The article presents a study of the strongly spin-orbit coupled singlet A(1)Σ(+) and triplet b(3)Π states of the RbCs molecule, which provide an efficient optical path to transfer ultracold molecules to their rovibrational ground state. Fourier-transform A(1)Σ(+) - b(3)Π → X(1)Σ(+) and (4)(1)Σ(+) → A(1)Σ(+) - b(3)Π laser-induced fluorescence (LIF) spectra were recorded for the natural mixture of the (85)Rb(133)Cs and (87)Rb(133)Cs isotopologues produced in a heat pipe oven. Overall 8730 rovibronic term values of A(1)Σ(+) and b(3)Π states were determined with an uncertainty of 0.01 cm(-1) in the energy range [9012, 14087] cm(-1), covering rotational quantum numbers J ∈ [6, 324]. An energy-based deperturbation analysis performed in the framework of the four A(1)Σ(+) - b(3)Π(Ω = 0, 1, 2) coupled-channels approach reproduces 97% of the experimental term values of both isotopologues with a standard deviation of 0.0036 cm(-1). The reliability of the deperturbed mass-invariant potentials and spin-orbit coupling functions of the interacting A(1)Σ(+) and b(3)Π states is additionally proved by a good reproduction of the A - b → X and (4)(1)Σ(+) → A - b relative intensity distributions. The achieved accuracy of the A - b complex description allowed us to use the latter to assign the observed (5)(1)Σ(+) → A - b and (3)(1)Π → A - b transitions. As is demonstrated, LIF to the A - b complex becomes as informative as to the ground X(1)Σ(+) state, which is confirmed by comparing the results of (4)(1)Σ(+) state analysis based on (4)(1)Σ(+) → A - b LIF with the data from V. Zuters et al. [Phys. Rev. A 87, 022504 (2013)] based on (4)(1)Σ(+) → X LIF.
We performed high-resolution Fourier-transform spectroscopy measurements and direct-potential-fit of the shelflike RbCs $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state. Overall, 2317 rovibronic ${v}^{\ensuremath{'}},{J}^{\ensuremath{'}}$ term values with ${v}^{\ensuremath{'}}\ensuremath{\in}[3,88]$, ${J}^{\ensuremath{'}}\ensuremath{\in}[7,276]$ were obtained with accuracy 0.01 cm${}^{\ensuremath{-}1}$ from the $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ laser-induced fluorescence (LIF) spectra. The mass-invariant potential energy curve constructed by means of the Chebyshev polynomial expansion reproduced the experimental term values of both
85Rb
133Cs and
87Rb
133Cs isotopologues with a standard deviation of 0.005 cm${}^{\ensuremath{-}1}$. We simulated the optical cycle $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}},{J}^{\ensuremath{'}\ensuremath{'}}=0)\ensuremath{\rightarrow}(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}},{J}^{\ensuremath{'}}=1)\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}\ensuremath{'}}=0,{J}^{\ensuremath{'}\ensuremath{'}}=0)$ appropriate to transfer translationally ultracold RbCs molecules into their absolute ground state from the weakly bound rovibronic levels of both singlet $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and triplet $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ ground states. The optimal transfer via the intermediate $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state with ${v}^{\ensuremath{'}}=58,60$, and 61 for
85Rb
133Cs as well as ${v}^{\ensuremath{'}}=59$ and 61 for
87Rb
133Cs was predicted. The required spin-allowed $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and spin-forbidden $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{-}a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ dipole transition moments were obtained within the framework of ab initio quasirelativistic calculations. The predicted $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+},a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ transition probabilities were consistent with the experimental relative intensity distributions for several $(4){\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{\ensuremath{'}})\ensuremath{\rightarrow}X,a({v}^{\ensuremath{'}\ensuremath{'}})$ LIF progressions.
We perform one- and two-photon high resolution spectroscopy on ultracold samples of RbCs Feshbach molecules with the aim to identify a suitable route for efficient ground-state transfer in the quantum-gas regime to produce quantum gases of dipolar RbCs ground-state molecules. One-photon loss spectroscopy allows us to probe deeply bound rovibrational levels of the mixed excited (A(1)Σ(+)-b(3)Π)0(+) molecular states. Two-photon dark state spectroscopy connects the initial Feshbach state to the rovibronic ground state. We determine the binding energy of the lowest rovibrational level |v'' = 0, J'' = 0> of the X(1)Σ(+) ground state to be D = 3811.5755(16) cm(-1), a 300-fold improvement in accuracy with respect to previous data. We are now in the position to perform stimulated two-photon Raman transfer to the rovibronic ground state.
The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the $A{ }^{1}{\ensuremath{\Sigma}}^{+}$-$b{ }^{3}\ensuremath{\Pi}$ complex. The
A-
b mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed
A-$b\ensuremath{\rightarrow}X$ transitions, while the second is derived in large part from $(4){ }^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}A$-
b emission and extends to higher
A-
b energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the
A state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the
b state is established with a considerable degree of certainty with help of data on the
85Rb133Cs and
87Rb133Cs isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two ${\ensuremath{\Omega}}^{p}={0}^{+}$ states, $A{ }^{1}{\ensuremath{\Sigma}}^{+}$ and $b{ }^{3}{\ensuremath{\Pi}}_{0+}$, happens to agree rather well with the results from both of these methods, while for the diagonal $b{ }^{3}\ensuremath{\Pi}$ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.
We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb 2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85 Rb and 133 Cs atoms colliding on the X 1 Σ + potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P 1/2 ) asymptote. We explore the nature of the Ω=0 + levels in this region, which have mixed A 1 Σ + and b 3 Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm −1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb 2 system; this is mostly because of the absence of an R −3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb 2 , the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm −1 . The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.
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.
This thesis reports the development of theoretical and experimental tools to understand and control the coupled A1Σ+ − b3Π0 system in ultracold 87Rb133Cs molecules, with applications in magic trapping and direct imaging of molecules. Building on detailed modelling of molecular structure and light–matter interactions, the work establishes conditions for long-lived rotational coherence and explores pathways towards quantum simulation and computation with RbCs. High-resolution spectroscopy of lowest vibrational levels in the coupled complex is performed, yielding vibrational splittings, rotational and hyperfine coupling constants, transition dipole moments and natural linewidths. Spectroscopy of a highly excited vibrational level of the complex is also performed, with the polarisation-dependent transition strengths and polarisabilities measured. These results demonstrate strong anisotropy of the initial state and enables direct detection of molecules. We then develop and validate a comprehensive description of rotationally magic trapping in RbCs. A general theory of dipole polarisability is applied near the transition from the rovibrational ground state in the X1Σ+ potential to the lowest vibrational states of the b3Π0+ potential, predicting rotationally magic frequencies at which differential polarisabilities between rotational states vanishes. Experimentally, we build and characterise a new magic-wavelength trapping system based on a 1145 nm laser. Measurements of magic frequencies for spinstretched superpositions, combined with long coherence times in the magic trap, confirm the model. Dephasing due to dipole–dipole interactions are observed, while long-lived rotational coherence is demonstrated with non-dipolar states. Extending the theory and experiments to non-stretched states by diagonalising the full AC Stark Hamiltonian shows nonlinear Stark shifts driven by laser-induced hyperfine couplings and identifies local magic conditions where intensity gradients vanish, enabling tailored coherence protection across a wide range of internal state.