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arXiv:2505.14798

Laser cooling Rydberg molecules -- a detailed study of the helium dimer

Lucía Verdegay, Zeng, Bingcheng, Daniel Y. Knapp, Jack C. Roth, Maximilian Beyer

Published May 20, 2025• 0 citations
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Abstract

The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He$_2^*$ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He$_2^*$ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He$_2^*$. The sensitivity of the vibrational levels of He$_2^+$ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.

DOI
10.48550/arxiv.2505.14798

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The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He2∗_2^*2∗​ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He2∗_2^*2∗​ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He2∗_2^*2∗​. The sensitivity of the vibrational levels of He2+_2^+2+​ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.
Abstract The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He 2 * would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck–Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin–rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He 2 * molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He 2 * . The sensitivity of the vibrational levels of He 2 * with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.
Laser cooling and trapping are central to modern atomic physics. It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields and a number of Nobel prizes. Prior to the work presented in this thesis, laser cooling had not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for a wide range of applications. The first direct laser cooling of a molecule and further results we present here provide a new route to ultracold temperatures for molecules. In particular, these methods bridge the gap between ultracold temperatures and the approximately 1 kelvin temperatures attainable with directly cooled molecules (e.g. with cryogenic buffer gas cooling or decelerated supersonic beams). Using the carefully chosen molecule strontium monofluoride (SrF), decays to unwanted vibrational states are suppressed. Driving a transition with rotational quantum number R=1 to an excited state with R'=0 eliminates decays to unwanted rotational states. The dark ground-state Zeeman sublevels present in this specific scheme are remixed via a static magnetic field. Using three lasers for this scheme, a given molecule should undergo an average of approximately 100,000 photon absorption/emission cycles before being lost via unwanted decays. This number of cycles should be sufficient to load a magneto-optical trap (MOT) of molecules. In this thesis, we demonstrate transverse cooling of an SrF beam, in both Doppler and a Sisyphus-type cooling regimes. We also realize longitudinal slowing of an SrF beam. Finally, we detail current progress towards trapping SrF in a MOT. Ultimately, this technique should enable the production of large samples of molecules at ultracold temperatures for molecules chemically distinct from competing methods.
For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable ${A}^{{\ensuremath{'}}^{2}}\mathrm{\ensuremath{\Delta}}$ and ${A}^{2}\mathrm{\ensuremath{\Pi}}$ states and, further, the lifetime of the $\mathrm{\ensuremath{\Delta}}$ state have been estimated since the loss procedure via the $\mathrm{\ensuremath{\Delta}}$ state might fatally break the main quasicycling $\mathrm{\ensuremath{\Sigma}}\ensuremath{-}\mathrm{\ensuremath{\Pi}}$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and ggg factors for both XXX and AAA states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.
An optical scheme to create the simplest heteronuclear metal ultracold LiBe molecule is proposed based on ab initio quantum chemistry calculations. The potential energy curves, dipole moments, and transition dipole moments of $1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}, 1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}$, and $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Pi}}$ states are calculated using the multireference configuration interaction and large basis sets. The analytical functions deduced from the obtained curves are used to determine the rovibrational energy levels, the Franck-Condon factors, and the Einstein coefficients of the states through solving the Schr\"odinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained rovibrational energy levels. The Franck-Condon factors (f00:0.998,f11:0.986,f22:0.920)({f}_{00}:0.998, {f}_{11}:0.986, {f}_{22}:0.920)(f00​:0.998,f11​:0.986,f22​:0.920) for the $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}(v=0)\ensuremath{\leftrightarrow}1\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}\phantom{\rule{0.28em}{0ex}}({v}^{\ensuremath{'}}=0)$ transition are highly diagonally distributed, and the calculated radiative lifetime (74.87 ns) of the $2\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{\ensuremath{\Sigma}}^{+}$ state is found to be short enough for rapid laser cooling. The results demonstrate that LiBe could be a very promising candidate for laser cooling and a three-cycle laser cooling scheme for the molecule has been proposed.
This thesis investigates the suitability of BH molecules for laser cooling and describes progress towards the laser cooling of this molecule. We produce a molecular beam of BH and measure the branching ratios for the excited electronic state, A^{1}\Pi(v_{0}=0), to decay to the various vibrational states of the ground electronic state, X^{1}\Sigma. We verify that the branching ratio for the spin-forbidden transition to an intermediate triplet state is inconsequentially small. We measure the frequency of the lowest rotational transition of the X state, and the hyper fine structure in the relevant levels of both the X and A states, and determine the nuclear electric quadrupole and magnetic dipole coupling constants. We use a semiclassical model of the molecule-light interaction to investigate the expected cycling behaviour on the main cooling transition using light with modulated polarisation. The results of the model are compared with the effect of modulating the polarisation experimentally using an electro-optic modulator. In order to repump the population that leaks into the first vibrationally excited state, we have designed, built and tested a suitable repump laser and have demonstrated that we can drive the repump transition. We have also designed a Zeeman slower for slowing molecules to low velocity so that they can be trapped. Our results show that a relatively simple laser cooling scheme can be used to cool, slow and trap BH molecules.
The first part of this project involved continued development of theoretical models of diatomic molecular electronic level structure for application to the production of ultracold diatomic molecules via photoassociation. Recently, there has been considerable interest in producing molecules at the temperatures achieved for laser-cooled atoms, for applications to "coherent chemistry," studies of molecule-atom and molecule-molecule interactions. Bose condensates of molecules and for quantum computing. It is advantageous to produce cold molecules from laser-cooled atoms. but this requires an accurate model of the energy level structure near the dissociation limit for excited atoms, and for other intermediate states. With this in mind. we have modeled experimental photoassociation data from Rb2. spectroscopic data on the lowest excited states of Na2, and hyperfine structure of the lowest triplet state of Cs2. The second part involved continued development of experimental techniques for intense atomic beam collimation using a bichromatic laser field. We solved the equations for evolution of atoms in such a laser field, expressed the results in the form of trajectories on the Bloch sphere for a two-level atoms, and then used these results to design and perform efficient atomic beam reflection experiments. At the same time, we are developing methods to use these highly collimated beams of metastable helium atoms for precision lithography, using sensitized surfaces.