Adiabatic Elimination in a Lambda System

This paper deals with different ways to extract the effective two-dimensional lower level dynamics of a lambda system excited by off-resonant laser beams. We present a commonly used procedure for elimination of the upper level, and we show that it may lead to ambiguous results. To overcome this problem and better understand the applicability conditions of this scheme, we review two rigorous methods which allow us both to derive an unambiguous effective two-level Hamiltonian of the system and to quantify the accuracy of the approximation achieved: the first one relies on the exact solution of the Schrodinger equation, while the second one resorts to the Green's function formalism and the Feshbach projection operator technique.Comment: 14 pages, 3 figure

Hyperfine, rotational and Zeeman structure of the lowest vibrational levels of the 87^{87}Rb2_2 \tripletex state

We present the results of an experimental and theoretical study of the electronically excited \tripletex state of $^{87}$Rb$_2$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to $v'=15$ using laser spectroscopy of ultracold Rb$_2$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47\,GHz splitting into a \cog and \clg component caused mainly by a strong second order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe to first order this structure using a simplified effective Hamiltonian.Comment: 10 pages, 7 figures, 2 table

Validity of adiabaticity in Cavity QED

This paper deals with the concept of adiabaticity for fully quantum mechanically cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time dependent two-level systems.Comment: 10 pages, 9 figure

Electronic structure and spectroscopy of O2 and O2+

We carried out a comprehensive SCF MRD--CI ab initio study of the electronic structure of O$_2$ and O$_2^+$. Potential energy curves (PECs) of about 150 electronic states of O$_2$ and about 100 of O$_2^+$, as well as a number of states of O$_2^{++}$ were computed. The cc--pVQZ basis set augmented with diffuse functions was employed. Spectroscopic parameters ($T_e, T_v, \omega_e, \omega_ex_e, B_e,$ $D_e, D_0$, $\mu$, IP, etc.) are reported. A preliminary sample of the results will be presented. The electronic absorption spectrum of O$_2$ has proved difficult to analyze/interpret due to the unusually large number of electronic states which arise from the peculiar open--shell structure of both the oxygen atomic fragments and the O$_2$ molecule. For instance, there are 62 valence molecular electronic states which correlate to the six lowest dissociation limits resulting from the three valence O atom fragment states ($^3$P, $^1$D, $^1$S). In addition, there are several $nl\lambda$ Rydberg series converging to the X$^2\Pi_g$ ground ionic state and to the lowest two excited states of the cation, a$^4\Pi_u$$_i$ and A$^2\Pi_u$. Furthermore, a number of interactions of various types among several electronic states result in rovibronic perturbations which manifest themselves, e.g., as irregular vibronic structure, hence severely complicating the assignment of the absorption features and the analysis and interpretation of the spectrum. An overview of the electronic states and spectroscopy of O$_2$ will be presented. A chief motivation of this study of O$_2$ was to try to provide a theoretical insight on the nature, energetic position, shape, and dissociation asymptotes, of electronic states located in the 4 eV energy region encompassed between the O$_2^+$ ground state X$^2\Pi_g$ (IP$=12.07$ eV) and the first excited state of the cation a$^4\Pi_u$$_i$ (IP$=16.10$ eV). This in order to aid in the interpretation of experimental data related to the mechanism(s) of the neutral dissociation of the O$_2^{**}$ (Rydberg) superexcited states, which competes with autoionization. We are currently striving to compute PECs of relatively highly excited states of O$_2$ located in the 12--16 eV energy region which might help to visualize possible pathways for the neutral XUV photodissociation of the I, I$^{\prime}$ and I$^{\prime\prime}$ $^3\Pi_u$ superexcited states of O$_2$ leading to the O($^3$P) + O$^{*}$($^3$S, $^5$S) dissociation limits.Ope

Zero kinetic energy-pulsed field ionization and resonance enhanced multiphoton ionization photoelectron spectroscopy: Ionization dynamics of Rydberg states in HBr

The results of rotationally resolved resonance enhanced multiphoton ionization photoelectron spectroscopy and zero kinetic energy‐pulsed field ionization studies on HBr via various rotational levels of the F^ 1Δ_2 and f^ 3Δ_2 Rydberg states are reported. These studies lead to an accurate determination of the lowest ionization threshold as 94 098.9±1 cm^(−1). Observed rotational and spin–orbit branching ratios are compared to the results of ab initio calculations. The differences between theory and experiment highlight the dominant role of rotational and spin–orbit interactions for the dynamic properties of the high‐n Rydberg states involved in the pulsed field ionization process

Observation of Feshbach resonances in an ultracold gas of 52{}^{52}Cr

We have observed Feshbach resonances in elastic collisions between ultracold ${}^{52}$Cr atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of ${}^{52}$Cr and thus the absence of a Fermi-contact interaction leads to regularly-spaced resonance sequences. By comparing resonance positions with multi-channel scattering calculations we determine the s-wave scattering length of the lowest $^{2S+1}\Sigma_{g}^{+}$ potentials to be \unit[112(14)]{a_0}, \unit[58(6)]{a_0} and -\unit[7(20)]{a_0} for S=6, 4, and 2, respectively, where a_{0}=\unit[0.0529]{nm}.Comment: 4 pages, 2 figures, 1 tabl

Experimental studies of the NaCs 12(0+) [7¹Σ+] state

We present results from experimental studies of the 11(0+) and 12(0+) electronic states of the NaCs molecule. An optical-optical double resonance method is used to obtain Doppler-free excitation spectra. Selected data from the 11(0+) and 12(0+) high-lying electronic states are used to obtain Rydberg-Klein-Rees and Inverse Perturbation Approach potential energy curves. Interactions between these two electronic states are evident in the patterns observed in the bound-bound and bound-free fluorescence spectra. A model, based on two separate interaction mechanisms, is presented to describe how the wavefunctions of the two states mix. The electronic parts of the wavefunctions interact via spin-orbit coupling, while the individual rotation-vibration levels interact via a second mechanism, which is likely to be non-adiabatic coupling. A modified version of the BCONT program was used to simulate resolved fluorescence from both upper states. Parameters of the model that describe the two interaction mechanisms were varied until simulations were able to adequately reproduce experimental spectra.National Science Foundation (U.S.) (grant no. PHY-0968898)National Science Foundation (U.S.) (grant no. PHY-1403060)National Science Foundation (U.S.) (grant no. CHE–1361865

Spin-dipole induced lifetime of the least-bound quintet sigma state of He(2S)+He(2S)

The properties of the least-bound vibrational level (v=14) of the quintet sigma state formed during the ultracold collision of two spin-polarized metastable helium atoms are crucial to studies of photoassociation spectroscopy of metastable helium. We report a calculation of the autoionization lifetime of this state induced by spin-dipole coupling of the quintet sigma state to the singlet sigma state from which Penning and associative ionization processes are highly probable. We find a lifetime of about 150 microseconds, significantly larger than the recent experimental estimates of (4-5) microseconds.Comment: REVTEX4, four double-column page

Phonons in the multiferroic langasite Ba_3\_3NbFe_3\_3Si_2\_2O_14\_{14} : evidences for symmetry breaking

The chiral langasite Ba$\_3$NbFe$\_3$Si$\_2$O$\_{14}$ is a multiferroic compound. While its magnetic order below T$\_N$=27 K is now well characterised, its polar order is still controversial. We thus looked at the phonon spectrum and its temperature dependence to unravel possible crystal symmetry breaking. We combined optical measurements (both infrared and Raman spectroscopy) with ab initio calculations and show that signatures of a polar state are clearly present in the phonon spectrum even at room temperature. An additional symmetry lowering occurs below 120~K as seen from emergence of softer phonon modes in the THz range. These results confirm the multiferroic nature of this langasite and open new routes to understand the origin of the polar state

Formation of collective spins in frustrated clusters

Using magnetization, specific heat and neutron scattering measurements, as well as exact calculations on realistic models, the magnetic properties of the \lacuvo compound are characterized on a wide temperature range. At high temperature, this oxide is well described by strongly correlated atomic $S$=1/2 spins while decreasing the temperature it switches to a set of weakly interacting and randomly distributed entangled pseudo spins $\tilde S=1/2$ and $\tilde S=0$. These pseudo-spins are built over frustrated clusters, similar to the kagom\'e building block, at the vertices of a triangular superlattice, the geometrical frustration intervening then at different scales.Comment: 10 page