Low Angular Momentum States Research Articles

Dynamics of the angular momentum in narrow quantum rings with Rashba and Dresselhaus spin-orbit interactions

The quantum dynamics of the electron's spin and orbital angular momenta in semiconductor quantum rings is analyzed. Both Rashba and Dresselhaus spin-orbit interactions (SOIs) in their quasi-two-dimensional forms are taken into account. The narrow quantum rings are treated with models including one and two radial modes. We find that when either Rashba or Dresselhaus SOI acts alone, the different angular momentum states are coupled in blocks of two (for a single radial mode) or four (for two radial modes). We also show that the full Hilbert space splits into two disjoint subspaces, which are not coupled by either of the two SOIs, thereby decoupling accordingly the state evolution. When both SOI mechanisms are present, in principle infinitely many states are coupled, but we find by numerical computation of the quantum dynamics that for typical evolution times in practice only a few neighboring states are involved in the dynamics. Thus the exchange of angular momenta proceeds only via very few states. Furthermore, we find a trend that when initially high orbital momenta are prepared, the time evolution of spin and orbital momenta is almost unaffected by the availability of a second radial mode, in sharp contrast to the case of preparing the system in low orbital angular momentum states. The implications of our findings for the coherent control of angular momentum in quantum rings are pointed out.

Preparation of Long-Lived, Non-Autoionizing Circular Rydberg States of Strontium.

Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a 4D metastable level are impervious to autoionization over more than a few millisecond time scale. This makes it possible to trap and laser-cool Rydberg atoms. Moreover, we observe singlet to triplet transitions due to the core optical manipulations, opening the way to a microwave to optical quantum interface.

Reduced matrix elements for collisionally induced transitions of 12CH4

Reduced matrix elements (RMEs) for collisionally induced transitions are an important component of semi-classical line shape calculations. They give the quantum mechanical probability for a transition in the radiating molecule occurring due to a collision with one of the bath molecules. The RMEs for both the radiating and perturbing molecules are part of the quantum mechanical component of a semi-classical calculation. Evaluating the reduced matrix elements requires wavefunctions for the molecules in question. In this work, RMEs for ro-vibrational states of methane are evaluated using ab initio wavefunctions. These RMEs are compared with RMEs evaluated using a Hamiltonian model to the fourth order in the Td formalism. Comparisons are made for the ground and ν3 states, where the ν3 state is treated as an isolated state by an Effective Hamiltonian. The formulas for the reduced matrix elements are developed in both formalisms. The comparison shows good agreement for low angular momentum states, where the isolated state approximation should be valid. Using sum rules as a check of the RMEs revealed that all symmetry components of the wavefunctions are needed in a line shape calculation. Line shape parameters are evaluated using the ab initio RMEs for a number of ν3 transitions measured by Benner et al. [JQSRT 50, 65, 1993].

Transport on flexible Rydberg aggregates using circular states

Assemblies of interacting Rydberg atoms show promise for the quantum simulation of transport phenomena, quantum chemistry and condensed matter systems. Such schemes are typically limited by the finite lifetime of Rydberg states. Circular Rydberg states have the longest lifetimes among Rydberg states but lack the energetic isolation in the spectrum characteristic of low angular momentum states. The latter is required to obtain simple transport models with few electronic states per atom. Simple models can however even be realized with circular states, by exploiting dipole-dipole selection rules or external fields. We show here that this approach can be particularly fruitful for scenarios where quantum transport is coupled to atomic motion, in adiabatic excitation transport or quantum simulations of electron-phonon coupling in light harvesting. Additionally, we explore practical limitations of flexible Rydberg aggregates with circular states and to which extent interactions among circular Rydberg atoms can be described using classical models.

Rotational and angular distributions of NO products from NO-Rg (Rg = He, Ne, Ar) complex photodissociation

We present the results of an investigation into the rotational and angular distributions of the NO à state fragment following photodissociation of the NO-He, NO-Ne, and NO-Ar van der Waals complexes excited via the à ← X̃ transition. For each complex, the dissociation is probed for several values of Ea, the available energy above the dissociation threshold. For NO-He, the Ea values probed were 59, 172, and 273 cm(-1); for NO-Ne they were 50 and 166 cm(-1); and for NO-Ar they were 44, 94, 194, and 423 cm(-1). The NO à state rotational distributions arising from NO-He are cold, with most products in low angular momentum states. NO-Ne leads to broader NO rotational distributions but they do not extend to the maximum possible given the energy available. In the case of NO-Ar, the distributions extend to the maximum allowed at that energy and show the unusual shapes associated with the rotational rainbow effect reported in previous studies. This is the only complex for which a rotational rainbow effect is observed at the chosen Ea values. Product angular distributions have also been measured for the NO à photodissociation product for the three complexes. NO-He produces nearly isotropic fragments, but the anisotropy parameter, β, for NO-Ne and NO-Ar photofragments shows a surprising change in sign from negative to positive as Ea increases within the unstructured excitation profile. Franck-Condon selection of a broader distribution of geometries including more linear geometries at lower excitation energies and more T-shaped geometries at higher energies can account for the changing recoil anisotropy. Two-dimensional wavepacket calculations are reported to model the rotational state distributions and the bound-continuum absorption spectra.

Analysis of a controlled phase gate using circular Rydberg states

We propose and analyze the implementation of a two qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9 \times10^{-6}$ for circular Cs atoms in a cryogenic environment.

Experimental investigation of long-lived Rydberg states in ultracold argon

We report on our investigation of the formation and survival of long-lived Rydberg states in argon produced by pulsed laser excitation of ultracold metastable state argon atoms in a magneto-optical trap. The states studied have a ${}^{2}{P}_{1/2}$ core. Low angular momentum Rydberg states with this core normally autoionize rapidly. If, however, atoms are excited in the presence of electric fields, higher angular momentum states, traditionally termed ``ZEKE states'' (ZEKE is derived from ``zero kinetic energy'') can be formed. The lifetime of these states can be orders of magnitude greater than low angular momentum states. In this paper, we report on the time dependence of ZEKE Rydberg state population in an ultracold environment.

Fundamental constants and tests of theory in Rydberg states of one-electron ions

The nature of the theory of circular Rydberg states of hydrogen-like ions allows highly accurate predictions to be made for energy levels. In particular, uncertainties arising from the problematic nuclear size correction which beset low angular-momentum states are negligibly small for the high angular-momentum states. The largest remaining source of uncertainty can be addressed with the help of quantum electrodynamics calculations, including a new nonperturbative result reported here. More stringent tests of theory and an improved determination of the Rydberg constant may be possible if predictions can be compared with precision frequency measurements in this regime. The diversity of information can be increased by utilizing a variety of combinations of ions and Ryberg states to determine fundamental constants and test theory.

Trapped Rydberg ions: from spin chains to fast quantum gates

We study the dynamics of Rydberg ions trapped in a linear Paul trap, and discuss the properties of ionic Rydberg states in the presence of the static and time-dependent electric fields constituting the trap. The interactions in a system of many ions are investigated and coupled equations of the internal electronic states and the external oscillator modes of a linear ion chain are derived. We show that strong dipole–dipole interactions among the ions can be achieved by microwave dressing fields. Using low-angular momentum states with large quantum defect, the internal dynamics can be mapped onto an effective spin model of a pair of dressed Rydberg states that describes the dynamics of Rydberg excitations in the ion crystal. We demonstrate that excitation transfer through the ion chain can be achieved on a nanosecond timescale and discuss the implementation of a fast two-qubit gate in the ion chain.

Angularly localized Skyrmions

Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.

Highly excited symmetry-breaking infrared and THz transitions in methanol-D1

In this paper, symmetry-breaking transitions have been identified in the Fourier transform infrared (FTIR) and Terra Hertz (THz) fast scan spectra of asymmetrically deuterated methanol CH2DOH involving three quanta of the lowest lying vibrational state (ν1). These transitions have an upper state belonging to highly excited torsional state with the torsional quantum number v=11 (e5) (with the axial component of total rotational angular momentum K=5 and 6) in the Internal Axis Method (IAM) formalism developed by Quade and his co-workers [J. Mol. Spectrosc. 146 (1991) 238; J. Mol. Spectrosc. 146 (1991) 252], which was later extended by Mukhopadhyay [Spectrochim. Acta A 53 (1997) 2457; Spectrochim. Acta A 53 (1997) 1947] to include highly excited torsional–rotational states. The originating lower states belong to the o1 (v=3) with K=4 and 5. In analogy with pure methanol these transitions terminate to the third excited torsional state, which has very small torsional matrix elements to be observable in normal FTIR spectra. The location of the e5 states suggests that the calculated energy levels using the parameters of Liu and Quade [J. Mol. Spectrosc. 146 (1991) 252] are reasonable and very helpful to assign such highly excited transitions, considering that their studies include low angular momentum states. In addition the very existence of these transitions proves that the matrix elements calculated by Mukhopadhyay [Spectrochim. Acta A 53 (1997) 1947] are very useful and dependable. Thus they represent a valuable tool for entangling the complex spectrum of this asymmetrically deuterated methanol. In order to provide confirmatory evidence the THz spectra obtained using the Fast Scanning Submillimeter Spectroscopy Technique (FASSST) at the Ohio State University [Rev. Instr. 68 (1997) 1675; Anal. Chem. 70 (1998) 719A] were searched for the ground state transitions that can be calculated precisely from IR combination relations. All the transitions that can be predicted with K=4 and 5 in the o1 states are indeed identified in the FASSST spectrum. To our knowledge this is the first reported work involving direct transitions to such highly excited torsional state of CH2DOH. This work will enable the determination of higher order barrier terms and provide enough understanding of the energy levels for the identification of many unidentified transitions. To our knowledge, this is the first time such high frequency symmetry-breaking transitions have been observed in asymmetrically deuterated methanol.

Highly excited symmetry-breaking infrared and THz transitions in methanol-D 1

In this paper, symmetry-breaking transitions have been identified in the Fourier transform infrared (FTIR) and Terra Hertz (THz) fast scan spectra of asymmetrically deuterated methanol CH 2DOH involving three quanta of the lowest lying vibrational state ( ν 1). These transitions have an upper state belonging to highly excited torsional state with the torsional quantum number v=11 (e 5) (with the axial component of total rotational angular momentum K=5 and 6) in the Internal Axis Method (IAM) formalism developed by Quade and his co-workers [J. Mol. Spectrosc. 146 (1991) 238; J. Mol. Spectrosc. 146 (1991) 252], which was later extended by Mukhopadhyay [Spectrochim. Acta A 53 (1997) 2457; Spectrochim. Acta A 53 (1997) 1947] to include highly excited torsional–rotational states. The originating lower states belong to the o 1 ( v=3) with K=4 and 5. In analogy with pure methanol these transitions terminate to the third excited torsional state, which has very small torsional matrix elements to be observable in normal FTIR spectra. The location of the e 5 states suggests that the calculated energy levels using the parameters of Liu and Quade [J. Mol. Spectrosc. 146 (1991) 252] are reasonable and very helpful to assign such highly excited transitions, considering that their studies include low angular momentum states. In addition the very existence of these transitions proves that the matrix elements calculated by Mukhopadhyay [Spectrochim. Acta A 53 (1997) 1947] are very useful and dependable. Thus they represent a valuable tool for entangling the complex spectrum of this asymmetrically deuterated methanol. In order to provide confirmatory evidence the THz spectra obtained using the Fast Scanning Submillimeter Spectroscopy Technique (FASSST) at the Ohio State University [Rev. Instr. 68 (1997) 1675; Anal. Chem. 70 (1998) 719A] were searched for the ground state transitions that can be calculated precisely from IR combination relations. All the transitions that can be predicted with K=4 and 5 in the o 1 states are indeed identified in the FASSST spectrum. To our knowledge this is the first reported work involving direct transitions to such highly excited torsional state of CH 2DOH. This work will enable the determination of higher order barrier terms and provide enough understanding of the energy levels for the identification of many unidentified transitions. To our knowledge, this is the first time such high frequency symmetry-breaking transitions have been observed in asymmetrically deuterated methanol.

Neutrino–deuteron scattering in effective field theory

The evolution of the giant dipole resonance (GDR) in hot 120Sn and 208Pb nuclei was studied by measuring high energy γ-rays from the decay of the resonance. The excited nuclei were populated by inelastic scattering of α-particles at 40 and 50 MeV/nucleon. The resonance width was observed to increase systematically with excitation energy in both systems. Inelastic scattering populates low angular momentum states in the target. The observed width increase is thus attributed to fluctuations in the nuclear shape induced by temperature.

High resolution spectrum of NO2 loosely bound states: densities of states and long range forces

More than 1700 rovibronic states of low angular momentum (J = 1/2–7/2) have been observed by laser induced fluorescence (LIF) at high precision and resolution, ≃0.004 cm−1, in a range covering 133 cm−1 below the NO2 lowest photodissociation threshold D0. This allowed us to significantly improve and complete previous experimental results devoted to the states lying in the vicinity of D0 (A. Delon, S. Heilliette and R. Jost, Chem. Phys., 1998, 238, 465). The density of loosely bound vibronic levels exceeds the expected density over the entire observed energy range and exhibits an abrupt increase in the last 30 cm−1 below D0. The number of observed vibronic levels between D0 − 133 cm−1 and D0 is about twice the expected number of levels. The rovibronic eigenstates cannot be assigned any other quantum numbers than J and the overall symmetry. This indicates strong intramolecular couplings, and this is consistent with the fact that the densities of observed rovibronic states J = 1/2, 3/2, 5/2 and 7/2 have reached their maximum value, as compared with the density of vibronic levels. Moreover, R0/P2 intensity ratios, involving the same upper levels, scatter around their average value by four orders of magnitude. The above mentioned anomalous properties of the loosely bound states of NO2 (density and intensity ratios) are assumed to be the consequences of the long range electrostatic forces between the fragments NO and O. To quantify this hypothesis, we propose a simple analytic relation between the isotropic contribution of the long range part of the potential energy surface and the density of observed loosely bound states.

Quasiclassical Born–Oppenheimer Approximations

We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born–Oppenheimer approximation. These cases include the so-called bouncing ball modes, low angular momentum states in perturbed circular billiards, resonant states in perturbed rectangular billiards, and whispering gallery modes. Some rare, special eigenstates, concentrated close to the edge or along a diagonal of a nearly rectangular billiard are found. This kind of state has apparently previously escaped notice.

Quantum propagation of neutral atoms in a magnetic quadrupole guide

We consider the quantized motion of neutral atoms at very low temperature in a two-dimensional magnetic quadrupole structure formed, for example, by four current-carrying wires along the z direction. The magnetic field $\mathbf{B}$ in the guide is proportional to the vector $(x,\ensuremath{-}y).$ We show that this field can be used to make a single-mode atomic de Broglie waveguide which has bound states of low angular momentum, even though the field at the center of the guide goes to zero. We investigate the spectrum and decay rate of the transverse modes for spin-1/2 and spin-1 atoms.

Coorbital Dynamics at Large Eccentricity and Inclination

We show that coorbital dynamics at large eccentricity and inclination exhibit hitherto unknown types of stable motion in the gravitational three-body problem. In the solar system, the secular stability is observed in the evolution of specific near-Earth asteroids. In particular, the slow diffusion of such objects through the Earth's coorbital region which leads to temporary capture suggests the existence of undiscovered retrograde moons of the Earth. In the Coulomb problem, the Kozai resonance is a primary candidate for stable low angular momentum states in two-electron atoms.

SOLUTIONS OF A DIRAC HYDROGENLIKE MESON AND SCALAR CONFINEMENT AT LOW ORBITAL ANGULAR MOMENTUM STATES

Wave functions of a heavy-light quark [Formula: see text] system described by a covariant Dirac Hamiltonian are analyzed. By assuming that the confinement potential is a Lorentz scalar (S), the slope of the Isgur–Wise function is calculated at zero recoil point. The result obtained is ξ′(1)= -0.93± 0.05. This means that the solutions are perfectly consistent. If relativistic corrections in the light quark wave functions are included the result is ξ′(1)=-1.01± 0.04. From heavy-light data this suggests that if relativistic effects are considered, scalar confinement is reliable in low orbital angular momentum states.

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in 120Sn and 208Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for 120Sn and 40 MeV/nucleon for 208Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in 208Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.

Giant dipole resonance built on highly excited states of 120Sn nuclei populated by inelastic alpha scattering.

High energy {gamma} rays from the decay of the giant resonance in hot {sup 120}Sn nuclei were measured in the excitation energy range of 30{endash}130 MeV. The excited nuclei were populated by inelastic scattering of {alpha} particles at 40 and 50 MeV/nucleon. The resonance width was observed to increase monotonically with increasing excitation energy, from 5 MeV at the ground state to {approximately}12 MeV at the largest excitation energy. Inelastic scattering predominantly populates low angular momentum states, and the observed width increase is thus attributed to fluctuations in the nuclear shape induced by temperature. {copyright} {ital 1996 The American Physical Society.}