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Breaking Feshbach molecules

Felix Klose

Published Oct 9, 2026• 0 citations
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Abstract

This thesis studies the effects of breaking Feshbach molecules of ⁶Li confined in an Optical-Dipole Trap (ODT). We discuss the effects of breaking molecules using background collisions between Feshbach molecules and H₂ particles in our vacuum system and resonant photons. In the case of background collisions we show that despite the collisions being energetic enough to always eject one of the constituent atoms, the remaining atom will only receive a weak kick. We show that the probability of the magnitude of the kick is related to the Feshbach molecule wavefunction. We describe an experiment for measuring this probability distribution, through measuring the time dynamics of the number of atoms and molecules in our trap as a function of the trap-depth and magnetic field, and discuss some preliminary results. Our results reveal that breaking molecules using pulses of light, resonant with one of the atomic transitions, results in similar dynamics. For both experiments we derive and discuss a phenomenological rate-equation model. We also characterized the magnetic trapping potential through a measurement of the associated trap-frequencies. Using the results of these measurements and incorporating the optical trapping potential due to the ODT and effects due to gravity, we calculate the trap-depth as a function of the magnetic field, power, and small vertical displacements. We demonstrate that vertical misalignment affects the trap similarly to changes in the magnetic field.

DOI
10.14288/1.0456545

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This thesis studies the effects of breaking Feshbach molecules of ⁶Li confined in an Optical-Dipole Trap (ODT). We discuss the effects of breaking molecules using background collisions between Feshbach molecules and H₂ particles in our vacuum system and resonant photons. In the case of background collisions we show that despite the collisions being energetic enough to always eject one of the constituent atoms, the remaining atom will only receive a weak kick. We show that the probability of the magnitude of the kick is related to the Feshbach molecule wavefunction. We describe an experiment for measuring this probability distribution, through measuring the time dynamics of the number of atoms and molecules in our trap as a function of the trap-depth and magnetic field, and discuss some preliminary results. Our results reveal that breaking molecules using pulses of light, resonant with one of the atomic transitions, results in similar dynamics. For both experiments we derive and discuss a phenomenological rate-equation model. We also characterized the magnetic trapping potential through a measurement of the associated trap-frequencies. Using the results of these measurements and incorporating the optical trapping potential due to the ODT and effects due to gravity, we calculate the trap-depth as a function of the magnetic field, power, and small vertical displacements. We demonstrate that vertical misalignment affects the trap similarly to changes in the magnetic field.
We perform radio-frequency dissociation spectroscopy of weakly bound 6Li2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability, this allows us to resolve the discrete trap levels in the radio-frequency dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the 6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of the broad 6Li Feshbach resonances with an accuracy better than 7×10(-4) of the resonance widths. This eliminates the dominant uncertainty for current precision measurements of the equation of state of strongly interacting Fermi gases. As an important consequence, our results imply a corrected value for the Bertsch parameter ξ measured by Ku et al. [Science 335, 563 (2012)], which is ξ=0.370(5)(8).
This thesis describes the production of molecular Bose-Einstein condensates (BEC) of 6Li2 dimers and binding energy measurements of p-wave Feshbach molecules. A σ− Zeeman slower is used to produce a continuous beam of isotopically enriched 6Li atoms at speeds low enough to load a magneto-optical trap (MOT). We currently have a flux of slowed atoms of ~ 5 · 106 atoms/s loading the MOT with more than 108 atoms. We then transfer up to 106 atoms in an almost equal spin mixture of the two lowest hyperfine states into an optical dipole trap. We achieved condensates in three different crossed optical dipole trap geometries. The initial low power optical dipole trap was formed using light from a 25WVersaDisk Yb:YAG laser at 1030 nm. It consisted of a 15 W beam crossed with a 13 W beam at about 80 degrees with a waist of approximately 30 μm in each beam. By translating the focus of the second beam we could change the trap geometry from near symmetric to elongated. Nowadays, we produce condensates in a crossed dipole trap formed by a 100 W fibre laser. Both arms are focussed to a waist of 40 μm, cross each other at 14 degrees and have laser powers of ~80 W and ~70 W, respectively. Evaporative cooling is achieved by reducing the laser power near the broad s-wave Feshbach resonance at 834 G. By tuning to the low magnetic field side (770 G) of the Feshbach resonance molecules are formed through three-body recombination at sufficiently low temperatures. Further evaporation leads to the creation of a molecular BEC. After reducing the laser power by a factor of about 1000 in approximately 3 s we have observed more than 30 000 condensed molecules. During the evaporation the temperature decreases from about 100 μK to below 100 nK. We present measurements of the binding energies of 6Li p-wave Feshbach molecules formed in combinations of the |F = 1/2,mF = +1/2i (|1i) and |F = 1/2,mF = −1/2i (|2i) states. The binding energies scale linearly with magnetic field detuning for all three resonances. The relative molecular magnetic moments are found to be 113 ± 7 μK/G, 111 ± 6 μK/G and 118 ± 8 μK/G for the |1i − |1i, |1i − |2i and |2i − |2i resonances, respectively, in good agreement with theoretical predictions.
We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally with trap depth and approach zero at zero depth. We show that the large observed shifts originate from a large differential ac Stark shift between the incoming pair of potassium-39 atoms and the weakly bound Feshbach molecule, which in turn originates from an unexpectedly large dynamic polarizability of the Feshbach molecule. The polarizabilities of the Feshbach molecules extracted from the measured shifts of the 33.6 G and 39.9 G resonances are about four to seven times the sum of the polarizabilities of the two incoming potassium-39 atoms, that is, about four to seven times larger than the usual polarizability of weakly bound Feshbach molecules. The large polarizabilities of the Feshbach molecules are attributed to a near-coincidence between the frequency of the 1063.9 nm ODT laser and the frequency of a molecular transition from the last vibrational level of the lowest triplet a3Σ+u potential to a vibrational level of the excited b3Σ+g potential. Other potassium-39 Feshbach resonances we have studied exhibit a zero or very small shift, corresponding to molecular polarizabilities close to the sum of the polarizabilities of the two incoming potassium-39 atoms.
We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, which are composed of the fermionic isotopes 161Dy and 40K. Employing a magnetic sweep across a resonance located near 7.3 G, we produce up to 5000 molecules at a temperature of about 50 nK. For purification from the remaining atoms, we apply a Stern-Gerlach technique based on magnetic levitation of the molecules in a very weak optical dipole trap. With the trapped molecules we finally reach a high phase-space density of about 0.1. We measure the magnetic field dependence of the molecular binding energy and the magnetic moment, refining our knowledge of the resonance parameters. We also demonstrate a peculiar anisotropic expansion effect observed when the molecules are released from the trap and expand freely in the magnetic levitation field. Moreover, we identify an important lifetime limitation that is imposed by the 1064-nm infrared trap light itself and not by inelastic collisions. The light-induced decay rate is found to be proportional to the trap light intensity and the closed-channel fraction of the Feshbach molecule. These observations suggest a one-photon coupling to electronically excited states to limit the lifetime and point to the prospect of loss suppression by optimizing the wavelength of the trapping light. Our results represent important insights and experimental steps on the way to achieve quantum-degenerate samples of DyK molecules and novel superfluids based on mass-imbalanced fermion mixtures.
This thesis reports on experiments with ultracold atomic and molecular quantum gases. Magnetically tunable Feshbach resonances are used to associate diatomic molecules from atomic 87Rb in a three-dimensional optical lattice. In a first experiment, molecules are formed by a sudden jump of the magnetic field to the resonance. This induces coherent atom-molecule oscillations with large amplitude. In another experiment, a dissipative analog of the one-dimensional Tonks-Girardeau gas is realized with molecules in an optical lattice. Inelastic collisions between the molecules lead to particle loss. This interaction is so strong that the system reaches the strongly correlated regime, and the molecules, which are bosons, are forced to behave much like fermions. The strong correlations suppress the molecule loss rate by up to three orders of magnitude.
The production of a quantum gas with strong long - range dipolar interactions is a major scientific goal in the research field of ultracold gases. In their ro - vibrational ground state Li -K dimers possess a large permanent dipole moment, which could possibly be exploited for the realization of such a quantum gas. A production of these molecules can be achieved by the association of Li and K at a Feshbach resonance, followed by a coherent state transfer. In this thesis, detailed theoretical an experimental preparations to achieve state transfer by means of Stimulated Raman Adiabatic Passage (STIRAP) are described. The theoretical preparations focus on the selection of an electronically excited molecular state that is suitable for STIRAP transfer. In this context, molecular transition dipole moments for both transitions involved in STIRAP transfer are predicted for the first time. This is achieved by the calculation of Franck -Condon factors and a determination of the state in which the 6Li - 40K Feshbach molecules are produced. The calculations show that state transfer by use of a single STIRAP sequence is experimentally very well feasible. Further, the optical wavelengths that are needed to address the selected states are calculated. The high accuracy of the data will allow to carry out the molecular spectroscopy in a fast and efficient manner. Further, only a comparatively narrow wavelength tuneability of the spectroscopy lasers is needed. The most suitable Feshbach resonance for the production of 6Li - 40K molecules at experimentally manageable magnetic field strengths is occurring at 155G. Experimentally, this resonance is investigated by means of cross - dimensional relaxation. The application of the technique at various magnetic field strengths in the vicinity of the 155G Feshbach resonance allows a determination of the resonance position and width with so far unreached precision. This reveals the production of molecules on the atomic side of the resonance, thereby establishing the first observation of a many body effect in the crossover regime of a narrow Feshbach resonance. Further, mass dependent factors, with which the equilibration of an induced anisotropic temperature of the trapped particle samples can be described, are experimentally determined for the first time. The type of resonance as well as the measured molecular lifetimes are found to be very well suited for STIRAP transfer. A Raman laser system is designed based on the transition wavelengths and durations of state transfer which are predicted. As the wavelengths of the Raman lasers differ widely but coherence of the light fields is needed, the technical realization of a laser system is challenging. As a part of the laser system, the construction and characterization of a reference optical resonator are presented. Laser frequency stabilization with a linewidth of approximately 500Hz and an Allan deviation below 10−12 for timespans up to several ten seconds are demonstrated. Further, the stabilization of a frequency comb to this reference laser is demonstrated. For the laser spectroscopy of electronically excited Li -K states an interferometric laser frequency stabilization will be used. The device is a commercial design, for which a calibration procedure that enhances the precision by several orders of magnitude is worked out within this thesis. The calibration scheme includes the precise measurement of the stabilization’s wavelength dependent frequency deviations by means of a frequency comb. By the implementation of several calibration steps a remaining frequency deviation of less than 5.7MHz (rms 1.6MHz) in the whole relevant wavelength range 750 - 795 nm is achieved. Only the exceptional precision of the fully calibrated device permits the usage for the Li -K spectroscopy, while the demonstrated wide tuning capability facilitates the completion of the latter in a fast and convenient manner.