John Huennekens

Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium line

The intensity dependent absorption was measured on the D1 line (6S1=2 ! 6P1=2 transition) in atomic cesium. The magnetic field applied to the vapour and the spatial cross section of the laser beam were controlled and varied during data collection. A three-level rate equation model is presented in an attempt to explain the results. We show that this well known approach does not sucessfully model the data obtained in the absence of a magnetic field. Hence, a more complex and complete model that explicitly includes all of the hyperfine magnetic sublevels (a multilevel model) is presented. This approach accurately models all of the data collected. The good agreement betweeen this model and the data allows the determination of the transit relaxation rate (due to atomic time of flight through the laser beam), 0t D.1:13 0:20/vrms=D, where vrms is the two-dimensional root-mean-squared speed of the atom and D is the FWHM of the Gaussian laser beam spatial profile.

Bound–free 1 3Π→1 3Σ+ emission from the NaK molecule: Determination of the 1 3Σ+ repulsive wall above the dissociation limit

We report the observation of bound–free emission on the 1 3Π→1 3Σ+ band of the NaK molecule. The spectra, which consist of oscillating continua in the near‐infrared, have been analyzed to determine parameters describing the repulsive wall of the 1  3Σ+ state above the dissociation limit. Spectra calculated using a potential of the form Ae−BR +C for the 1 3Σ+ state were compared to experimental spectra to yield the following values: A=5.94×105 cm−1, B=1.605 A−1, C=−220.520 cm−1. This potential, which is referenced to the bottom of the RKR 1 3Σ+ well (De =209.1 cm−1), is valid over the range R=3.4–4.5 A (R=6.4–8.5 a.u.). The relative transition dipole moment of the 1 3Π→1 3Σ+ band has also been determined over a limited range in R (7.5<R<8.9 a.u.) through the study of relative intensities of various maxima within each oscillating spectrum. In the simulated spectra, the dipole moment was represented by a functional form D(R)=m(R−R0)+D0 where D0 was used to normalize the results to a recent theoretical calcul...

Experimental studies of the NaK 1 3Δ state

The NaK 1 3Δ state has been studied by the perturbation-facilitated optical–optical double resonance technique. Mixed singlet–triplet levels, A(2)1Σ+(vA,J)∼b(1)3Π(vb,J), were pumped from thermally populated rovibrational levels of the ground state, X(1)1Σ+(vX,J±1), using a single-mode cw dye laser. A single-mode cw Ti:Sapphire laser was then used to further excite the NaK molecules to various 1 3Δ(vΔ,NΔ,JΔ) rovibrational levels which were detected by observing collision-induced 3Λ→a(1)3Σ+ fluorescence in the green part of the spectrum. The measured energies of the 1 3Δ(vΔ,NΔ) levels were fit to a Dunham expansion, and the Dunham coefficients were used to construct the RKR potential curve. Absolute numbering of the 1 3Δ state vibrational levels was established by a comparison of experimental and calculated 1 3Δ(vΔ,NΔ,JΔ)←b(1)3Π(vb,Jb) absorption line strengths. A deperturbation program was used to determine the vibration-dependent 1 3Δ state spin–orbit interaction parameter. Hyperfine structure of the 1 3Δ...

Spin–orbit perturbations between the A(2)1Σ+ and b(1)3Π0 states of NaK

We have studied spin–orbit perturbations between the A(2) 1Σ+ and b(1) 3Π0 states of the NaK molecule by accurately measuring the energies of mutually perturbing levels, and by measuring ratios of A(2) 1Σ+ → X(1) 1Σ+ and b(1) 3Π0 → a(1) 3Σ+ emission intensities, for five perturbed pairs. This allows two partially independent determinations of each perturbation matrix element ‖〈1 3Π0(v’t, J’)‖Hso‖21Σ+(v’s,J’)〉‖. From these matrix elements, and calculated vibrational overlap integrals 〈v’t‖v’s〉, the electronic part of the perturbation matrix element, Hel≡‖〈1 3Π0(v’t, J’)‖Hso‖2 1Σ+(v’s, J’)〉‖/‖〈v’t‖v’s〉‖, was obtained. Our results for Hel from the two methods are consistent, and independent of vibrational and rotational quantum numbers, as expected. The determined best value for Hel is (15.64±0.39) cm−1.

A study of the predissociation of NaK molecules in the 6 1Σ+ state by optical–optical double resonance spectroscopy

Predissociation of a high-lying 1Σ+ state of NaK is studied using the optical–optical double resonance technique. A single-mode ring dye laser is set to a particular 2(A)1Σ+(v,J)←1(X)1Σ+(v′′,J′′) transition. Another single-mode laser (Ti–sapphire) is then used to excite the molecule from the 2(A)1Σ+(v,J) level, to rovibrational levels of a higher predissociating electronic state, which we identify as 6 1Σ+. The predissociation is monitored by the atomic potassium emission on the 3 2D3/2→4 2P1/2 transition at 1.17 μm, while bound state radiative processes are monitored by total violet fluorescence from the upper state to the various rovibrational levels of the ground 1(X)1Σ+ state. By scanning the Ti–sapphire laser, different rovibrational levels of the 6 1Σ+ state can be excited. The vibrational levels probed range from v=13 to 20 with rotational states ranging from 9 to 99. The bound state energy level positions are measured from the center frequencies of lines recorded with the Ti–sapphire laser excitat...

The 4 3Σ+ state of NaK: Potential energy curve and hyperfine structure

High-resolution spectra, including hyperfine structure, have been observed for numerous vibrational-rotational levels (v,N) of the 4 3Σ+ Rydberg state of the NaK molecule. The data have been used to construct a Rydberg–Klein–Rees potential curve, and this molecular potential has been further refined using the inverse perturbation approximation method. Bound-free emission from the 4 3Σ+ electronic state to the repulsive a(1) 3Σ+ state has also been measured and used to determine both the absolute vibrational numbering and the transition dipole moment function M(R). The experimentally derived potential curve and M(R) are compared with recent theoretical calculations of Magnier et al.; the agreement is very good. Each of the levels (v,N) is typically split into three sets of sublevels by the Fermi contact interaction bI⋅S. Further splitting (of order 0.004 cm−1) has been attributed to the spin-rotation interaction γN⋅S. The patterns observed exhibit a clear transition from Hund’s case bβS for small N toward ...

Electromagnetically induced transparency in an open V-type molecular system

We report the experimental observation of electromagnetically induced transparency (EIT) in an inhomogeneously broadened V-type Na2 molecular system. The experiment is performed with both co- and counterpropagating arrangements for the propagation directions of the coupling and probe laser beams. In our theoretical model we employ the density matrix formalism, as well as perturbative methods for obtaining the probe field absorption profile for both open and closed systems. Simulations of the experimental data show excellent agreement with the predictions derived from the basic theory. Our fluorescent intensity measurements show that, in the copropagating configuration, the EIT plus saturation window depth is about 95%, while under similar conditions in the counterpropagating geometry we observed 40%‐45% reduction in the fluorescence signal around the line center. To separate the two simultaneously occurring mechanisms in a V-type system (i.e., EIT and saturation) that are induced by the coupling field, we have carried out theoretical calculations which show that, in the copropagating case, a significant fraction of the depth of the dip is due to the coherent effect of EIT. When the coupling and probe beams are in the counterpropagating configuration, the dip is mostly due to saturation effects alone.

The K239 2Σg+3 state: Observation and analysis

The K239 2Σg+3 state has been observed by perturbation-facilitated infrared-infrared double resonance spectroscopy and two-photon excitation. Resolved fluorescence spectra into the aΣu+3 state have been recorded. The observed vibrational levels have been assigned as the v=23–25, 27, 28, 31–33, 38–45, 47, and 53 levels by comparing the observed and calculated spectra of the 2Σg+3→aΣu+3 transitions. Molecular constants have been obtained using a global fitting procedure with a comprehensive set of experimental data. Fine and hyperfine splittings have been resolved in the excitation spectra. Perturbations between the 2Σg+3 and 2Πg3 states were observed. The hyperfine patterns of the 2Σg+3 levels are strongly affected by the perturbation. The perturbation-free and weakly perturbed levels follow the case bβS coupling scheme, while the perturbed levels follow case bβJ coupling. A Fermi contact constant, bF=65±10MHz, has been obtained. Intensity anomalies of rotational lines appeared both in the 2Σg+3∼2Πg3←bΠu3 ...

Measurement of the self-broadening rate coefficients of the cesium resonance lines

Abstract The self-broadening rate coefficients of the cesium D 1 [6 2 S 1 2 − 6 2 P 1 2 ] and D 2 [6 2 S 1 2 − 6 2 P 3 2 ] resonance lines are determined from the 6 2 P 1 2 → 6 2 D 3 2 , 6 2 P 3 2 → 7 2 D 3 2 and 6 2 P 3 2 → 7 2 D 5 2 transition lineshapes, which are mapped out using single-mode cw lasers. The self-broadening rates are found from Voigt function fits (including hyperfine structure) to the experimental lineshapes. Our measured D1 and D2 broadening coefficients, kbr(D1) = (5.7 ± 1.0) × 10−7 cm3 sec−1 and kbr(D2) = (6.7 ± 1.1) × 10−7 cm3 sec−1, are compared to previous experimental and theoretical values in the literature. The present D2 broadening coefficient is smaller, and the D1 broadening coefficient is larger, than theoretical values.

Hyperfine structure of the 13Δg, 2 3Πg, and 33Σg+ states of 6Li7Li

The hyperfine splittings of the 1 3Δg, 2 3Πg, and 3 3Σg+ states of 6Li7Li have been resolved by sub-Doppler, continuous wave, perturbation facilitated optical–optical double resonance excitation spectroscopy through newly identified A 1Σu+ (vA′=5, J′=24)∼b 3Πu (vb′=12, N′=23, J′=24) mixed window levels. The 3 3Σg+ and 1 3Δg states follow the case bβS coupling scheme. The Fermi contact interaction between the 7Li nucleus and the electron spin is the dominant term for the observed hyperfine splittings. The Fermi contact constants for the 7Li nucleus in the 6Li7Li molecule have been determined to be 110 MHz for the 3 3Σg+ state and 107 MHz for the 1 3Δg state. The 2 3Πg state has doubly excited character and its hyperfine coupling is different from that of the 3 3Σg+ and 1 3Δg states. The Fermi contact constants of triplet Rydberg states of 6Li7Li versus 7Li2 are discussed, and insights into the physical basis for case bβS coupling are illustrated.The hyperfine splittings of the 1 3Δg, 2 3Πg, and 3 3Σg+ states of 6Li7Li have been resolved by sub-Doppler, continuous wave, perturbation facilitated optical–optical double resonance excitation spectroscopy through newly identified A 1Σu+ (vA′=5, J′=24)∼b 3Πu (vb′=12, N′=23, J′=24) mixed window levels. The 3 3Σg+ and 1 3Δg states follow the case bβS coupling scheme. The Fermi contact interaction between the 7Li nucleus and the electron spin is the dominant term for the observed hyperfine splittings. The Fermi contact constants for the 7Li nucleus in the 6Li7Li molecule have been determined to be 110 MHz for the 3 3Σg+ state and 107 MHz for the 1 3Δg state. The 2 3Πg state has doubly excited character and its hyperfine coupling is different from that of the 3 3Σg+ and 1 3Δg states. The Fermi contact constants of triplet Rydberg states of 6Li7Li versus 7Li2 are discussed, and insights into the physical basis for case bβS coupling are illustrated.