Splitting Of Ground State Research Articles

Optical properties of Mn3+ ions in Cs2NaAlF6 and Cs2NaGaF6 single crystals

The optical properties of Mn3+ ions in the elpasolites Cs2NaGaF6 and Cs2NaAlF6 have been investigated by absorption spectroscopy at 4.2 K. The absorption spectra are dominated by the spin-allowed 5E → 5T2 transition and the transition between the two Jahn-Teller components of the 5E level. The crystal-field parameter Dq was determined and a low crystal-field situation was established for both Mn3+-doped fluorides. The Jahn-Teller stabilization energies of the 5E and 5T2 levels were calculated and the obtained values shown a strong Jahn-Teller splitting in the 5E ground state.

Pressure effect on hydrogen tunneling and vibrational spectrum inα-Mn

The pressure effect on the tunneling mode and vibrational spectra of hydrogen in $\ensuremath{\alpha}\ensuremath{-}{\text{MnH}}_{0.07}$ has been studied by inelastic neutron scattering. Applying hydrostatic pressure of up to 30 kbar is shown to shift both the hydrogen optical modes and the tunneling peak to higher energies. First-principles calculations show that the potential for hydrogen in $\ensuremath{\alpha}$-Mn becomes overall steeper with increasing pressure. At the same time, the barrier height and its extent in the direction of tunneling decrease and the calculations predict significant changes of the dynamics of hydrogen in $\ensuremath{\alpha}$-Mn at 100 kbar, when the estimated tunneling splitting of the hydrogen ground state exceeds the barrier height.

The hydrogen tunneling splitting in malonaldehyde: A full-dimensional time-independent quantum mechanical method.

The accurate time-independent quantum dynamics calculations on the ground-state tunneling splitting of malonaldehyde in full dimensionality are reported for the first time. This is achieved with an efficient method developed by us. In our method, the basis functions are customized for the hydrogen transfer process which has the effect of greatly reducing the size of the final Hamiltonian matrix, and the Lanczos method and parallel strategy are used to further overcome the memory and central processing unit time bottlenecks. The obtained ground-state tunneling splitting of 24.5 cm(-1) is in excellent agreement with the benchmark value of 23.8 cm(-1) computed with the full-dimensional, multi-configurational time-dependent Hartree approach on the same potential energy surface, and we estimate that our reported value has an uncertainty of less than 0.5 cm(-1). Moreover, the role of various vibrational modes strongly coupled to the hydrogen transfer process is revealed.

Conformational Equilibrium and Potential Energy Functions of the O-H Internal Rotation in the Axial and Equatorial Species of 1-Methylcyclohexanol.

The rotational spectra of four conformers (At, Ag, Et, Eg) of the tertiary alcohol 1-methylcyclohexanol were assigned by pulsed jet Fourier transform microwave spectroscopy. The transitions of two gauche conformers were split in two separated component lines, but it was not possible-from the available measured transitions-to accurately determine their vibrational ΔE0+0- ground-state splittings, respectively. In addition, the rotational spectra of the four OD deuterated isotopologues were measured and assigned. For the gauche species of this isotopologue we were able to determine the tunneling splittings, ΔE0+0-(Ag, OD) = 15.581(5) GHz and ΔE0+0-(Eg, OD) = 18.17(3) GHz, respectively. From these splittings the inversion barriers for Ag and Eg were determined, by using a flexible model, to be B2(Ag) = 356(10) and B2(Eg) = 320(10) cm(-1), respectively.

Frequency metrology using highly charged ions

Due to the scaling laws of relativistic fine structure splitting, many forbidden optical transitions appear within the ground state configurations of highly charged ions (HCI). In some hydrogen-like ions, even the hyperfine splitting of the 1s ground state gives rise to optical transitions. Given the very low polarizability of HCI, such laser-accessible transitions are extremely impervious to external perturbations and systematics that limit optical clock performance and arise from AC and DC Stark effects, such as black-body radiation and light shifts. Moreover, AC and DC Zeeman splitting are symmetric due to the much larger relativistic spin-orbit coupling and corresponding fine-structure splitting. Appropriate choice of states or magnetic sub-states with suitable total angular momentum and magnetic quantum numbers can lead to a cancellation of residual quadrupolar shifts. All these properties are very advantageous for the proposed use of HCI forbidden lines as optical frequency standards. Extremely magnified relativistic, quantum electrodynamic, and nuclear size contributions to the binding energies of the optically active electrons make HCI ideal tools for fundamental research, as in proposed studies of a possible time variation of the fine structure constant. Beyond this, HCI that cannot be photoionized by vacuum-ultraviolet photons could also provide frequency standards for future lasers operating in that range.

ChemInform Abstract: Radical Ligand‐Containing Single‐Molecule Magnets

AbstractReview: 372 refs.

Steps towards the hyperfine splitting measurement of the muonic hydrogen ground state: pulsed muon beam and detection system characterization

The high precision measurement of the hyperfine splitting of the muonic-hydrogen atom ground state with pulsed and intense muon beam requires careful technological choices both in the construction of a gas target and of the detectors. In June 2014, the pressurized gas target of the FAMU experiment was exposed to the low energy pulsed muon beam at the RIKEN RAL muon facility. The objectives of the test were the characterization of the target, the hodoscope and the X-ray detectors. The apparatus consisted of a beam hodoscope and X-rays detectors made with high purity Germanium and Lanthanum Bromide crystals. In this paper the experimental setup is described and the results of the detector characterization are presented.

Tunable Splitting of the Ground-State Degeneracy in Quasi-One-Dimensional Parafermion Systems.

Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practice, this degeneracy is never exact, and the magnitude of the ground-state degeneracy splitting imposes constraints on the time scales over which information is topologically protected. In this Letter, we use an instanton approach to evaluate the splitting of topological ground-state degeneracy in quasi-1D systems with parafermion zero modes, in the specific case where parafermions are realized by inducing a superconducting gap in pairs of fractional quantum Hall edges. We show that, like 1D topological superconducting wires, this splitting has an oscillatory dependence on the chemical potential, which arises from an intrinsic Berry phase that produces interference between distinct instanton tunneling events. These Berry phases can be mapped to chiral phases in a (dual) quantum clock model using a Fradkin-Kadanoff transformation. Comparing our low-energy spectrum to that of phenomenological parafermion models allows us to evaluate the real and imaginary parts of the hopping integral between adjacent parafermionic zero modes as functions of the chemical potential.

The FAMU experiment: muonic atoms to probe the proton structure

The goal of the FAMU experiment is the measurement of the proton Zemach radius using muonic hydrogen, a subject that has raised much interest in recent years due to its implications in the so-called proton radius puzzle. In order to extract the Zemach radius, the FAMU collaboration aims at measuring the hyperfine splitting of the µp ground state, since the effect of the proton finite size affects the HF transition energy. The proposed experimental method requires a detection system which is suited for time resolved X-ray spectroscopy: in this contribution the results of the first measurements performed at the RIKEN-RAL muon facility in order to verify the fitness of the detection system in the pulsed intense muon beam are presented. The characteristic X-rays from atomic transitions in muonic atoms formed in different targets have been detected using a HPGe detector and five scintillating counters based on LaBr3(Ce) crystals, whose output has been recorded for 5 ps using a 500 MHz digitizer to measure both the energy and the time spectrum of the detected events. With a detailed pulse analysis considering pile-up events, both the expected characteristic X-rays and lifetimes of various elements were measured, paving the way for future measurements to be carried out in early 2016.

Ground state of the holes localized in II-VI quantum dots with Gaussian potential profiles

We report on the theoretical study of the hole states in II-IV quantum dots of a spherical and ellipsoidal shape, described by a smooth potential confinement profiles, that can be modelled by a Gaussian functions in all three dimensions. The universal dependencies of the hole energy, $g$-factor and localization length on a quantum dot barrier height, as well as the ratio of effective masses of the light and heavy holes are presented for the spherical quantum dots. The splitting of the four-fold degenerate ground state into two doublets is derived for anisotropic (oblate or prolate) quantum dots. Variational calculations are combined with numerical ones in the framework of the Luttinger Hamiltonian. Constructed trial functions are optimized by comparison with the numerical results. The effective hole $g$-factor is found to be independent on the quantum dot size and barrier height and is approximated by simple universal expression depending only on the effective mass parameters. The results can be used for interpreting and analyzing experimental spectra measured in various structures with the quantum dots of different semiconductor materials.

An ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1-4-mode subspaces.

We report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer. This PES is a least-squares fit to 13475 CCSD(T)-F12a/haTZ (VTZ for H and aVTZ for C and O) energies. The energy-weighted, root-mean-square fitting error is 11 cm-1 and the barrier for the double-proton transfer on the PES is 2848 cm-1, in good agreement with the directly-calculated ab initio value of 2853 cm-1. The zero-point vibrational energy of 15 337 ± 7 cm-1 is obtained from diffusion Monte Carlo calculations. Energies of fundamentals of fifteen modes are calculated using the vibrational self-consistent field and virtual-state configuration interaction method. The ground-state tunneling splitting is computed using a reduced-dimensional Hamiltonian with relaxed potentials. The highest-level, four-mode coupled calculation gives a tunneling splitting of 0.037 cm-1, which is roughly twice the experimental value. The tunneling splittings of (DCOOH)2 and (DCOOD)2 from one to three mode calculations are, as expected, smaller than that for (HCOOH)2 and consistent with experiment.

Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives.

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

Spectroscopic and Computational Investigation of Low-Spin Mn(III) Bis(scorpionate) Complexes.

Six-coordinate MnIII complexes are typically high-spin (S = 2), however, the scorpionate ligand, both in its traditional, hydridotris(pyrazolyl)borate form, Tp- and Tp*- (the latter with 3,5-dimethylpyrazole substituents) and in an aryltris(carbene)borate (i.e., N-heterocyclic carbene, NHC) form, [Ph(MeIm)3B]-, (MeIm = 3-methylimidazole) lead to formation of bis(scorpionate) complexes of MnIII with spin triplet ground states; three of which were investigated herein: [Tp2Mn]SbF6 (1SBF6), [Tp*2Mn]SbF6 (2SBF6), and [{Ph(MeIm)3B}2Mn]CF3SO3 (3CF3SO3). These trigonally symmetric complexes were studied experimentally by magnetic circular dichroism (MCD) spectroscopy (the propensity of 3 to oxidize to MnIV precluded collection of useful MCD data) including variable temperatures and fields (VTVH-MCD) and computationally by ab initio CASSCF/NEVPT2 methods. These combined experimental and theoretical techniques establish the 3A2g electronic ground state for the three complexes, and provide information on the energy of the "conventional" high-spin excited state (5Eg) and other, triplet excited states. These results show the electronic effect of pyrazole ring substituents in comparing 1 and 2. The tunability of the scorpionate ligand, even by perhaps the simplest change (from pyrazole in 1 to 3,5-dimethylpyrazole in 2) is quantitatively manifested through perturbations in ligand-field excited-state energies that impact ground-state zero-field splittings. The comparison with the NHC donor is much more dramatic. In 3, the stronger σ-donor properties of the NHC lead to a quantitatively different electronic structure, so that the lowest lying spin triplet excited state, 3Eg, is much closer in energy to the ground state than in 1 or 2. The zero-field splitting (zfs) parameters of the three complexes were calculated and in the case of 1 and 2 compare closely to experiment (lower by < 10%, < 2 cm-1 in absolute terms); for 3 the large magnitude zfs is reproduced, although there is ambiguity about its sign. The comprehensive picture obtained for these bis(scorpionate) MnIII complexes provides quantitative insight into the role played by the scorpionate ligand in stabilizing unusual electronic structures.

Spin-phonon and lattice contributions to the ground-state splitting of Gd3+ and Eu2+ in scheelite crystals

The EPR spectra of Gd3+ in CaWO4 single crystals have been studied at temperatures T = 1.8, 4.2, and 114–300 K, and the temperature dependence of the parameters b (T) of the spin Hamiltonian has been found. The behavior of b 2 0 (T) has been analyzed. The spin-phonon and static lattice contributions b 2 0 (F) and b 2 0 (L) to b 2 0 (T) have been revealed. For this purpose, the variation of b 2 0 (L) has been calculated taking into account the thermal shifts of oxygen ions in CaWO4. Similar analysis has been carried out for CaWO4: Eu2+ based on the EPR data of other authors (Bronstein, Voterra and Harvey, Kiefte). It has been shown that at b 2 0 (F) > 0, the variation of b 2 0 (F) as a function of T for these impurity centers is described well by the Pfister model and a sign change of b 2 0 (T) for Eu2+ is determined by thermal expansion of the lattice.

Fluctuation-dissipation relation in a resonantly driven quantum medium.

Noise associated with the spontaneous emission in a coherently driven medium is calculated. The significant field-induced modification of relation between the noise power and damping constant in a thermal reservoir is obtained. The nonlinear noise exchange between different atomic frequencies leads to violation of standard relations dictated by the fluctuation-dissipation theorem. The developed general method is applied to the EIT system, attractive for realization of different quantum-information processing devices. It is shown that there is a significant factor defining the thermal noise at operating frequency in the EIT system. It is the averaged number of thermal photons at low frequency of ground state splitting.

Holes localized in nanostructures in an external magnetic field: g-factor and mixing of states

The energy spectrum and wave functions of holes in the valence band in semiconductor nanosystems, including quantum wells, quantum wires, and quantum dots, in an external magnetic field are theoretically investigated. The dependence of Zeeman splitting of the hole ground state upon variation in the size-quantization parameters with regard to the complex structure of the valence band and magnetic field-induced mixing of hole states is traced. Analytical formulas for describing the Zeeman effect in the valence band in the limiting cases of a quantum disk, spherically symmetric quantum dot, and quantum wire are presented. It is demonstrated that the g-factor of a hole is extremely sensitive to the hole-state composition (heavy or light hole) and, consequently, to the geometry of the size-quantization potential.

Theory of spin inelastic tunneling spectroscopy for superconductor-superconductor and superconductor-metal junctions

We address the tunneling conductance and spin inelastic tunneling spectroscopy of localized paramagnetic moments in a superconducting environment, pertaining to recent measurements on Fe-octaethylporphyrin-chloride using superconducting scanning tunneling microscopy. We demonstrate that the Cooper pair correlations in the tip and substrate generate a finite uniaxial anisotropy field acting on the local spin moment, and we argue that this field may be a source for the observed changes in the conductance spectrum for decreasing distance between the scanning tunneling tip and the local magnetic moment. We make a side-by-side comparison between the superconductor-superconductor junction and normal-metal--superconductor junction, and find qualitative agreement between the two setups while quantitative differences become explicit. When simulating the effects of electron pumping, we obtain additional peaks in the conductance spectrum that can be attributed to excitations between higher-energy spin states. The transverse anisotropy field couples basis states of the local spin which opens for transitions between spin states that are otherwise forbidden by conservation of angular momentum. Finally, we explore the influences of temperature, which tend to enable in-gap transitions, and an external magnetic field, which enables deeper studies of the spin excitation spectrum. We especially notice the appearance of a low and high excitation peak on each side of the main coherence peak as an imprint of transitions between the Zeeman split ground states.

Mode-Specific Tunneling Splittings for a Sequential Double-Hydrogen Transfer Case: An Accurate Quantum Mechanical Scheme.

We present the first accurate quantum dynamics calculations of mode-specific tunneling splittings in a sequential double-hydrogen transfer process. This is achieved in the vinylidene-acetylene system, the simplest molecular system of this kind, and by large-scale parallel computations with an efficient theoretical scheme developed by us. In our scheme, basis functions are customized for the hydrogen transfer process; a 4-dimensional basis contraction strategy is combined with the preconditioned inexact spectral transform method; efficient parallel implementation is achieved. Mode-specific permutation tunneling splittings of vinylidene states are reported and tremendous mode-specific promotion effects are revealed; in particular, the CH2 rock mode enhances the ground-state splitting by a factor of 10(3). We find that the ground-state vinylidene has a reversible-isomerization time of 622 ps, much longer than all previous estimates. Our calculations also shed light on the importance of the deep intermediate well and vibrational excitation in the double-hydrogen transfer processes.

Self-induced transparency and coherent population trapping of ^87Rb vapor in a mode-locked laser

Simultaneous self-induced transparency and a dark line resonance are observed inside a mode-locked laser. The circulating pulse, tuned to the 795-nm optical resonance of rubidium, has sufficient intensity to create at each passage a population inversion-return to ground state, typical of self-induced transparency. A drop in fluorescence (dark line resonance), is observed as the repetition rate is tuned to a submultiple of the hyperfine ground-state splitting.

Biexciton formation and exciton coherent coupling in layered GaSe.

Nonlinear two-dimensional Fourier transform (2DFT) and linear absorption spectroscopy are used to study the electronic structure and optical properties of excitons in the layered semiconductor GaSe. At the 1s exciton resonance, two peaks are identified in the absorption spectra, which are assigned to splitting of the exciton ground state into the triplet and singlet states. 2DFT spectra acquired for co-linear polarization of the excitation pulses feature an additional peak originating from coherent energy transfer between the singlet and triplet. At cross-linear polarization of the excitation pulses, the 2DFT spectra expose a new peak likely originating from bound biexcitons. The polarization dependent 2DFT spectra are well reproduced by simulations using the optical Bloch equations for a four level system, where many-body effects are included phenomenologically. Although biexciton effects are thought to be strong in this material, only moderate contributions from bound biexciton creation can be observed. The biexciton binding energy of ∼2 meV was estimated from the separation of the peaks in the 2DFT spectra. Temperature dependent absorption and 2DFT measurements, combined with "ab initio" theoretical calculations of the phonon spectra, indicate strong interaction with the A1 (') phonon mode. Excitation density dependent 2DFT measurements reveal excitation induced dephasing and provide a lower limit for the homogeneous linewidth of the excitons in the present GaSe crystal.