This dissertation describes methods and results of spectroscopic studies of the NaCs molecule. NaCs is of particular interest in many labs where experimental studies of ultra-cold molecules are being conducted. Data obtained in the present work will also be useful as benchmarks for various theoretical calculations. Our goals in studying this molecule were to map out high lying electronic states and to understand how these states interact with one another. Sodium and cesium metal were heated in a heat-pipe oven to form a vapor of NaCs molecules. These molecules were excited using narrow band, continuous wave (cw), tunable lasers. We employed the optical-optical double resonance (OODR) technique to obtain Doppler-free spectra of transitions to rotational and vibrational levels of high lying electronic states. One state of particular interest was the 12(0+) electronic state. Rovibrational level energies corresponding to this state were measured and used to generate a potential energy curve using computer programs to implement both the Rydberg-Klein-Rees (RKR) method and the inverted perturbation approach (IPA). By observing fluorescence from the 12(0+) state resolved as a function of wavelength, we determined that this state interacts with the nearby 11(0+) electronic state, which was previously mapped out by Ashman et al. A two-stage coupling model was devised to describe the resolved fluorescence originating from these two interacting states. The electronic states interact via spin-orbit coupling, while the individual rovibrational levels interact via a second mechanism, likely nonadiabatic coupling. This two-stage coupling between the levels of these states causes quantum interference between fluorescence pathways associated with different components of the wavefunctions describing these levels. This interference results in more complicated resolved fluorescence spectra. The model was used to fit parameters describing these interactions so that the resolved fluorescence spectra could be reproduced. The NaCs 43 π electronic state was also studied in this work. Energies of many rovibrational levels belonging to the 43 π electronic state were measured. This state is interesting because it likely has a potential energy curve with a double minimum, which results in a different type of quantum interference, directly observed in resolved spectra. The state also very likely has interactions with the 11(0+) and 12(0+) states. Energies of many rovibrational levels lying above the energy of the barrier between the two minima were measured, and it appears that we also observed a few levels lying below the barrier. Since the laser wavelengths necessary to excite the lowest vibrational levels were not available, an experimental potential curve could not be produced. Therefore, rovibrational level energies and spectroscopic constants are tabulated.
This dissertation presents the study of how two laser pulses can bind sodium and cesium atoms at ultracold temperature (
T=200muK) into an ultracold, polar, diatomic molecule with a definite quantum state. \nA single-channel scattering model represents the initial continuum state, and two different models represent the intermediate state: one excluding spin-orbit coupling effects in the intermediate state, the other accounting for such effects. \nWe calculate the
A1Sigma+−b3Pi spin-orbit coupled wave functions using a basis expansion technique, and validate the results by comparing to experimentally obtained, spin-orbit coupled energy levels. \nThe computation of photoassociation rates between the continuum state and the intermediate states reveals the crucial importance of spin-orbit coupling. \nFurthermore, this study shows how the spectral bandwidth (narrow \\vs broad), the chirping (chirped vs. unchirped), the detunings, the intensities, and the pulse delay (intuitive \\vs counter-intuitive sequence) of the lasers affect the transfer of population from the continuum scattering state to a comparatively low-lying (
vX=32,JX=0) rovibrational state of the
X1Sigma+ ground electronic state of NaCs. \nThe transfer process relies either on a sequence of
pi-pulses, or uses stimulated Raman adiabatic passage (STIRAP). \nLasers with narrow spectral bandwidth (
0.5GHz) always yield a final population in
ketX1Sigma+,vX=32,JX=0 higher than 95\\% in less than 4 ns.
Comprehensive spectroscopic studies of hot and ultracold samples of NaCs molecules were combined to complete the investigation of the $(3)\ensuremath{\Omega}=1$ $\ensuremath{\leftarrow}$
X ${}^{1}{\ensuremath{\Sigma}}^{+}$ transition for the NaCs molecule. Polarization labeling, photoassociation, and pulsed laser depletion spectroscopy were used to collect data on rovibrational levels of the $(3)\ensuremath{\Omega}=1$ state [here described as the
c ${}^{3}{\ensuremath{\Sigma}}^{+}$ state in Hund's case (a) notation]. The highest observed level was
v=72 located $~$5 GHz below the atomic asymptote Na(
32S1/2)
+ Cs(
62P3/2). Approximately 1400 levels were used to construct the potential energy curve of the $(3)\ensuremath{\Omega}=1$ state for the full range of interatomic distances.
High resolution Fourier transform spectra (FTS) of laser induced fluorescence (LIF) of $C\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+};D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}\ensuremath{\rightarrow}A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ and $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ transitions in
Na85Rb and
Na87Rb were obtained. An analysis of the direct LIF spectra together with the rotational relaxation satellites provided highly accurate rovibronic term values for $(4\ensuremath{\leqslant}J\ensuremath{\leqslant}163)$ of the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ complex, covering about 1950 mostly singlet levels $0\ensuremath{\leqslant}{v}_{A}\ensuremath{\leqslant}49$ and a considerable number
(>360) of the predominantly triplet $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0,1}$ sublevels. The direct deperturbation analysis of the singlet-triplet
A−−b complex was performed by means of the inverted channel-coupling approach with Hund's coupling case
a basis functions. The electronic matrix elements of the model $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian were defined as piecewise analytical functions of the internuclear distance. Besides the Born-Oppenheimer potential energy curves of the mutually perturbed states and the off-diagonal spin-orbit (SO)
A−−b coupling function, the SO splitting of the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ state was determined due to the pronounced electronic-rotation interaction between the $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{0}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}_{1}$ components observed for high
J levels. Overall, 24 mass-invariant fitting parameters have been required to reproduce about 2300 experimental term values of both isotopomers with a standard deviation of $0.012\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is consistent with the uncertainty of the FTS experiment. An analytical mapping procedure based on a reduced variable representation of the radial coordinate was used to diminish the computational effort for the uniform finite-difference grid solution of the coupled-channel equations. The derived nonadiabatic
A−−b wave functions were used to evaluate the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}--b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}--D\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Pi}$, $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ rovibronic transition probabilities. The relative intensity distributions predicted for the $D\ensuremath{\rightarrow}A--b$ and $A--b\ensuremath{\rightarrow}X$ LIF progressions agree with their experimental counterparts within the accuracy of the measurements. The calculated
A−−b−−a,
X transition probabilities were applied for simulation of the stimulated Raman $a\ensuremath{\rightarrow}A--b\ensuremath{\rightarrow}X$ processes, which can lead to efficient formation of ultracold NaRb molecules in the ground level
vX=0;
JX=0.
In this dissertation, I explore several aspects of Rydberg physics with laser spectroscopy. The experiments center around the use of a very deep, cavity-generated, one-dimensional optical lattice in a cold atom sample. The optical lattice produces elongated clouds of dense, cold atoms via dipole trapping and is able to generate extreme light shifts in the atoms due to its high intensity. I describe experiments which may be divided into two main classes. In the first, I use the dipole trap to prepare a dense sample of atoms for photoassociation of Rb atom pairs into diatomic Rydberg molecules. The Rydberg molecules are formed by low-energy scattering of the Rydberg electron of one atom from the other atom, which is a ground-state atom. This novel binding mechanism also has relevance for chemical physics. I present binding energy measurements for eight different cases of Rydberg molecules. The binding energies reveal information about electron-atom collisions, such as their scattering lengths, and about the spin couplings present within the molecular system. In the second class of experiments, I introduce two proposed measurements in which the optical lattice is ramped to very high intensity during the laser excitation, creating AC Stark shifts in the transition frequencies. In one measurement, low-lying atomic states are probed. Measurements of the light shifts are expected to yield data on the dynamic polarizability and the photoionization cross section of the 5
D3/2-state in rubidium in a 1064-nm light field. I show corresponding preliminary experimental data. The polarizability and photo-ionization cross-section measurements will provide tests of atomic structure theory, which is important both at a fundamental level and for applications such as atomic clocks. In another proposed measurement, Rydberg atoms in the lattice experience ponderomotive shifts and strong mixing of their angular-momentum states, allowing direct optical excitation of the lattice-mixed high-angular-momentum states. I describe the theoretical basis and experimental preparation for spectroscopically characterizing the lattice-mixed states. The ability to optically excite selected high-angular-momentum states without the use of static or RF fields may be useful for quantum information processing and simulation.
Abstract We present a study of two-photon pathways for the transfer of NaCs molecules to their rovibrational ground state. Starting from NaCs Feshbach molecules, we perform bound-bound excited state spectroscopy in the wavelength range from 900 nm to 940 nm, covering more than 30 vibrational states of the c 3 Σ + , b 3 Π , and B 1 Π electronic states. Analyzing the rotational substructure, we identify the highly mixed c 3 Σ 1 + | v = 22 ⟩ ∼ b 3 Π 1 | v = 54 ⟩ state as an efficient bridge for stimulated Raman adiabatic passage. We demonstrate transfer into the NaCs ground state with an efficiency of up to 88(4)%. Highly efficient transfer is critical for the realization of many-body quantum phases of strongly dipolar NaCs molecules and high fidelity detection of single molecules, for example, in spin physics experiments in optical lattices and quantum information experiments in optical tweezer arrays.
Recent progress in studies of Rydberg double-well electronic energy states of MeNg (Me = 12-group atom, Ng = noble gas atom) van der Waals (vdW) molecules is presented and analysed. The presentation covers approaches in experimental studies as well as ab initio-calculations of potential energy curves (PECs). The analysis is shown in a broader context of Rydberg states of hetero- and homo-diatomic molecules with PECs possessing complex 'exotic' structure. Laser induced fluorescence (LIF) excitation spectra and dispersed emission spectra employed in the spectroscopical characterization of Rydberg states are presented on the background of the diverse spectroscopic methods for their investigations such as laser vaporization-optical resonance (LV-OR), pump-and-probe methods, and polarization labelling spectroscopy. Important and current state-of-the-art applications of Rydberg states with irregular potentials in photoassociation (PA), vibrational and rotational cooling, molecular clocks, frequency standards, and molecular wave-packet interferometry are highlighted.