First-excited State Research Articles

Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates

We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type of control problem is typically solved using derivative-based methods in a high-dimensional control space such as gradient-ascent pulse engineering (GRAPE) and Krotov's method or derivative-free methods in a reduced control space such as Nelder-Mead with a chopped random basis (CRAB). We discuss how these methods can be combined in gradient optimization using parametrization (GROUP) including the finite bandwidth of the control electronics. We compare these methods and find that GROUP converges much faster than Nelder-Mead with CRAB and achieves better results than GRAPE and Krotov's method on the control problem presented here.

Observation of geometric phase in a dispersively coupled resonator-qutrit system**Project supported by the National Basic Research Program of China (Grant No. 2014CB921201) and the National Natural Science Foundation of China (Grant Nos. 11434008 and 11574380).

We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit’s ground state and first-excited state along different circular trajectories in phase space. We identify the resonator’s phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit π-phase gate with a process fidelity of 0.851±0.001.

Circularly polarized zero-phonon transitions of vacancies in diamond at high magnetic fields

We study the circularly polarized photoluminescence of negatively charged (${\mathrm{NV}}^{\ensuremath{-}}$) and neutral (${\mathrm{NV}}^{0}$) nitrogen-vacancy ensembles and neutral vacancies (${\mathrm{V}}^{0}$) in diamond crystals exposed to magnetic fields of up to 10 T. We determine the orbital and spin Zeeman splitting as well as the energetic ordering of their ground and first-excited states. The spin-triplet and -singlet states of the ${\mathrm{NV}}^{\ensuremath{-}}$ are described by an orbital Zeeman splitting of about 9 $\ensuremath{\mu}\mathrm{eV}/\mathrm{T}$, which corresponds to a positive orbital $g$-factor of ${g}_{L}=0.164$ under application of the magnetic field along the (001) and (111) crystallographic directions, respectively. The zero-phonon line (ZPL) of the ${\mathrm{NV}}^{\ensuremath{-}}$ singlet is defined as a transition from the ${}^{1}{E}^{\ensuremath{'}}$ states, which are split by ${g}_{L}{\ensuremath{\mu}}_{\text{B}}B$, to the ${}^{1}{A}_{1}$ state. The energies of the zero-phonon triplet transitions show a quadratic dependence on intermediate magnetic field strengths, which we attribute to a mixing of excited states with nonzero orbital angular momentum. Moreover, we identify slightly different spin Zeeman splittings in the ground (gs) and excited (es) triplet states, which can be expressed by a deviation between their spin $g$-factors: ${g}_{S,\text{es}}={g}_{S,\text{gs}}+\mathrm{\ensuremath{\Delta}}g$ with values of $\mathrm{\ensuremath{\Delta}}g=0.014$ and 0.029 in the (001) and (111) geometries, respectively. The degree of circular polarization of the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs depends significantly on the temperature, which is explained by an efficient spin-orbit coupling of the excited states mediated through acoustic phonons. We further demonstrate that the sign of the circular polarization degree is switched under rotation of the diamond crystal. A weak Zeeman splitting similar to $\mathrm{\ensuremath{\Delta}}g{\ensuremath{\mu}}_{\text{B}}B$ measured for the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs is also obtained for the ${\mathrm{NV}}^{0}$ zero-phonon lines, from which we conclude that the ground state is composed of two optically active states with compensated orbital contributions and opposite spin-1/2 momentum projections. The zero-phonon lines of the ${\mathrm{V}}^{0}$ show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the $^{1}T_{2}$ states to the $^{1}A$ ground state defines the zero-phonon emission at 1.674 eV, while the $^{1}T_{2}\ensuremath{\rightarrow}^{1}E$ transition is responsible for the zero-phonon line at 1.666 eV. The $^{1}T_{2}$ ($^{1}E$) states are characterized by an orbital Zeeman splitting with ${g}_{L}=0.071$ (0.128).

Analytical and numerical analysis of the complete Lipkin–Meshkov–Glick Hamiltonian

The Lipkin–Meshkov–Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schrödinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the [Formula: see text] interaction, which promotes or degrades pairs of particles, and a second one, the [Formula: see text] interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the [Formula: see text] term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behavior can be well understood by considering the extrapolations of the analytical results. Of particular interest is the study of how the [Formula: see text] interaction affects the energy gap between the ground state and the first-excited state.

Lifetimes of low-lying excited states in Kr503686

The evolution of nuclear magic numbers at extremes of isospin is a topic at the forefront of contemporary nuclear physics. $N=50$ is a prime example, with increasing experimental data coming to light on potentially doubly-magic $^{100}$Sn and $^{78}$Ni at the proton-rich and proton-deficient extremes, respectively. Experimental discrepancies exist in the data for less exotic systems. In $^{86}$Kr the $B(E2;2^+_1\rightarrow0^+_1)$ value - a key indicator of shell evolution - has been experimentally determined by two different methodologies, with the results deviating by $3\sigma$. Here, we report on a new high-precision measurement of this value, as well as the first measured lifetimes and hence transition strengths for the $2^+_2$ and $3^-_{(2)}$ states in the nucleus. The Doppler-shift attenuation method was implemented using the TIGRESS gamma-ray spectrometer and TIGRESS integrated plunger (TIP) device. High-statistics Monte-Carlo simulations were utilized to extract lifetimes in accordance with state-of-the-art methodologies. Lifetimes of $\tau(2^+_1)=336\pm4\text{(stat.)}\pm20\text{(sys.)}$ fs, $\tau(2^+_2)=263\pm9\text{(stat.)}\pm19\text{(sys.)}$ fs and $\tau(3^-_{(2)})=73\pm6\text{(stat.)}\pm32\text{(sys.)}$ fs were extracted. This yields a transition strength for the first-excited state of $B(E2;2^+_1\rightarrow0^+)=259\pm3\text{(stat.)}\pm16\text{(sys.)}$ e$^2$fm$^4$. The measured lifetime disagrees with the previous Doppler-shift attenuation method measurement by more than $3\sigma$, while agreeing well with a previous value extracted from Coulomb excitation. The newly extracted $B(E2;2^+_1\rightarrow0^+_1)$ value indicates a more sudden reduction in collectivity in the $N=50$ isotones approaching $Z=40$.

Constructiveness and destructiveness of temperature in asymmetric quantum pseudo dot qubit system

By using the variational method of the Pekar type, we theoretically study the temperature effects on the asymmetric quantum pseudo dot qubit with a pseudoharmonic potential under an electromagnetic field. The numerical results are analyzed and discussed in detail and show that the relationships of the ground and first excited state energies, the electron oscillation period and the electron probability density in the superposition state of the ground state and the first-excited state with the temperature, the chemical potential, the pseudoharmonic potential, the electric field strength, the cyclotron frequency, the electron phonon coupling constant, the transverse and longitudinal effective confinement length, respectively.

Ultrafast internal conversion in 4-aminobenzonitrile occurs sequentially along the seam

Upon UV light absorption, 4-aminobenzonitrile undergoes an ultrafast radiationless decay process from a charge-transfer state to a locally-excited state. This pathway proceeds through an extended seam of conical intersections between the second- and first-excited singlet electronic states. Quantum dynamics simulations show that planar geometries dominate the earlier times (<20 fs), after which the whole seam becomes explored, as the wavepacket spreads and breathes along both sides of the unstable ridge with respect to the amino-bending coordinate.

Probing the N = 14 subshell closure: g factor of the [formula omitted] state

The first-excited state g factor of 26Mg has been measured relative to the g factor of the Mg24(21+) state using the high-velocity transient-field technique, giving g=+0.86±0.10. This new measurement is in strong disagreement with the currently adopted value, but in agreement with the sd-shell model using the USDB interaction. The newly measured g factor, along with E(21+) and B(E2) systematics, signal the closure of the νd5/2 subshell at N=14. The possibility that precise g-factor measurements may indicate the onset of neutron pf admixtures in first-excited state even–even magnesium isotopes below 32Mg is discussed and the importance of precise excited-state g-factor measurements on sd shell nuclei with N≠Z to test shell-model wavefunctions is noted.

The influences of electric field and temperature on state energies of a strong-coupling polaron in an asymmetric Gaussian potential quantum well

We investigate the electric field effect on the ground state (GS), the first-excited state (FES) and the excitation energies of a strong-coupled polaron in an asymmetric Gaussian potential (AGP) quantum well (QW) by using a variational method of the Pekar type (VMPT). By employing the quantum statistics theory (QST), we also study the temperature effects on the state energies (SE). It is found that the SE of polaron are an increasing function of temperature. The polaron's SE are decreasing functions of electric field, but the excitation energy is an increasing one.

Hydrogenic impurity bound polaron in an anisotropic quantum dot

The effect of the electron–phonon interaction on an electron bound to a hydrogenic impurity in a three-dimensional (3D) anisotropic quantum dot (QD) is studied theoretically. We use the Landau–Pekar variational approach to calculate the binding energy of ground state (GS) and first-excited state (ES) with considering electron–phonon interaction. The expressions of the GS and ES energies under investigation depict a rich variety of dependent relationship with the variational parameters in three different limiting cases. Numerical calculations were performed for ZnSe QDs with different confinement lengths in the xy-plane and the z-direction, respectively. It is illustrated that binding energies of impurity polarons corresponding to each level are larger in small QDs. Furthermore, the contribution to binding energy from phonon is about 15% of the total binding energy.

Reorientation-effect measurement of the first 2+ state in 12C: Confirmation of oblate deformation

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the 〈21+‖E2ˆ‖21+〉 diagonal matrix element in 12C from particle−γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (21+) states in 12C have been calculated using chiral NN N4LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 21+ state at 4.439 MeV. The polarizability of the 21+ state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12C. Spectroscopic quadrupole moments of QS(21+)=+0.053(44) eb and QS(21+)=+0.08(3) eb are determined, respectively, yielding a weighted average of QS(21+)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 21+ state of 12C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei.

Widths of P26(1+) and mass of P26(g.s.)

For the ${1}^{+}$ first-excited state of $^{26}\mathrm{P}$, the lifetime and the upper limit on the proton width have been combined with shell-model spectroscopic factors to place an upper limit on the proton single-particle (sp) width. With a potential model, this limit on sp width allows an upper limit on the ${1}^{+}$ resonance energy of ${E}_{\mathrm{r}}&lt;124\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$. Combining with the known ${1}^{+}$ excitation energy provides a limit on the proton separation energy of $^{26}\mathrm{P}(\mathrm{g}.\mathrm{s}.)$ of ${S}_{\mathrm{p}}&gt;40\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$, considerably better than a recent result of ${S}_{\mathrm{p}}&gt;\ensuremath{-}135\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ from a similar procedure that used $R$-matrix sp widths.

Influences of temperature on asymmetric quantum dot qubit in Coulombic impunity potential

Using the variational method of the Pekar-type, we study the influences of the temperature on the asymmetric quantum dot (QD) qubit in the Coulombic impunity potential. Then we derive the numerical results and formulate the derivative relationships of the electron probability density and the electron oscillation period in the superposition state of the ground state and the first-excited state with the electron–phonon coupling constant, the Coulombic impurity potential, the transverse and longitudinal confinement strengths at different temperatures, respectively.

Variational approach to the soft-Coulomb potential in low-dimensional quantum systems

The variational method is used to obtain the ground- and first-excited states for the soft-Coulomb central potential, 1/r2+d2, characterized by a bias distance d, taken into account as a fixed parameter. Applications are presented for spatially indirect excitons, i.e., photo-generated electron-hole (e-h) bound pairs, where the two charges are kept separated in two different regions of a heterostructure. We consider one- or two-dimensional systems, namely, quantum wires or wells, respectively, and compare the results with numerical calculations obtained by finite-difference diagonalization of the Hamiltonian. An explicit example is given for GaAs-based heterostructures.

Temperature effects on bound polaron in triangular quantum dot qubit subjected to an electromagnetic field

In this work, the variational method of the Pekar type is used to theoretically study the temperature effects on the bound polaron in the triangular quantum dot (QD) qubit subjected to an electromagnetic field. We analyze and discuss in detail the numerical results and show that the relationships of the ground and first excited state energies, the electron probability density and the electron oscillation period in the superposition state of the ground state and the first-excited state with the temperature, the cyclotron frequency, the electron-phonon coupling constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively.

First-excited state g factor of Te136 by the recoil in vacuum method

Electromagnetic properties of atomic nuclei such as $E2$ transition rates and $M1$ magnetic moments (or $g$ factors) are crucial characteristics of structure. For unstable nuclei produced as reaccelerated radioactive beams, measurements of $g$ factors present numerous challenges. This paper develops the important recoil-in-vacuum technique to obtain a $g$ factor for the ${2}^{+}$ state in ${}^{136}$Te. The result fits existing systematics but also highlights anomalous values in other $N=84$ isotones, thus presenting an important challenge to theory in the region just above doubly magic ${}^{132}$Sn.

Energy Transfer in an Optically Pumped D2O Gas THz Laser

We report on the mid-infrared (MIR) and terahertz (THz) wave spectra of D2O gas pumped using a fundamental transverse mode transversely excited atmospheric CO2 laser with an emission wavelength of 9.26 μm. We obtain MIR emission lines at center wavelengths of 9.262, 9.491, and 9.752 μm, which correspond to the vibrational-energy-level-transition lines of D2O. We observe an intense THz stimulated Raman emission line of 385 μm and a weak cascade-transition line of 359 μm for transitions from rotational levels 422 to 413 and 413 to 404 in the first-excited vibration state of the D2O molecule gas. We establish a four-energy-level system for modeling the laser kinetics of the dual-wavelength (385 and 359 μm) superradiation THz laser. For the optically pumped D2O gas 385 μm THz laser, in considering the cavity effect and insertion loss of a THz cavity oscillator, an approximation treatment of the THz laser kinetics can be made based on a three-energy-level system.

Magnetically Ordered State and Crystalline-Electric-Field Effects in SmBe13

The physical properties of single-crystalline SmBe$_{13}$ with a NaZn$_{13}$-type cubic structure have been studied by electrical resistivity ($\rho$), specific heat ($C$), and magnetization ($M$) measurements in magnetic fields of up to 9 T. The temperature ($T$) dependence of $\rho$ shows normal metallic behavior without showing the Kondo -ln$T$ behavior, suggesting the weak hybridization effect in this system. Analyses of the temperature dependence of $C$ suggest that the Sm ions of this compound are trivalent and that the crystalline-electric-field (CEF) ground state is a $\Gamma_8$ quartet with a first-excited state of a $\Gamma_7$ doublet located at the energy scale of $\sim$ 90 K. Mean-field calculations based on the suggested CEF level scheme can reasonably well reproduce the $T$ dependence of magnetic susceptibility ($\chi$) below $\sim$ 70 K. These results in the paramagnetic state strongly indicate that the 4$f$ electrons are well localized with the Sm$^{3+}$ configuration. At low temperatures, the 4$f$ electrons undergo a magnetic order at $T_{\rm M}$ $\sim$ 8.3 K, where $\chi$($T$) shows an antiferromagnetic-like cusp anomaly. From the positive Curie--Weiss temperature obtained from the mean-field calculations and from a constructed magnetic phase diagram with multiple regions, we discussed the magnetic structure of SmBe$_{13}$ below $T_{\rm M}$, by comparing with other isostructural MBe$_{13}$ compounds showing helical-magnetic ordering.

A comparison of untagged gamma-ray and tagged-neutron yields from 241AmBe and 238PuBe sources

Untagged gamma-ray and tagged-neutron yields from 241AmBe and 238PuBe mixed-field sources have been measured. Gamma-ray spectroscopy measurements from 1 to 5MeV were performed in an open environment using a CeBr3 detector and the same experimental conditions for both sources. The shapes of the distributions are very similar and agree well with previous data. Tagged-neutron measurements from 2 to 6MeV were performed in a shielded environment using a NE-213 liquid-scintillator detector for the neutrons and a YAP(Ce) detector to tag the 4.44MeVgamma-rays associated with the de-excitation of the first-excited state of 12C. Again, the same experimental conditions were used for both sources. The shapes of these distributions are also very similar and agree well with previous data, each other, and the ISO recommendation. Our 238PuBe source provides approximately 2.6 times more 4.44MeVgamma-rays and 2.4 times more neutrons over the tagged-neutron energy range, the latter in reasonable agreement with the original full-spectrum source-calibration measurements performed at the time of their acquisition.

Electromagnetic Moments of Radioactive ^{136}Te and the Emergence of Collectivity 2p⊕2n Outside of Double-Magic ^{132}Sn.

Radioactive ^{136}Te has two valence protons and two valence neutrons outside of the ^{132}Sn double shell closure, providing a simple laboratory for exploring the emergence of collectivity and nucleon-nucleon interactions. Coulomb excitation of ^{136}Te on a titanium target was utilized to determine an extensive set of electromagnetic moments for the three lowest-lying states, including B(E2;0_{1}^{+}→2_{1}^{+}), Q(2_{1}^{+}), and g(2_{1}^{+}). The results indicate that the first-excited state, 2_{1}^{+}, composed of the simple 2p⊕2n system, is prolate deformed, and its wave function is dominated by excited valence neutron configurations, but not to the extent previously suggested. It is demonstrated that extreme sensitivity of g(2_{1}^{+}) to the proton and neutron contributions to the wave function provides unique insight into the nature of emerging collectivity, and g(2_{1}^{+}) was used to differentiate among several state-of-the-art theoretical calculations. Our results are best described by the most recent shell model calculations.