Two- and three-body contacts in the unitary Bose gas

Abstract

In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Here, using Ramsey interferometry, we study coherent evolution of the resonantly interacting Bose gas, and show that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics, and provide a direct measurement of the associated three-body contact.A fundamental challenge in many-body quantum physics is to connect the macroscopic behaviour of a system to the microscopic interactions between its constituents. In ultracold atomic gases the strength of interactions is most commonly characterised by the s-wave scattering length a, which can be tuned via Feshbach resonances [1]. On resonance a diverges and one reaches the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases [2][3][4], while the unitary Bose gas represents a new experimental frontier [5][6][7][8][9][10].In these systems, universal properties of the short-range particle correlations imply universal thermodynamic relations between macroscopic observables such as the momentum distribution, energy, and the spectroscopic response [11][12][13][14][15][16][17][18][19]. In the case of (mass-balanced) two-component Fermi gases, at the heart of these relations is a single fundamental thermodynamic parameter, the two-body contact density C 2 , which measures the strength of two-particle correlations. However, the case of the Bose gas is more subtle. In this system Efimov physics gives rise to three-body bound states [20][21][22][23][24][25][26], and more generally introduces three-particle correlations that cannot be deduced from the knowledge of pairwise ones [17][18][19]27]. The implication for many-body physics is that complete understanding of the macroscopic coherent phenomena requires knowledge of both C 2 and its three-body analogue C 3 [17][18][19].The relative importance of three-particle correlations generally grows with the strength of interactions. At moderate interaction strengths C 2 was measured spectroscopically, but C 3 was not observed [24]. However, the momentum distribution of the unitary Bose gas [7] suggested deviations from two-body physics [19,28].Here we interferometrically measure both C 2 and C 3 in a resonantly interacting thermal Bose gas, and find excellent agreement with theoretical predictions. The idea of our experiment is illustrated in Fig. 1. We perform radio-frequency (RF) Ramsey interferometry on a gas of atoms with two internal (spin) states, ↑ and ↓, and use a magnetic Feshbach resonance to enhance ↑↑ interactions, while both ↑↓ and ↓↓ interactions are negligible. For a measurement at a given magneticRamsey interferometry of a many-body system. The first π/2 pulse pu...

Efimov–van der Waals universality for ultracold atoms with positive scattering lengths

“…Although the values for a +,1 in Table III are likely to suffer from thermal effects (the condition |a| ≪ a c = / √ mk B T [37] ensuring the absence of thermal effects is not strictly satisfied), our finite temperature calculations covering the range of temperatures relevant for the experiments (see Table I) indicate that thermal effects might lead to no more than a 10% variation from the zero temperature result. We also note that for 7 Li and 39 K the resonances are substantially less broad than the ones for 133 Cs (see Ref. [13]), thus opening up the possibility of finite-width effects as responsible for the deviations among the experimental data in Table III.…”

“…For instance, the value for a * ,1 for 133 Cs from Ref. [55], as well as the results for 7 Li from Ref. [56], were obtained using a Feshbach resonance that is not well separated from another nearby resonance, possibly affecting the observed value for a * ,1 .…”

“…The recent theoretical and experimental progress in the exploration of ultracold quantum gases in the strongly interacting regime have largely established the relevance of the three-body Efimov physics [1][2][3] for the understanding of both dynamics and stability of such systems [4][5][6][7][8][9][10][11][12]. The control of interatomic interactions through magnetic-field dependent Feshbach resonances [13] allows for dramatic changes in the s-wave two-body scattering length, a, making it possible to tune systems to the vastly different collective (mean-field) regimes of attractive, a < 0, and repulsive, a > 0 interactions.…”

Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

“…Recent experimental studies allow to access in particular the high-momentum region of the momentum distribution [14,15]. The high-momentum tails of the momentum distribution n(k) of a gas with contact interactions display a universal n(k) ∝ 1/k 4 decay [16,17], which originates from the zero-range interaction potential: bosons with contact interactions have a cusp in the many-body wavefunction whenever the relative distance of each pair of particles vanishes.…”

Quasiparticle Energy in a Strongly Interacting Homogeneous Bose-Einstein Condensate

“…We produce quasipure homogeneous 39 K BECs of N = (50 − 160) × 10 3 atoms in a cylindrical optical box trap of variable radius, R = (15 − 30) µm, and length, L = (30 − 50) µm. The BEC is produced in the lowest hyperfine state, which features a Feshbach resonance centred at 402.70(3) G [30]. By varying N , L, and R, we vary n in the range (0.2 − 2.0) × 10 12 cm −3 .…”