Evidence for universal relations describing a gas with p-wave interactions

Abstract

Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with s-wave symmetry, i.e., without relative angular momentum.We report measurements of two new physical quantities, the "p-wave contacts", and present evidence that they encode the universal aspects of p-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of 40 K, in which s-wave interactions are suppressed by polarising the sample, while p-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive p-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant p-wave quantum gas. 1 arXiv:1505.08151v4 [cond-mat.quant-gas] 13 Apr 2016 A fundamental question provoked by observation of natural systems is how macroscopic and collective properties depend on microscopic few-body interactions. Ultracold neutral atoms provide a model system in which to explore this question, since in certain conditions,few-body interactions can be tuned and characterised precisely. Over the last decade, a direct link has been made in these systems between thermodynamic properties and the underlying isotropic (s-wave) interactions. At the centre stage is a quantity called the "contact" [1][2][3][4][5][6], which describes how the energy of a system changes when the interaction strength is changed. Surprisingly, the contact is also the pivot of a set of universal relations, that constrain numerous microscopic properties, including the two-particle correlation function at short range. These relations apply regardless of temperature, density, or interaction strength [1-3, 5], to fermions and bosons [7][8][9], and in one-, two-, and three-dimensional systems [7,[10][11][12]. Contact relations have also been extended to Coulomb gases [13] and neutron-proton interactions [14]. Despite the breadth of this discussion, measurements of the contact have so far been restricted to systems with s-wave interactions.In general, the relative wave function of any pair of particles can be decomposed into components with angular momentum equal to an integer multiple of quanta. In a spinpolarised Fermi gas, quantum statistics forbids short-range interactions with even values of . Therefore, the first allowed scattering channel has = 1 (p-wave), which is typically weak due to the centrifugal barrier (see Fig. 1): the scattering cross section decreases with the square of...

Fermion superfluid with hybridized s- and p-wave pairings

“…Indeed, in a very recent experiment [3], a steady state with strong p-wave correlations has been achieved in a Fermi gas at a low temperature T = 0.2T F (T F is the Fermi temperature) within a time scale of ∼ 0.5ms. It is thus hopeful that pairing physics can be explored near a p-wave FR at lower temperatures, where a steady state with interesting pairing correlations arXiv:1512.09313v2 [cond-mat.quant-gas] 8 Jan 2016…”

“…The background color denotes the spin polarization P = (n ↑ − n ↓ )/(n ↑ + n ↓ ). associated with the p + ip pairing symmetry, reminiscent of the A phase in 3 He [16,17].…”

“…In recent years, ultracold Fermi gases have emerged as an excellent platform for the study of fermion superfluid in the strong-coupling regime via the Feshbach resonance (FR) technique [1]. Apart from the widely explored s-wave FRs, the p-wave FRs have also been realized in ultracold Fermi gases of 40 K [2,3] or 6 Li [4] atoms. The s-and p-wave FRs are associated with distinct fermion superfluids.…”

Multichannel molecular state and rectified short-range boundary condition for spin-orbit-coupled ultracold fermions near p -wave resonances

“…Besides s-wave, the p-wave interacting atomic gases have also attracted great attention in recent years [8,27], in particular, in view of the very recent explorations of universal properties near p-wave resonance [28][29][30][31]. In this work, we study the interplay of SOC and strong pwave interaction to the short-range and long-range twobody physics.…”

“…Despite the negligible short-range consequence, SOC can greatly change the long-range (low-energy) scattering properties from near the threshold [13,14,16] to intermediate energy regime [16][17][18]. Moreover, with conventional s-wave models it has been found that SOC can induce shallow molecules [19] and universal trimers [20,21] more easily, and lead to various fascinating many-body phenomena in both bosons and fermions atomic systems [22][23][24][25][26].Besides s-wave, the p-wave interacting atomic gases have also attracted great attention in recent years [8,27], in particular, in view of the very recent explorations of universal properties near p-wave resonance [28][29][30][31]. In this work, we study the interplay of SOC and strong pwave interaction to the short-range and long-range twobody physics.…”