Trapped quantum gases can be cooled to impressively low temperatures 1,2 , but it is unclear whether their entropy is low enough to realize phenomena such as d-wave superconductivity and magnetic ordering 3 . Estimated critical entropies per particle for quantum magnetic ordering are ∼0.3k B and ∼0.03k B for bosons in three-and two-dimensional lattices, respectively 4 , with similar values for Néel ordering of latticetrapped Fermi gases 5 . Here we report reliable single-shot temperature measurements of a degenerate Rb gas by imaging the momentum distribution of thermalized magnons, which are spin excitations of the atomic gas. We record average temperatures fifty times lower than the Bose-Einstein condensation temperature, indicating an entropy per particle of ∼0.001k B at equilibrium, nearly two orders of magnitude lower than the previous best in a dilute atomic gas 2,6 and well below the critical entropy for antiferromagnetic ordering of a Bose-Hubbard system. The magnons can reduce the temperature of the system by absorbing energy during thermalization and by enhancing evaporative cooling, allowing the production of low-entropy gases in deep traps.In many experiments on strongly interacting atomic-gas systems, the low-entropy regime is reached by first preparing a weakly interacting bulk Bose gas at the lowest possible temperature, and then slowly transforming the system to become strongly interacting 7-11 . To discern whether the transformation is adiabatic and to determine indirectly the thermodynamic properties of the strongly interacting system, the system is returned to the weakly interacting regime where relations between temperature, entropy and other properties are known. Therefore, methods to lower entropies and measure temperatures of weakly interacting gases are important for the study of both weakly and strongly interacting atomic-gas systems.In this Letter, we report cooling a Bose gas to a few per cent of the condensation temperature, T c , corresponding to an entropy per particle S/N ≈ 1 × 10 −3 k B , where k B is the Boltzmann constant. Surprisingly, we achieve this low entropy using a standard technique: forced evaporation in an optical dipole trap, which we find remains effective in a previously uncharacterized regime. The lowest temperatures we report are achieved at very shallow final trap depths, as low as 20 nK, set by stabilizing the optical intensity with a longterm fractional reproducibility better than 10 −2 . In addition, we demonstrate and characterize a method of cooling that lowers the entropy without changing the trap depth, possibly allowing the lowentropy regime to be reached or maintained in systems where the trap depth is constrained.Both thermometry and cooling require a means of distinguishing thermal excitations. For example, forced evaporative cooling 12,13 depends on the ability to selectively expel high-energy excitations from the system. Similarly, thermometry of a degenerate quantum gas requires one to identify the excitations that distinguish a zero-temperature from...
We measure the dispersion relation, gap, and magnetic moment of a magnon in the ferromagnetic F = 1 spinor Bose-Einstein condensate of (87)Rb. From the dispersion relation we measure an average effective mass 1.033(2)(stat)(10)(sys) times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. The measured mass is higher than theoretical predictions of mean-field and beyond-mean-field Beliaev theory for a bulk spinor Bose gas with s-wave contact interactions. We observe a magnon energy gap of h × 2.5(1)(stat)(2)(sys) Hz, which is consistent with the predicted effect of magnetic dipole-dipole interactions. These dipolar interactions may also account for the high magnon mass. The effective magnetic moment of -1.04(2)(stat)(8)(sys) times the atomic magnetic moment is consistent with mean-field theory.
The precision of compact inertial sensing schemes using trapped-and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here, we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counter-propagating sound waves within the condensate and use in situ absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of ∼ rad s −1 / √ Hz, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at 10 4 − 10 6 times higher density and in a volume 10 9 times smaller than free-falling atom interferometers.
We observe the condensation of magnon excitations within an F = 1 87 Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a longitudinally spin-polarized gas, allowed to equilibrate to a non-degenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization whereupon they condense. We find magnon condensation to be described quantitatively as the condensation of free particles in an effective potential that is uniform within the ferromagnetic condensate volume, evidenced by the number and distribution of magnons at the condensation transition. Transverse magnetization images reveal directly the spontaneous, inhomogeneous symmetry breaking by the magnon quasi-condensate, including signatures of Mermin-Ho spin textures that appear as phase singularities in the magnon condensate wavefunction.
We demonstrate a two-element oven and Zeeman slower that produce simultaneous and overlapped slow beams of rubidium and lithium. The slower uses a three-stage design with a long, low-acceleration middle stage for decelerating rubidium situated between two short, high-acceleration stages for aggressive deceleration of lithium. This design is appropriate for producing high fluxes of atoms with a large mass ratio in a simple, robust setup.
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