States Of Rb Research Articles

Dissociative Recombination of K2+ and Rb2+ in Diode-Pumped Alkali Lasers: Potential Energy Curves and Atomic Products.

Dissociative recombination (DR) of K2+ and Rb2+ ions is one of the most important processes in K and Rb diode-pumped alkali lasers (DPALs) strongly affecting their power. We report on the calculations of potential energy curves of the K2+ and Rb2+ molecular ions and of the diabatic 1Σ+, 3Σ+, 1Δ, 3Δ, 1Π, 3Π, 1Φ, and 3Φ valence states of K2 and Rb2 that provide the routes for DR of the ions. These curves are required for subsequent calculations of DR rate constants. It was found that the most likely DR routes for K are along the dissociative states 61Σg+, 53Σu+, and 23Δu and for Rb only 61Σg+. The excited states of K atoms produced by DR are 42P and 52P. Most of the Rb atoms produced by DR are in the 62P excited state, while a small fraction of the atoms produced by the less likely routes along two states of Rb2 are in the 52P state. This conclusion contradicts the kinetic scheme for K and Rb DPAL proposed elsewhere, and thus the kinetic schemes of these DPALs should be modified according to the present results.

A direct potential fitting RKR method: Semiclassical vs. quantal comparisons

Quantal and semiclassical (SC) eigenvalues are compared for three diatomic molecular potential curves: the X state of CO, the X state of Rb2, and the A state of I2. The comparisons show higher levels of agreement than generally recognized, when the SC calculations incorporate a quantum defect correction to the vibrational quantum number, in keeping with the Kaiser modification. One particular aspect of this is better agreement between quantal and SC estimates of the zero-point vibrational energy, supporting the need for the Y00 correction in this context. The pursuit of a direct-potential-fitting (DPF) RKR method is motivated by the notion that some of the limitations of RKR potentials may be innate, from their generation by an exact inversion of approximate quantities: the vibrational energy Gυ and rotational constant Bυ from least-squares analysis of spectroscopic data. In contrast, the DPF RKR method resembles the quantal DPF methods now increasingly used to analyze diatomic spectral data, but with the eigenvalues obtained from SC phase integrals. Application of this method to the analysis of 9500 assigned lines in the I2A←X spectrum fails to alter the quantal-SC disparities found for the A-state RKR curve from a previous analysis. On the other hand, the SC method can be much faster than the quantal method in exploratory work with different potential functions, where it is convenient to use finite-difference methods to evaluate the partial derivatives required in nonlinear fitting.

Observations and analysis with the spline-based Rydberg–Klein–Rees approach for the 31Σg+ state of Rb2

Ro-vibrational term values of the 3(1)Σg (+) state of (85,85)Rb2 and (85,87)Rb2 and resolved fluorescence spectra to the A(1)Σu (+) state are recorded following optical-optical double resonance excitation. The experimental data are heavily perturbed, and as a result, the standard analysis based on Dunham series representation of the energy levels fails. The analysis is done via modeling the adiabatic potential function with the Rydberg-Klein-Rees potential constructed from the generalized smoothing spline interpolation of the vibrational energies Gv and rotational constants Bv.

Archimedean-Spiral-Based Microchip Ring Waveguide for Cold Atoms

We present a scheme for generating a ring magnetic waveguide on a single-layer atom chip. The wire layout consists of two interleaved Archimedean spirals of the same size. The waveguide avoids the trapping perturbation caused by the input and output ports, resulting in an enclosed guiding loop for neutral atoms in weak-field seeking states. Such a configuration can create a tight and deep trap potential with a small current. Taking the |F = 2, mF = 2〉 state of 87Rb as an example, the trap frequency and depth are estimated to be 18 kHz and 335 μK, respectively, with a dc current of 2 A.

Complete wavelength mismatching effect in a Doppler broadened Y-type six-level EIT atomic medium

We present a theoretical study of the Doppler broadened Y-type six-level atomic system, using a density matrix approach, to investigate the effect of varying control field wavelengths and closely spaced hyperfine levels in the 5P3/2 state of 87Rb. The closely spaced hyperfine levels in our six-level system affect the optical properties of Y-type system and cause asymmetry in absorption profiles. Depending upon the choices of π-probe, σ+-control and σ−-control fields transitions, we consider three regimes: (i) perfect wavelength matching regime (λp=λc1=λc2), (ii) partial wavelength mismatching regime (λp≠λc1=λc2), and (iii) complete wavelength mismatching regime (λp≠λc1≠λc2). The complete wavelength mismatching regime is further distinguished into two situations, i.e., λc1<λc2 and λc1>λc2. We have shown that in the room temperature atomic vapor, the asymmetric transparency window gets broadened in the partial wavelength mismatching regime as compared to the perfect wavelength matching regime. This broad transparency window also splits at the line center in the complete wavelength mismatching regime.

Observation and assignment of the [formula omitted] state of [formula omitted

The 21∏g state of Rb2 has been observed using the infrared infrared double resonance method. The low part of the potential curve of the state is characterized for the first time. The absolute vibrational numbers are determined with isotope effect. The molecular constants of this state are obtained from a Dunham fit and the potential curve of the state is constructed using the Rydberg–Klein–Rees method.

Measurement of the Absolute Photoionization Cross Section for the 5P3/2 State of 87Rb in a Vapor Cell Magneto-optic Trap

We report the measurement of the absolute photoionization cross section for the 5P3/2 state of 87Rb at wavelength of 473 nm, which results in the photoelectron energies of 33 meV above the ionization threshold, using cold atoms confined in a vapor-loaded magneto-optical trap. The 87Rb 5P3/2 photoionization cross section at 473 nm is determined to be σPI = 10.5 ± 2.2 Mb. Considering the spatial distribution of the trapped atoms, the average intensity of the ionization laser seen by an atom in the MOT instead of ionizing laser intensity IPI is used in our calculations for the photoionization cross sections. The excited state fraction is also accurately estimated using the latest experimental result.

A high phase-space density mixture of 87Rb and 133Cs: towards ultracold heteronuclear molecules

We report the production of a high phase-space density mixture of 87Rb and 133Cs atoms in a levitated crossed optical dipole trap as the first step towards the creation of ultracold RbCs molecules via magneto-association. We present a simple and robust experimental setup designed for the sympathetic cooling of 133Cs via interspecies elastic collisions with 87Rb. Working with the |F = 1,mF = +1〉 and the |3, +3〉 states of 87Rb and 133Cs respectively, we measure a high interspecies three-body inelastic collision rate ∼10−25−10−26 cm6 s−1 which hinders the sympathetic cooling. Nevertheless by careful tailoring of the evaporation we can produce phase-space densities near quantum degeneracy for both species simultaneously. In addition we report the observation of an interspecies Feshbach resonance at 181.7(5) G and demonstrate the creation of Cs2 molecules via magneto-association on the 4(g)4 resonance at 19.8 G. These results represent important steps towards the creation of ultracold RbCs molecules in our apparatus.

Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance

We investigate controlled phase separation of a binary Bose-Einstein condensate (BEC) in the proximity of mixed-spin-channel Feshbach resonance in the |F = 1, mF = +1> and |F = 2,mF = -1> states of 87Rb at a magnetic field of 9.10 G. Phase separation occurs on the lower magnetic-field side of the Feshbach resonance while the two components overlap on the higher magnetic-field side. The Feshbach resonance curve of the scattering length is obtained from the shape of the atomic cloud by comparison with the numerical analysis of coupled Gross-Pitaevskii equations.

Molecular dissociation and nascent product state distributions detected with atomic wavepacket interferometry and parametric four-wave mixing: Rb2 predissociation observed by quantum beating in Rb at 18.2 THz

Dissociation of a diatomic molecule and the excited-state distribution of the nascent atomic fragments can be detected and characterized by atomic wavepacket interferometry and a coherent nonlinear optical process, such as parametric four-wave mixing (PFWM), in ultrafast pump–probe experiments. Underlying these experiments is a reliance on atom–atom interaction to alter the properties of an atomic wavepacket which, in turn, impacts the phase and amplitude of a coherent optical signal. Specifically, quantum beating in the atomic species provides a sensitive, in situ probe of molecular dissociation by detecting approaching dissociation fragments through long-range dipole–dipole interaction. The resulting influence of this interaction on the amplitude and phase of the quantum beating is observed in temporal or Fourier domains by probing the wavepacket by interferometry and PFWM with 100–150 fs laser pulses. The wavepacket thus serves as a detector of molecular dissociation fragments and the dynamics of atom–atom interactions are converted into the macroscopic domain by the PFWM signal and idler waves. Femtosecond pump–probe experiments are described in which the predissociation of electronically excited Rb2 states in the ∼24 000–28 000 cm−1 interval, and the distribution of nascent atomic fragments into Rb excited states (7s, 5d, 6s, 4d and 5p) spanning an energy range >1.25 eV, have been observed in Rb vapour with atomic number densities of ∼6 × 1013–3 × 1017 cm−3. Quantum beating at 18.2 THz (corresponding to the Rb 7s–5dJ (J = 5/2) energy defect of ∼608 cm−1) is superimposed onto the axially phase matched PFWM signal wave generated at λS ∼ 420 nm (Rb 62PJ → 52S1/2 transitions) and recovered by Fourier analysis of the signal wave intensity as the pump–probe time delay (Δt) is scanned. The dominant exit channels for Rb2 predissociation are found to be sensitive to the interval of internuclear separation R in which the molecular wavepacket, produced by the pump pulse through two-photon association of Rb–Rb collision pairs, is localized. Generating Rb2 wavepackets on 3Λu (Λ = Σ, Δ) potential surfaces at large R (∼7–9 Å) favours the Rb 7s and 5d dissociation channels. In contrast, producing dimer wavepackets localized in the R ∼ 3–4 Å region suppresses Rb (7s, 5d) generation and favours the production of Rb atomic fragments (primarily 5p) with less internal energy, but maximum velocities of ∼15–20 Å ps−1. Laser excitation spectroscopy on the nanosecond time scale suggests that the (3)3Δu and (7)3Σ+u states of Rb2 (correlated with Rd (5d) + Rb (6s) in the separated atom limit), and possibly a 3Σ+u state derived from the Rb (7p) + Rb (5s) asymptote, are populated by two-photon absorption of Rb–Rb ground-state collision pairs and predissociation of these levels provides the excited atomic fragments subsequently detected by atomic wavepackets. The data presented here demonstrate the observation of the molecular dissociation transient and the determination of the nascent statistical distribution of atomic product states in a manner that is unencumbered by radiative lifetime or collisional effects. A wavepacket, in tandem with the dipole–dipole interaction and a coherent nonlinear optical process, provides a new avenue for pursuing atom–atom and atom–molecular interactions over a broad range in inter-particle separations.

Frequency shift of the magnetic resonance in 5s 2 S 1/2 rubidium atoms due to spin-exchange collisions with optically oriented cesium atoms

For the case of cesium atoms optically oriented in a mixture of cesium and rubidium vapors, the temperature dependence of the frequency shift of a magnetic resonance excited in a set of Zeeman sublevels for two hyperfine states of 87Rb 5s2S1/2 atoms. It is shown that, in a weak magnetic field of about 2 × 10−6 T, this shift is determined by the spin-exchange interaction of rubidium atoms with optically oriented 133Cs atoms.

Studies on full vibrational spectra and dissociation energies of some diatomic molecular electronic states using algebraic approaches

An algebraic energy method (AEM) is suggested as an alternative theoretical approach to generate molecular dissociation energy D e 's. The AEM is used to evaluate accurate full vibrational energy spectra {E υ} and D e in this study for 14 diatomic electronic states of Li2, Na2, Rb2, K2 and Sr2 molecules: the 11Π g , , 23Πg, 13Δg and 23Δg states of Li2; the , , 13Δg and 23Δgstates of Na2; the and states of K2; the and 11Πg states of Rb2 and the state of Sr2 molecule. Studies show that present vibrational energies in the full spectrum {E υ} are accurate, and the AEM D e have an accuracy better than one percent when they are compared with experimental dissociation energies. The AEM can generate reliable D e 's for electronic states whose molecular dissociation energies may be difficult to obtain experimentally and/or theoretically.

Spontaneous Macroscopic Spin Polarization in Independent Spinor Bose-Einstein Condensates

We present experimental evidence for the spontaneous formation of a macroscopic spin polarization in overlapping regions of two independent Bose-Einstein condensates produced in different hyperfine states of 87Rb. The condensates are independent in the sense that we do not explicitly introduce a relative phase between them. A single "spin-tip" pulse maps the transverse spin polarization into longitudinal spin polarization, and the atomic density distributions are measured with a Stern-Gerlach imaging method. The resulting matter-wave interference patterns are anticorrelated.

Magnetism in ultracold quantum gases

We study the static and dynamic magnetic properties of ultracold quantum gases, in particular the spinor physics of F = 1 and F = 2 Bose-Einstein condensates of 87Rb atoms. Our data lead to the conclusion, that the F = 2 ground state of 87Rb is polar, while we find the F = 1 ground state to be ferromagnetic. The dynamics of spinor systems is linked to an interplay between coherent mean-field interactions, losses and interactions with atoms in the thermal cloud. Within this rich parameter space we observe indications for coherent spinor dynamics and novel thermalization regimes.

Direct potential fit analysis of the X 1Σg+ state of Rb2: Nothing else will do!

High resolution A-X emission data involving vibrational levels of the ground X 1Σg+ electronic state up to v″=113, spanning 99.8% of the potential well, have been acquired for three isotopomers of Rb2. While a good fit (σ̄f=1.03) to the 12 148 transition frequencies (with uncertainties ±0.001 cm−1) is obtained from an unconstrained combined-isotopomer Dunham-type analysis, it requires a large number (62) of expansion parameters, and the resulting empirical centrifugal distortion constants (CDCs) are unreliable for extrapolation to higher-J. Moreover, Dunham expansion fits using constrained theoretical values of the first six CDCs (up to Ov) fail to properly represent the data, as even higher-order CDCs are required. However, a direct fit of these data to an analytical “modified Lennard-Jones” potential energy function involving only 16 fitted parameters yields essentially the same quality of fit as did the unconstrained Dunham fit, and should be reliable for extrapolation to arbitrarily high J. This potential form incorporates the proper R−6 asymptotic behavior of the potential, and is constrained to have the theoretically predicted C6 dispersion coefficient. Although the dataset involves the three isotopomers 85,85Rb2, 85,87Rb2, and 87,87Rb2, none of the present analyses was able to determine any Born–Oppenheimer breakdown effects.

Hyperfine interaction constants of the 10, 11 and 12 [formula omitted] states in 87Rb measured by the quantum beat method

The magnetic-dipole interaction constant A and electric-quadrupole interaction constant B were measured in a sequence of 2 D 3 2 states of 87Rb. The values obtained are ∥A(10 2 D 3 2 )∥=1.315(17) MHz , ∥A(11 2 D 3 2 )∥=0.955(11) MHz , ∥A(12 2 D 3 2 )∥=0.715(12) MHz , ∥B(10 2 D 3 2 )∥=0.070(11) MHz , B(11 2 D 3 2 )=0.049(6) MHz , and ∥B(12 2 D 3 2 )∥=0.037(8) MHz with B A >0 for all the states.

Magnetic-dipole and electric-quadrupole interaction constants in the 102D5/2state of87Rb

Hyperfine interaction constants A and B in the 102D5/2 state of 87Rb were obtained by the analysis of quantum beats in the fluorescence 102D5/2-52P3/2 following two-quantum excitation. The resulting values are mod A mod =0.510 (10) MHz, mod B mod =0.098 (11) MHz and A/B<0.

Ground and excited states of Rb2+and Cs2+by means of quasi-relativistic pseudo-potentials including core polarisation

Pseudo-potentials for Rb and Cs have been generated that represent the effects of core-valence correlation by a polarisation potential and that reproduce spin-orbit splittings in the atoms to within 10-7 au(<or approximately=1%). These potentials were used to calculate the potential curves of the X 2 Sigma g1/2, 1 2 Sigma u1/2, and 1 2 Pi u3/2 states of Rb2+ and Cs2+. In the latter case, experimental data exist for the spin-orbit splitting of the Pi u states. The calculated and the measured values agree excellently.

The low-lying level structure of87Rb

The low-lying states of87Rb are studied in the framework of a quasiparticle-core coupling model. The agreement between the calculated and experimental level spectra, stripping strength, ground state static electromagnetic moments and theE2 transition rate of the first excited state is good. Electromagnetic moments and transition rates for other excited states are predicted.

Radiofrequency multiple-quantum transitions in the presence of an optical pumping cycle

The theoretical behaviour of radiofrequency transitions with Delta m>or=1 in an atomic vapour under the simultaneous action of a longitudinal optical pumping, a static field introducing small decoupling between I and J and a relaxation mechanism is investigated. It is shown that the information contained in the eigenvalues and eigenvectors of the Hamiltonian of the atom 'dressed' by the RF field can be used to simplify significantly the equations of the time evolution of the atomic density matrix. Although an analytical solution is obtained only in a few simple cases a numerical solution is possible for any RF polarization. Several previous treatments are shown to be limiting cases of the general equations presented here. From the analysis of the recent experimental results of Arimondo and Corbalan (1974) on the ground state of 87Rb, it turns out that the observable quantities are strongly dependent on all the parameters describing the simultaneous action of the pumping cycle, relaxation and the RF interaction. Thus accurate descriptions of the pumping cycle and the relaxation mechanism are required for any comparison with theory of experimental results for the widths and shifts of multiple-quantum transitions.