This thesis reports on calculations of the scattering properties of a variety of ultracold alkali-metal mixtures. In particular, we have calculated the scattering properties of homonuclear mixtures of 85Rb, in a variety of incoming channels, and we have calculated the properties of heteronuclear mixtures of the isotopologues of Rb and Cs, and K and Cs. In general, we are interested in the location and character of Feshbach resonances in these mixtures with a view towards ultracold molecule formation. In 85Rb there is a rich Feshbach structure and potential uses for the resonances that we ﬁnd, in the scattering lengths of the various incoming channels, are discussed. In 85RbCs there is a rich Feshbach structure and the prospects for ultracold molecule formation using this system are detailed. Similarly, we detail the Feshbach resonances of 87RbCs and discuss our results in the context of the successful formation of ultracold ground-state molecules. In the isotopologues of KCs each system has a rich Feshbach structure and we detail the location and width of the resonances, as well as the potential for ultracold molecule formation using each of the isotopes of potassium. In addition to scattering calculations, we have also calculated the location and character of the highest-lying bound states of each system. We have investigated the energy dependence of the scattering length using accurate coupled-channel calculations on 6Li, 39K and 133Cs to explore the behaviour of the eﬀective range in the vicinity of both broad and narrow Feshbach resonances. We present an alternative parametrization of the eﬀective range and further demonstrate that an analytical form of an energy and magnetic ﬁeld-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length. Lastly, we examine the eﬀect of additional external ﬁelds on alkali-metal collisions and discuss how external ﬁelds can be used to manipulate the interaction properties of a system.This thesis reports on calculations of the scattering properties of a variety of ultracold alkali-metal mixtures. In particular, we have calculated the scattering properties of homonuclear mixtures of 85Rb, in a variety of incoming channels, and we have calculated the properties of heteronuclear mixtures of the isotopologues of Rb and Cs, and K and Cs. In general, we are interested in the location and character of Feshbach resonances in these mixtures with a view towards ultracold molecule formation. In 85Rb there is a rich Feshbach structure and potential uses for the resonances that we ﬁnd, in the scattering lengths of the various incoming channels, are discussed. In 85RbCs there is a rich Feshbach structure and the prospects for ultracold molecule formation using this system are detailed. Similarly, we detail the Feshbach resonances of 87RbCs and discuss our results in the context of the successful formation of ultracold ground-state molecules. In the isotopologues of KCs each system has a rich Feshbach structure and we detail the location and width of the resonances, as well as the potential for ultracold molecule formation using each of the isotopes of potassium. In addition to scattering calculations, we have also calculated the location and character of the highest-lying bound states of each system. We have investigated the energy dependence of the scattering length using accurate coupled-channel calculations on 6Li, 39K and 133Cs to explore the behaviour of the eﬀective range in the vicinity of both broad and narrow Feshbach resonances. We present an alternative parametrization of the eﬀective range and further demonstrate that an analytical form of an energy and magnetic ﬁeld-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length. Lastly, we examine the eﬀect of additional external ﬁelds on alkali-metal collisions and discuss how external ﬁelds can be used to manipulate the interaction properties of a system.

Jan 1, 20151 citation

Long-lived fermionic Feshbach molecules with tunable p -wave interactions

Marcel Duda, Xing-Yan Chen, Roman Bause +3 more

Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong $p$ -wave interactions; however, their lifetimes were measured to be short. Here we characterize the $p$ -wave collisions of ultracold fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ Feshbach molecules for different scattering lengths and temperatures. By increasing the binding energy of the molecules, the two-body loss coefficient reduces by three orders of magnitude, leading to a second-long lifetime 20 times longer than that of ground-state NaK molecules. We exploit the scaling of elastic and inelastic collisions with the scattering length and temperature to identify a regime where the elastic collisions dominate over the inelastic ones, allowing the molecular sample to thermalize. Our results provide a benchmark for four-body calculations of molecular collisions and pave the way for investigating quantum many-body phenomena with fermionic Feshbach molecules.Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong $p$-wave interactions; however, their lifetimes were measured to be short. Here we characterize the $p$-wave collisions of ultracold fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ Feshbach molecules for different scattering lengths and temperatures. By increasing the binding energy of the molecules, the two-body loss coefficient reduces by three orders of magnitude, leading to a second-long lifetime 20 times longer than that of ground-state NaK molecules. We exploit the scaling of elastic and inelastic collisions with the scattering length and temperature to identify a regime where the elastic collisions dominate over the inelastic ones, allowing the molecular sample to thermalize. Our results provide a benchmark for four-body calculations of molecular collisions and pave the way for investigating quantum many-body phenomena with fermionic Feshbach molecules.

arXiv:2202.06940Physical Review AMay 31, 20238 citations

Theory of Ultracold Feshbach Molecules

Thomas M. Hanna, Hugo E. L. Martay, Thorsten Köhler

Jun 25, 20091 citation

Feshbach resonances, molecular bound states, and prospects of ultracold-molecule formation in mixtures of ultracold K and Cs

Hannah J. Patel, Caroline L. Blackley, Simon L. Cornish +1 more

We consider the possibilities for producing ultracold mixtures of K and Cs and forming KCs molecules by magnetoassociation. We carry out coupled-channel calculations of the interspecies scattering length for $^{39}\mathrm{KCs}$ , $^{41}\mathrm{KCs}$ , and $^{40}\mathrm{KCs}$ and characterize Feshbach resonances due to $s$ -wave and $d$ -wave bound states, with widths ranging from below 1 nG to 5 G. We also calculate the corresponding bound-state energies as a function of magnetic field. We give a general discussion of the combinations of intraspecies and interspecies scattering lengths needed to form low-temperature atomic mixtures and condensates and identify promising strategies for cooling and molecule formation for all three isotopic combinations of K and Cs.We consider the possibilities for producing ultracold mixtures of K and Cs and forming KCs molecules by magnetoassociation. We carry out coupled-channel calculations of the interspecies scattering length for $^{39}\mathrm{KCs}$, $^{41}\mathrm{KCs}$, and $^{40}\mathrm{KCs}$ and characterize Feshbach resonances due to $s$-wave and $d$-wave bound states, with widths ranging from below 1 nG to 5 G. We also calculate the corresponding bound-state energies as a function of magnetic field. We give a general discussion of the combinations of intraspecies and interspecies scattering lengths needed to form low-temperature atomic mixtures and condensates and identify promising strategies for cooling and molecule formation for all three isotopic combinations of K and Cs.

arXiv:1409.1099Physical Review ASep 25, 201424 citations

Ultracold Feshbach Molecules

Rudolf Grimm, Francesca Ferlaino, Steven Knoop

CRC Press eBooksJun 25, 20092 citations

Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong

p

-wave interactions; however, their lifetimes were measured to be short. Here we characterize the

p

-wave collisions of ultracold fermionic

^{23}\mathrm{Na}^{40}\mathrm{K}

Feshbach molecules for different scattering lengths and temperatures. By increasing the binding energy of the molecules, the two-body loss coefficient reduces by three orders of magnitude, leading to a second-long lifetime 20 times longer than that of ground-state NaK molecules. We exploit the scaling of elastic and inelastic collisions with the scattering length and temperature to identify a regime where the elastic collisions dominate over the inelastic ones, allowing the molecular sample to thermalize. Our results provide a benchmark for four-body calculations of molecular collisions and pave the way for investigating quantum many-body phenomena with fermionic Feshbach molecules.

^{39}\mathrm{KCs}

^{41}\mathrm{KCs}

, and

^{40}\mathrm{KCs}

and characterize Feshbach resonances due to

s

-wave and

d

-wave bound states, with widths ranging from below 1 nG to 5 G. We also calculate the corresponding bound-state energies as a function of magnetic field. We give a general discussion of the combinations of intraspecies and interspecies scattering lengths needed to form low-temperature atomic mixtures and condensates and identify promising strategies for cooling and molecule formation for all three isotopic combinations of K and Cs.