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Physical Review A

Experimental conditions for obtaining halo p -wave dimers in quasi-one-dimension

Francisco Fonta, Kenneth M. O’Hara

Published Oct 19, 2020• 9 citations
Publisher

Abstract

We calculate the binding energy and closed-channel fraction of $p$-wave Feshbach molecules in quasi-one-dimension (quasi-1D) by examining the poles of the $p$-wave $S$ matrix. We show that under the right experimental conditions, the quasi-1D $p$-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 ${a}_{1\mathrm{D}}$ is the 1D scattering length. We calculate these experimental conditions for both $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ over a range of transverse confinements. We expect that in this halo dimer regime the three-body loss associated with the $p$-wave Feshbach resonance will be greatly suppressed, potentially allowing for a stable $p$-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 $p$-wave resonance and show that there is a qualitative difference between the two.

DOI
10.1103/physreva.102.043319

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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 Eb\ensuremath∼1/a1D2{E}_{b}\ensuremath{\sim}1/{a}_{1\mathrm{D}}^{2}Eb​\ensuremath∼1/a1D2​, 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 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 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.
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.
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 the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale ${a}_{\ensuremath{\perp}}$. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length aaa and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​. In the tightly bound ``dimer limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{\infty}$, we find bad=0{b}_{\mathit{ad}}=0bad​=0 and aad{a}_{\mathit{ad}}aad​ is linked to the 3D atom-dimer scattering length. In the weakly bound ``BCS limit'' ${a}_{\ensuremath{\perp}}∕a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: aad{a}_{\mathit{ad}}aad​ and bad{b}_{\mathit{ad}}bad​ depend both on ${a}_{\ensuremath{\perp}}∕a$ and on a parameter R∗{R}^{*}R∗ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.
We derive one-dimensional effective Hamiltonians for spin-orbit-coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For an energy regime around the two-body bound-state energy, the effective Hamiltonian takes a two-channel form, where the populations in transverse excited levels are described by dressed molecules in the closed channel. For an energy regime slightly above the continuum threshold, the effective Hamiltonian takes a single-channel form, where low-energy physics is governed by the one-dimensional interacting strength determined by three-dimensional scattering length and transverse confinement. We further discuss the effect of spin-orbit coupling and effective Zeeman field on the position of confinement-induced resonances and show that these resonances can be understood as Feshbach resonances between the threshold of the transverse ground state and the two-body bound state associated with the transverse excited states. We expect that the shift of confinement-induced resonances can be observed under present experimental technology at attainable temperatures.