Measurements of Tan’s Contact in an Atomic Bose-Einstein Condensate

Abstract

A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with delta-function interactions. We report on measurements of the contact, using RF spectroscopy, for an 85 Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short timescales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In investigating this issue, we have located an Efimov resonance for 85 Rb atoms with loss measurements and thus determined the three-body interaction parameter. In our contact spectroscopy, in a region of observable beyond-mean-field effects, we find no measurable contribution from three-body physics.Systems with strong quantum correlations represent a frontier in our understanding of the complex quantum systems found in nature, and atomic Bose-Einstein condensates (BEC) provide a versatile system in which to explore beyond mean-field physics. Ultracold atoms experience two-body, short-range interactions that are well described theoretically by a delta-function pseudopotential characterized by an s-wave scattering length a. In the simplest BEC experiments the values of a and of the density n are such that interactions are too weak, compared to the kinetic energy cost of correlations, to take the gas out of the mean-field regime. The presence of a lattice potential can greatly suppress this kinetic energy cost, thus freeing the system to explore a much richer portion of many-body state space [1]. The application of an external lattice potential, however, imposes an artificial orderliness not found in bosons in the wild. To explore strong interactions in a more naturalistic bulk three-dimensional gas, one can increase a by means of a magnetic-field-tunable Feshbach scattering resonance [2]. Such efforts are motivated for instance by a desire to make better conceptual connections to the iconic strongly correlated fluid, liquid helium.In practice it has proven difficult to study atomic BEC with increasing a and only a few experiments have measured beyond-mean-field interaction effects in these systems [3][4][5]. The difficulty comes from the fact that an increase in a is accompanied by a dramatic increase in the rate of inelastic three-body processes [6,7]. This leads to large losses and significant heating of the trapped gas on a timescale similar to that for global equilibrium of the trapped cloud. Probes of the gas that require global equilibrium, such as measurements of the density distribution or the amplitude or frequency of collective density oscillations in a trap, are therefore limited to systems that are only modestly out of the mean-field regime. Our strategy for exploring BEC with larger interaction strengths is to start from an equilibrated weakly interacting gas, change the interaction strength relatively quickly, forsa...

Universal dynamics of a degenerate unitary Bose gas

“…In addition, we note that on resonance, the shallow bound state that exists for finite positive a disappears, so that loss requires atoms to decay to deeply bound molecular states [29]. For 85 Rb atoms, the previous experimental observation of a relatively narrow, and therefore long-lived, Efimov resonance (characterized by a dimensionless width, η = 0.057 ≪ 1) [11] is indicative that atoms close together do not decay instantaneously to deeply bound molecular states.…”

“…For bosonic atoms, however, this route to strong interactions is stymied by the fact that three-body inelastic collisions increase as a to the fourth power [21][22][23]. This circumstance has limited experimental investigation of Bose gases with increasing interaction strength to studying either non-quantum-degenerate gases [24,25] or BECs with modest interaction strengths (na 3 < 0.008, where n is the atom number density) [9][10][11][12].The problem is that the loss rate scales as n 2 a 4 while the equilibration rate scales as na 2 v, where v is the average velocity. Thus, it would seem that the losses will always dominate as a is increased to ∞.…”

“…The microscopic structure of the first-discovered quantum fluid, superfluid liquid helium, is difficult to access due to limited experimental probes. While an ultracold atomic Bose gas with tunable interactions (characterized by its scattering length, a) had been proposed as an alternative strongly interacting Bose system [1][2][3][4][5][6][7][8] , experimental progress [9][10][11][12] has been limited by its short lifetime. Here we present time-resolved measurements of the momentum distribution of a Bose-condensed gas that is suddenly jumped to unitarity, i.e.…”

Efimov-driven phase transitions of the unitary Bose gas

“…This is assured through a parameter, the three-body hard core R 0 , that bounds from below the energies of the Efimov states. In cold-atom systems, this parameter is on the order of the van der Waals length l vdW [17][18][19] . Experimental coldatom systems are metastable, and particles disappear from the trap into deeply-bound states via the notorious three-body losses.…”

Comparing and contrasting nuclei and cold atomic gases

“…We denote this threshold a − . The surprising result is that measurements on different atoms and using different Feshbach resonances yield a − /r vdW ∼ −9.1 to within about 15% accuracy (Berninger et al 2011, Wild et al 2012, Knoop et al 2012). This implies that there is some generic universality even in the three-body parameter which cannot be captured by simple zero-range models that need the ρ 0 supplied from elsewhere.…”