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Journal of Physics B Atomic Molecular and Optical Physics

Proposal for Zeeman slowing of Rb2 molecules in a supersonic beam, inducing internal cooling

Manuel Alejandro Lefrán Torres, Henry Fernandes Passagem, David Rodríguez Fernández, Eduardo da Costa Paul, Cristian Mojica-Casique, Olivier Dulieu, Nadia Bouloufa-Maafa, Luís Gustavo Marcassa

Published Feb 21, 2023• 0 citations
Publisher

Abstract

Abstract We present a theoretical proposal on Zeeman slowing of a Rb2 supersonic beam, relying on transitions between rovibrational levels of the X 1 Σ g + electronic ground-state and the B 1 Π u electronic excited state. Translational cooling is induced by optical transitions from v X ⩽ 13 , J X ⩽ 13 to v B = 0 involving P ( J B = J X − 1 ) and Q ( J B = J X ) branches. This is achieved by shaping the spectrum of broadband laser sources, in addition to two single-frequency laser sources addressing the X 1 Σ g + ( v X = 2 , 3 , J X = 1 ) → B 1 Π u ( v B = 0 , J B = 1 ) transitions. Our Monte–Carlo simulations indicate that the velocity of the molecules can be slowed from 500 m s−1 down to a few m s−1 by a Zeeman slower with a 1.2 m length, after scattering about 150 000 photons. At the end of the slowing process, half of the molecules are internally cooled, predicted to be in the v X = 2 , 3 , J X = 1 ground-state levels. A final optical pumping step transferring the population to the v X = 0 , J X = 1 ground-state level could produce a molecular beam exiting the Zeeman slower which is cold in all the translational, vibrational, and rotational degrees of freedom. Such an approach could potentially be a great interest for coolin

DOI
10.1088/1361-6455/acbdd6

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Abstract We present a theoretical proposal on Zeeman slowing of a Rb2 supersonic beam, relying on transitions between rovibrational levels of the X 1 Σ g + electronic ground-state and the B 1 Π u electronic excited state. Translational cooling is induced by optical transitions from v X ⩽ 13 , J X ⩽ 13 to v B = 0 involving P ( J B = J X − 1 ) and Q ( J B = J X ) branches. This is achieved by shaping the spectrum of broadband laser sources, in addition to two single-frequency laser sources addressing the X 1 Σ g + ( v X = 2 , 3 , J X = 1 ) → B 1 Π u ( v B = 0 , J B = 1 ) transitions. Our Monte–Carlo simulations indicate that the velocity of the molecules can be slowed from 500 m s−1 down to a few m s−1 by a Zeeman slower with a 1.2 m length, after scattering about 150 000 photons. At the end of the slowing process, half of the molecules are internally cooled, predicted to be in the v X = 2 , 3 , J X = 1 ground-state levels. A final optical pumping step transferring the population to the v X = 0 , J X = 1 ground-state level could produce a molecular beam exiting the Zeeman slower which is cold in all the translational, vibrational, and rotational degrees of freedom. Such an approach could potentially be a great interest for coolin
Cold molecules are an invaluable tool for modern physics. Cold atoms have already revolutionized precision metrology, allowed for spectacular findings in quantum physics and opened the door for the creation and observation of novel states of matter. Cold molecules bring with them additional degrees of freedom which give rise to unique properties that enable new kinds of experiments. For these experiments it is of vital importance to start with a sufficiently large number of cold molecules. There are multiple paths for the slowing and cooling of atoms and most of the slowing techniques utilizing lasers for direct cooling have been transferred to the molecular case with its specific requirements. The Zeeman slowing technique is advantageous for loading a trap with cold particles but had not yet been transferred from atoms to the molecular case. In this thesis I will show the first realization of the Zeeman slowing technique for diatomic molecules. This thesis will discuss several preparatory steps: Our group has had some ideas to collimate the molecular beam with a conical nozzle outlet at the buffer gas cell which I investigated on potassium atoms generated by the ablation of 39K35Cl inside the buffer gas cell. I also realized a fluorescence spectroscopy of the |XΣ1/2, N = 1, v = 0⟩ → |AΠ1/2, N = 0, v = 0⟩ transition in magnetic fields up to 300 G and confirmed simulations regarding our two laser cycling scheme in the Paschen-Back regime by measuring the scattering rate of light on one molecule. Finally, I created pre-cooled 40Ca19F with a forward velocity of around 150 m s−1 from a 40Ca19F2 target with laser ablation inside a cryogenic buffer gas cell. With the Zeeman slowing technique I slowed the molecules down to 25 m s−1, a velocity where trapping can be possible. I have also shown the characteristic compression into specific velocity classes for not yet trappable velocities. Together these two findings demonstrate that molecular Zeeman slowing is possible and a real promising tool for future experiments.
Cold and ultracold molecules are highly desirable for a diverse range of applications in physics and chemistry such as precision measurements, tests of fundamental physics, quantum simulation and information processing, quantum chemistry, and the physics of strongly correlated quantum matter. Laser cooling is usually infeasible in molecules because their rotational and vibrational transitions make is difficult to come up with a closed scattering cycle. Recently, a narrow range of diatomic molecules, one of which is CaF, has been shown to possess a convenient electronic structure and a highly-diagonal Franck-Condon matrix and thus be amenable to laser cooling. This thesis describes experiments on laser cooling of CaF radicals produced in a supersonic source. We first investigate the increased fluorescence when multi-frequency resonant light excites the molecules from the four hyperfine levels of the ground X²∑+(N = 1, v = 0) state to the first excited A²π½ (J’ = 1=2; v’ = 0) state. The number of photons scattered per molecule increases significantly from one or two in the single frequency case to more than 50 before the molecules get pumped into the X²∑+(N = 1; v = 1) state. We demonstrate laser cooling and slowing of CaF using counter-propagating laser light which causes the molecules to scatter more than a thousand photons on the X (N = 1, v = 0, 1) <->A (J’ = 1=2; v’ = 0) transition. The effect of the laser cooling is to slow a group of molecules from 600 ms-1 to about 580 ms-1 and to narrow their velocity distribution from an initial temperature of 3 K down to 300 mK. In addition, chirping the frequency of the cooling light to keep it on resonance with the decelerating molecules doubles the deceleration and further compresses the velocity distribution. The effect of the laser cooling is limited by the optical pumping of molecules in the X (N = 1, v = 2) state.
A novel scheme is proposed for sequential cooling of rotation, translation, and vibration of molecules. More generally, this scheme manipulates and controls the states and energies of molecules. The scheme, while somewhat complex, is simpler and more feasible than simply providing a large number of synchronously but independently tunable lasers. The key component is a multiple single frequency laser (MSFL) in which a single narrow band pump laser generates an ensemble of resonant ‘‘stimulated Raman’’ (RSR) sidebands (subsequently amplified and selected) in a sample of the molecules to be cooled. Starting with a relatively cold molecular sample (e.g., a supersonic beam of Cs2), the rotation of molecules is cooled by sequential application of P branch electronic transition frequencies transverse to the molecular beam beginning at higher rotational angular momentum J. Then translation of molecules is cooled by application of multiple low J, P, and R branch transition frequencies which counterpropagate with the molecular beam and are synchronously chirped over their Doppler profiles. Finally, vibration of molecules is cooled by blocking the R(0) line of the 0–0 band. Only this specific order of rotation–translation–vibration appears feasible (using molecules produced by photoassociation of ultracold atoms avoids the requirement for translational cooling). Each step employs true dissipative cooling (i.e., reduction of system entropy in three degrees of freedom) by spontaneous emission and should yield a large translationally cold sample of molecules in the lowest (v=0, J=0) level of the ground electronic state, suitable for studies such as molecule trapping, ‘‘molecule optics,’’ or long range intermolecular states.
The use of a broadband, frequency shaped femtosecond laser on translationally cold cesium molecules has recently demonstrated to be a very efficient method of cooling also the vibrational degree of freedom. A sample of cold molecules, initially distributed over several vibrational levels, has thus been transfered into a single selected vibrational level of the singlet X1g ground electronic state. Our method is based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but limited in its frequency bandwidth with a spatial light modulator. In such a way we are able to eliminate transitions from the selected level, in which molecules accumulate. In this paper we briefly report the main experimental results and then address, in a detailed way by computer simulations, the perspectives for a complete" cooling of the molecules, including also the rotational degree of freedom. Since the pumping process strongly depends on the relative shape of the ground and excited potential curves, ro-vibrational cooling through different excited states is theoretically compared.
Abstract. Some of us have recently reported in Science [1] vibrational cooling of translationally cold Cs2 molecules into the lowest vibrational level v = 0 of the singlet X1Σg ground electronic state. Starting from a sample of cold molecules produced in a collection of vibrational levels of the ground state, our method was based on repeated optical pumping by laser light with a spectrum broad enough to excite all populated vibrational levels but frequency-limited in such a way to eliminate transitions from v = 0 level, in which molecules accumulate. In this paper this method is generalized to accumulate molecules into an arbitrary selected ”target ” vibrational level. It is implemented by using ultrashort pulse shaping techniques based on Liquid Crystal spatial light modulator. In particular a large fraction of the initially present molecule is transferred into a selected vibrational level such as v = 1, 2 and 7. Limitations of the method as well as the possible extension to rotational cooling are also discussed. PACS numbers: 06.60.Jn; 32.80.Qk; 33.20.Tp; 37.10.Mn; 42.65.Re; 42.79.Kr 1.
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.