We create atom-molecule dark states in a degenerate Fermi gas of $^{6}\mathrm{Li}$ in both weakly and strongly interacting regimes using two-photon Raman scattering to couple fermion pairs to bound molecular states in the ground singlet and triplet potential. Near the unitarity point in the BEC-BCS crossover regime, the atom number revival height associated with the dark state abruptly and unexpectedly decreases and remains low for magnetic fields below the Feshbach resonance center at 832.2 G. With a weakly interacting Fermi gas at 0 G, we perform precision dark-state spectroscopy of the least-bound vibrational levels of the lowest singlet and triplet potentials. From these spectra, we obtain binding energies of the ${v}^{\ensuremath{'}\ensuremath{'}}=9$, ${N}^{\ensuremath{'}\ensuremath{'}}=0$ level of the $a({1}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+})$ potential and the ${v}^{\ensuremath{'}\ensuremath{'}}=38$, ${N}^{\ensuremath{'}\ensuremath{'}}=0$ level of the $X({1}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+})$ potential with absolute uncertainty as low as 20 kHz. For the triplet potential, we resolve the molecular hyperfine structure.
We create atom-molecule dark states in a degenerate Fermi gas of 6Li in both weakly and strongly interacting regimes using two-photon Raman scattering to couple fermion pairs to bound molecular states in the ground singlet and triplet potential. Near the unitarity point in the BEC-BCS crossover regime, the atom number revival height associated with the dark state abruptly and unexpectedly decreases and remains low for magnetic fields below the Feshbach resonance center at 832.2 G. With a weakly interacting Fermi gas at 0 G, we perform precision dark-state spectroscopy of the least-bound vibrational levels of the lowest singlet and triplet potentials. From these spectra, we obtain binding energies of the v\ensuremath′\ensuremath′=9, N\ensuremath′\ensuremath′=0 level of the a(13\ensuremathΣu+) potential and the v\ensuremath′\ensuremath′=38, N\ensuremath′\ensuremath′=0 level of the X(11\ensuremathΣg+) potential with absolute uncertainty as low as 20 kHz. For the triplet potential, we resolve the molecular hyperfine structure.
This thesis describes a suite of experimental tools and spectroscopic measurements performed on ultracold ⁶Li molecules. The aim is to create the necessary ingredients for the coherent transfer of the population of ultracold, weakly bound, Feshbach molecules of ⁶Li to deeply bound ro-vibrational levels, making the eventual creation of a Bose-Einstein condensate (BEC) of ground state lithium dimers a reality at the University of British Columbia. Some of the technological milestones include the development of a unique laser system consisting of two Ti:Sapphire lasers frequency stabilized to a femtosecond frequency comb as well as the demonstration of the first in Canada BEC of Feshbach molecules. To determine a suitable path for the coherent transfer using stimulated Raman adiabatic passage (STIRAP) we measure the binding energies of the vibrational levels v''=20-26 of the c(1³Ʃ+g) and v''=29-35 of the A(1¹Ʃ+u) excited states of lithium dimers by the photoassociation of a degenerate Fermi gas of 6Li atoms, achieving accuracy of 600 kHz. For each vibrational level of the triplet potential, we resolve the rotational structure using a Feshbach resonance to enhance the photoassociation rates from p-wave collisions. We also, for the first time, determine the spin-spin and spin-rotation interaction constants for this state. Finally, we are the first to demonstrate exotic dark states in quantum gases of fermionic lithium where atom-molecule coherence is produced between a deeply bound singlet (or triplet) molecular level and atomic pairs in a weakly interacting Fermi gas at zero gauss or in the BEC-BCS crossover regime (i.e. Feshbach molecules or BCS-like pairs). We observe an abrupt and unanticipated change of the classic EIT signature (Electromagnetically Induced Transparency) of the dark-state (i.e. the suppression of single photon absorption to the excited state) in the vicinity of the broad Feshbach resonance at 832.2 gauss potentially indicating new physics not previously considered.
The pairing of fermionic particles is an essential ingredient of superconductivity and of the superfluidity of 3He. While such phenomena are accurately described by BCS theory in the limit of weak pairing strength, a complete understanding remains elusive when pairing strength is increased, such as in high temperature superconductors. We create ultracold gases of trapped fermionic 6Li atoms, through which we directly observe fermionic pairing. In our system, there are no impurities whatsoever, and parameters such as the number and temperature of the trapped atoms are precisely and independently controlled. In addition, a Feshbach resonance enables the continuous tuning of interaction strength and sign between the paired atoms. This control allows us to observe the smooth crossover of a molecular Bose Einstein condensate (MBEC) to a superfluid of weakly interacting Cooper pairs. With these tools, we have performed several fundamental measurements of pairing in fermionic systems.\nWe use optical molecular spectroscopy to precisely measure the closed-channel contribution to the many body state of paired 6Li atoms within a broad Feshbach resonance. The magnitude of this contribution is small, and supports the concept of universality for the description of broad Feshbach resonances. Moreover, the dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover, and for the first time, into the weakly interacting BCS regime.\nWe also prepare a polarized Fermi gas with unequal numbers of two spin states of 6Li atoms. The real-space densities of the polarized, strongly-interacting, two-component Fermi gas reveal two low temperature regimes. At the lowest temperatures, the gas separates into a phase with a uniformly paired superfluid core surrounded by a shell of normal, unpaired atoms. This phase separation is accompanied by a spatial deformation of the core. At higher temperatures, the uniformly paired core persists, though it does not deform. This temperature dependence is consistent with a tri-critical point in the phase diagram. These measurements of pairing in a polarized Fermi gas are relevant to predictions of exotic phases of quark matter and magnetized superconductors.
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).
We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold 6Li and 40K atoms across a wide Feshbach resonance. The background scattering lengths for 6Li and 40K have opposite signs, which lead to very different behaviors for these two types of atoms. For 40K, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For 6Li, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of 40K, there is a quantum phase transition at zero temperature from the superfluid to the normal Fermi gas at the positive detuning of the magnetic field where the s-wave scattering length passes its zero point. For 6Li, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give a detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.
The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics
We employ radio-frequency spectroscopy on weakly bound (6)Li(2) molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold (6)Li atoms based on a multichannel quantum scattering model. We determine the singlet and triplet scattering lengths to be a(s) = 45.167(8)a(0) and a(t) = -2140(18)a(0) (1a(0) = 0.052 917 7 nm), and the positions of the broad Feshbach resonances in the energetically lowest three s-wave scattering channels to be 83.41(15), 69.04(5), and 81.12(10) mT.