to mid-infrared lasers, we analyze the behavior of the returning electron wave packet and its scaling properties vs the wavelength of the laser. A few examples are given to demonstrate how the quantitative rescattering theory is capable of reproducing experimental harmonic spectra under various conditions. Future opportunities in employing harmonics generated by optimized mid-infrared lasers for probing molecular structure and for serving as useful table-top coherent light sources up to the x-ray region are also discussed.

Origin and implications of anA2-like contribution in the quantization of circuit-QED systems

By placing an atom into a cavity, the electromagnetic mode structure of the cavity is modified. In Cavity QED, one manifestation of this phenomenon is the appearance of a gauge-dependent diamagnetic term, known as the $A^2$ contribution. Although in atomic Cavity QED, the resulting modification in the eigenmodes is negligible, in recent superconducting circuit realizations, such corrections can be observable and may have qualitative implications. We revisit the canonical quantization procedure of a circuit QED system consisting of a single superconducting transmon qubit coupled to a multimode superconducting microwave resonator. A complete derivation of the quantum Hamiltonian of an open circuit QED system consisting of a transmon qubit coupled to a leaky transmission line cavity is presented. We introduce a complete set of modes that properly conserves the current in the entire structure and present a sum rule for the dipole transition matrix elements of a multi-level transmon qubit coupled to a multi-mode cavity. Finally, an effective multi-mode Rabi model is derived with coefficients that are given in terms of circuit parameters.

Measurement of Dipole Matrix Elements with a Single Trapped Ion.

We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e., the 4(2)S(1/2)↔4(2)P(1/2) transition of (40)Ca(+), for which we find the value 2.8928(43) ea(0). Moreover, the method allows us to deduce the lifetime of the 4(2)P(1/2) state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a long-standing discrepancy between calculated values and experimental results.

The origin of anisotropy and high density of states in the electronic structure of Cr2GeC by means of polarized soft x-ray spectroscopy and ab initio calculations

The anisotropy in the electronic structure of the inherently nanolaminated ternary phase Cr2GeC is investigated by bulk-sensitive and element selective soft x-ray absorption/emission spectroscopy. The angle-resolved absorption/emission measurements reveal differences between the in-plane and out-of-plane bonding at the (0001) interfaces of Cr2GeC. The Cr L2, 3, C K, and Ge M1, M2, 3 emission spectra are interpreted with first-principles density-functional theory (DFT) including core-to-valence dipole transition matrix elements. For the Ge 4s states, the x-ray emission measurements reveal two orders of magnitude higher intensity at the Fermi level than DFT within the General Gradient Approximation (GGA) predicts. We provide direct evidence of anisotropy in the electronic structure and the orbital occupation that should affect the thermal expansion coefficient and transport properties. As shown in this work, hybridization and redistribution of intensity from the shallow 3d core levels to the 4s valence band explain the large Ge density of states at the Fermi level.