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One-Dimensional p-Wave Contact

Kenneth G. Jackson

Published Mar 1, 2024• 0 citations
OpenAlex

Abstract

A proposed method to stabilize p-wave interacting gases and protect from three-body loss is to confine atoms to quasi-one-dimensional (q1D) geometries. A stable p-wave gas in 1D is predicted to have odd-wave scattering and two-body correlations. Loss measurements in lithium have been reported and show strong three-body loss, but such measurements in fermionic potassium have not been reported. In this thesis, we investigate these predictions by studying p-wave interacting fermionic potassium in both 3D and 1D. First, we present a precise characterization of 3D p-wave scattering in $^{40}$K including the role of a low energy shape resonance on scattering. We observe clear nonlinearity of the p-wave binding energy near threshold due to the shape resonance. We study the breakdown of effective range approximation for scattering using coupled-channels calculations. We extract a new 3D parameterization that allows us to precisely calculate quasi-one-dimensional scattering parameters. Then, switching to 1D, we show theoretically how p-wave scattering in quasi-one-dimensional geometries breaks into the expected odd-wave scattering sector for ground band atoms and a newly predicted even-wave sector for interband scattering. For this even-wave scattering, an orbital singlet means that the two-body wavefunction is still antisymmetric, as required by quantum statistics. Next, we present experimental measurements of the two-body contact via rf spectroscopy for both cases. For odd-wave scattering, we find that two-body correlations remain weak outside of the loss-dominated regime making the study of equilibrium odd-wave gases unlikely with our experimental conditions. Loss is similar in magnitude to that in $^6$Li.Even-wave correlations between identical fermions, however, are strong and comparable to the unitary even-wave contact. We compare to theory and note that we have revealed a new paradigm for interactions between identical fermions. Lastly, we conclude with discussion of new possibilities for future research.

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A proposed method to stabilize p-wave interacting gases and protect from three-body loss is to confine atoms to quasi-one-dimensional (q1D) geometries. A stable p-wave gas in 1D is predicted to have odd-wave scattering and two-body correlations. Loss measurements in lithium have been reported and show strong three-body loss, but such measurements in fermionic potassium have not been reported. In this thesis, we investigate these predictions by studying p-wave interacting fermionic potassium in both 3D and 1D. First, we present a precise characterization of 3D p-wave scattering in 40^{40}40K including the role of a low energy shape resonance on scattering. We observe clear nonlinearity of the p-wave binding energy near threshold due to the shape resonance. We study the breakdown of effective range approximation for scattering using coupled-channels calculations. We extract a new 3D parameterization that allows us to precisely calculate quasi-one-dimensional scattering parameters. Then, switching to 1D, we show theoretically how p-wave scattering in quasi-one-dimensional geometries breaks into the expected odd-wave scattering sector for ground band atoms and a newly predicted even-wave sector for interband scattering. For this even-wave scattering, an orbital singlet means that the two-body wavefunction is still antisymmetric, as required by quantum statistics. Next, we present experimental measurements of the two-body contact via rf spectroscopy for both cases. For odd-wave scattering, we find that two-body correlations remain weak outside of the loss-dominated regime making the study of equilibrium odd-wave gases unlikely with our experimental conditions. Loss is similar in magnitude to that in 6^66Li.Even-wave correlations between identical fermions, however, are strong and comparable to the unitary even-wave contact. We compare to theory and note that we have revealed a new paradigm for interactions between identical fermions. Lastly, we conclude with discussion of new possibilities for future research.
We study collisional loss of a quasi-one-dimensional spin-polarized Fermi gas near a p-wave Feshbach resonance in ultracold ^{6}Li atoms. We measure the location of the p-wave resonance in quasi-1D and observe a confinement-induced shift and broadening. We find that the three-body loss coefficient L_{3} as a function of the quasi-1D confinement has little dependence on confinement strength. We also analyze the atom loss with a two-step cascade three-body loss model in which weakly bound dimers are formed prior to their loss arising from atom-dimer collisions. Our data are consistent with this model. We also find a possible suppression in the rate of dimer relaxation with strong quasi-1D confinement. We discuss the implications of these measurements for observing p-wave pairing in quasi-1D.
The two- and three-body correlation functions of the ground state of an optically trapped ultracold spin-12\frac{1}{2}21​ Fermi gas (SFG) in a tight waveguide [one-dimensional (1D) regime] are calculated in the plane of even- and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D ppp-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D sss-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas, a spin-aligned 1D Fermi gas with infinitely attractive ppp-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.
This thesis concerns quasi-two-dimensional (quasi-2D) ultracold Fermi systems with short range interactions. Here, quasi-2D geometries are those that lie between two- and three-dimensions. We study few- and many-body systems composed of two or three distinguishable species of fermions. Of principle interest are the bound states that form in these systems and how these bound states are affected by the quasi-2D geometries. In the first research chapter, we focus on the two-dimensional (2D) regime of quasi- 2D. We begin by developing an effective 2D model of this 2D-like geometry. We use this model to analyse a Fermi system consisting of three fermionic species with equal interactions between all distinguishable pairs. Starting with the few-body problem, we show that there is always a three-body bound state (trimer) in the effective 2D model and that these 2D trimers are stable. This is notably different from the extremely unstable ‘Efimov’ trimers found in three-dimensional (3D) systems. Using a low-density expansion and a variational approach, we investigate the fate of the 2D trimers as the system’s density is increased from the three-body limit to the many-body limit. We find that remnants of trimers can persist in the form of strong three-body correlations in the many-body system. In the second research chapter, we analyse a realistic experimental system of three distinguishable fermions confined to quasi-2D. We develop a model that goes beyond the previous chapter in two regards. Firstly, we allow for unequal interactions between the pairs of fermions. Secondly, we use a full quasi-2D model that is not specific to the 2D-like regime. With this general model, we use the scattering and confinement parameters from experiments on ultracold 6Li atoms to calculate the trimer spectrum across the dimensional crossover from 2D to 3D. We show that one state smoothly evolves from an unstable 3D-like trimer to a 2D-like trimer as the attractive interactions are decreased. We furthermore compute the trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry. This opens the door to realising long-lifetime trimers in ultracold gas experiments and furthermore, the many-body state of trimers predicted in the preceding chapter. vii In the final research chapter, we examine an alternative approach to accessing quasi-2D geometries by using a system of coupled 2D planes. We study the two-component Fermi gas in this geometry, as a preliminary to studying the three-component gas. We find that the interplanar coupling can be tuned to drive a dimensional crossover from 2D to 3D. We study the effect of this dimensional crossover on the two- and many-body systems. In general, we find that two-body correlations are strengthened by weakening the coupling between 2D planes. In the many-body system, we use mean-field theory to find that the critical temperature of pairing is increased by weakening the coupling between 2D planes. This represents a first step towards a more general representation of quasi-2D geometries, namely: A system of coupled quasi-2D planes.
We revisit the confinement-induced ppp-wave resonance in quasi-one-dimensional (quasi-1D) atomic gases and study the induced molecules near resonance. We derive the reduced 1D interaction parameters and show that they can well predict the binding energy of shallow molecules in quasi-1D system. Importantly, these shallow molecules are found to be much more spatially extended compared to those in three dimensions (3D) without transverse confinement. Our results strongly indicate that a ppp-wave interacting atomic gas can be much more stable in quasi-1D near the induced ppp-wave resonance, where most weight of the molecule lies outside the short-range regime and thus the atom loss could be suppressed.
We calculate the binding energy and closed-channel fraction of ppp-wave Feshbach molecules in quasi-one-dimension (quasi-1D) by examining the poles of the ppp-wave SSS matrix. We show that under the right experimental conditions, the quasi-1D ppp-wave molecule behaves like a halo dimer with a closed-channel fraction approaching 0 at resonance and a binding energy following the universal relation ${E}_{b}\ensuremath{\sim}1/{a}_{1\mathrm{D}}^{2}$, where a1D{a}_{1\mathrm{D}}a1D​ is the 1D scattering length. We calculate these experimental conditions for both 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K over a range of transverse confinements. We expect that in this halo dimer regime the three-body loss associated with the ppp-wave Feshbach resonance will be greatly suppressed, potentially allowing for a stable ppp-wave superfluid to be created. For an easy comparison between the three-dimensional and the quasi-1D cases, we provide the same pole analysis of the Feshbach molecules applied to the three-dimensional ppp-wave resonance and show that there is a qualitative difference between the two.
We investigate the three-body recombination rate of a Fermi gas of 6^66Li atoms confined in quasi-1D near a ppp-wave Feshbach resonance. We confirm that the quasi-1D loss rate constant K3K_3K3​ follows the predicted threshold scaling law that K3K_3K3​ is energy independent on resonance, and find consistency with the scaling law K3∝(k a1D)6K_3 \propto (k \, a_{1D})^6K3​∝(ka1D​)6 far from resonance [Mehta et al. Phys. Rev. A 76, 022711 (2007)]. Further we develop a theory based on Breit-Wigner analysis that describes the loss feature for intermediate fields. Lastly we measure how the loss rate constant scales with transverse confinement and find that K3∝VL−1K_3 \propto V_L^{-1}K3​∝VL−1​, where VLV_LVL​ is the lattice depth. Importantly, at our attainable transverse confinements and temperatures, we see a 74-fold suppression of the on-resonant three-body loss rate constant in quasi-1D compared to 3D. With significant further enhancement of the transverse confinement, this suppression may pave the way for realizing stable ppp-wave superfluids.