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Thermometry and Cooling of a Bose-Einstein Condensate to 0.02 Times the Critical Temperature

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Thermometry and Cooling of a Bose-Einstein Condensate to 0.02 Times the Critical Temperature Thermometry and cooling of a Bose-Einstein condensate to 0.02 times the critical temperature 1, 1 1, 1 1, 2 Ryan Olf, ∗ Fang Fang, G. Edward Marti, † Andrew MacRae, and Dan M. Stamper-Kurn 1Department of Physics, University of California, Berkeley, California 94720, USA 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Dated: May 21, 2015) Ultracold gases promise access to many-body termine indirectly the thermodynamic properties of the quantum phenomena at convenient length and strongly interacting system, the system is returned to time scales. However, it is unclear whether the the weakly interacting regime where relations between entropy of these gases is low enough to real- temperature, entropy, and other properties are known. ize many phenomena relevant to condensed mat- Therefore, methods to lower entropies and measure tem- ter physics, such as quantum magnetism. Here peratures of weakly interacting gases are important for we report reliable single-shot temperature mea- the study of both weakly and strongly interacting atomic- surements of a degenerate 87Rb gas by imag- gas systems. ing the momentum distribution of thermalized In this Letter, we report cooling a Bose gas to a few magnons, which are spin excitations of the atomic percent of the condensation temperature, Tc, correspond- 3 gas. We record average temperatures as low as ing to an entropy per particle of 10− kB (kB is the Boltz- 0.022(1)stat(2)sys times the Bose-Einstein conden- mann constant), nearly two orders of magnitude lower sation temperature, indicating an entropy per than the previous best in a dilute atomic gas [2, 11]. particle, S/N 0.001 kB at equilibrium, that is Surprisingly, we achieve this low entropy using a stan- well below the≈ critical entropy for antiferromag- dard technique: forced evaporation in an optical dipole netic ordering of a Bose-Hubbard system. The trap, which we find remains effective in a previously un- magnons themselves can reduce the temperature characterized regime. The lowest temperatures we re- of the system by absorbing energy during ther- port are achieved at very shallow final trap depths, as malization and by enhancing evaporative cooling, low as 20 nK, set by stabilizing the optical intensity with 2 allowing low-entropy gases to be produced within a long-term fractional reproducibility better than 10− . deep traps. In addition, we demonstrate and characterize a method Trapped quantum gases can be brought to impres- of cooling that lowers the entropy without changing the sively low temperatures. A single-component Bose gas trap depth, possibly allowing the low entropy regime to was cooled to around 500 pK by adiabatic expansion be reached or maintained in systems where the trap depth [1], and a two-component lattice-trapped Bose gas was is constrained. cooled to 350 pK using a spin demagnetization technique Both thermometry and cooling require a means of dis- [2]. However, the entropies achieved in these systems tinguishing thermal excitations. For example, forced are still much higher than would be required to observe evaporative cooling [12, 13] depends on the ability to se- many-body quantum effects such as magnetic ordering lectively expel high-energy excitations from the system. or d-wave superconductivity of atoms in optical lattices Similarly, thermometry of a degenerate quantum gas re- [3]. Estimated critical entropies required to achieve quan- quires one to identify the excitations that distinguish a tum magnetic ordering of atoms in optical lattices include zero- from a non-zero-temperature gas. Both these tasks S/N 0.3 kB and S/N 0.03 kB for bosons in state- become difficult when S/N, or, equivalently, the fraction ∼ ∼ dependent three- and two-dimensional lattices, respec- of thermal excitations Nth/N, is small [14]. Time-of- tively [4], and similar values for N´eelordering of lattice- flight temperature measurements, in which the gas is re- trapped Fermi gases [5], with lower entropy needed for leased from the trap and allowed to expand before being less strongly interacting gases. imaged, have required Nth/N of at least several percent, In many experiments on strongly interacting atomic- limiting such thermometry of Bose gases to T 0.3 T ≥ c gas systems, the low-entropy regime is reached by first and of Fermi gases to T 0.05 TF , where Tc and TF are preparing a weakly interacting bulk Bose gas at the low- the Bose-Einstein condensation≥ and Fermi temperatures, arXiv:1505.06196v1 [cond-mat.quant-gas] 22 May 2015 est possible temperature, and then slowly transforming respectively. the system to become strongly interacting [6–10]. To dis- We extend thermometry to the deeply degenerate cern whether the transformation is adiabatic and to de- regime of a Bose gas by measuring the momentum dis- tribution of a small number of spin excitations, similar to the co-trapped impurity thermometry commonly em- ployed in Fermi gases [15–18]. Even in a highly degen- ∗ [email protected] † Present address: JILA, National Institute of Standards and erate Bose gas with a vanishingly small non-condensed Technology and University of Colorado, Boulder, Colorado fraction, the minority spin population can be made di- 80309-0440, USA; [email protected] lute enough to remain non-degenerate and thereby carry 2 a Create magnons age the momentum distribution of the magnons. Upon with RF extinguishing the trap light, the gas expands rapidly in Image with light the most tightly confined (vertical) direction, quickly re- Trap depth Trap Time tevap thold ducing the outward pressure within the gas. We then Final trap depth/k (nK) use a sequence of microwave and optical pulses to drive B away atoms not in the m =0 Zeeman state. Finally, 590 ± 40 130 ± 20 35 ± 10 590 ± 40 130 ± 20 25 ± 10 | F i b c we transfer the remaining atoms to an atomic state ( F =2, m =1 ) suitable to two-dimensional magnetic fo- | F i 200 µm cusing [20] so that their transverse spatial distribution, which we image, closely reflects their initial transverse ve- T=1.6 nK locity distribution. The majority gas is probed by imag- ing mF =0 atoms immediately after the application of an RF| pulse.i The advantage of using incoherent spin excitations to T=16.2 nK measure temperature is exhibited in Fig. 1, which com- pares the momentum distribution of the majority gas (b) to that of the magnons (c). At T . 0.3 Tc, the non- T=54.4 nK condensed fraction of the majority gas is obscured by the Integrated column density column Integrated condensed fraction, the distribution of which is broad- -10 -5 0 5 10 -10 -5 0 5 10 Wavenumber (µm-1) ened owing to interactions and imaging resolution. In contrast, the temperature can be easily extracted from FIG. 1. Magnon thermometry. (a) Magnons are created the momentum distribution of the thermalized minority- and decohere rapidly in a non-degenerate spinor Bose gas at spin gas. Temperatures extracted from the magnons an intermediate trap depth. Forced evaporative cooling to a [Fig. 2(a)] agree with those from the majority-spin dis- final, variable, trap depth reduces the temperature and the tribution under conditions where both can be measured. majority gas undergoes Bose-Einstein condensation. Images At lower temperatures, the magnon thermometer allows and corresponding integrated line profiles of the momentum measurements in a hitherto unmeasurable regime. distribution of the majority (b) and magnon gas (c) are each Our measurements reveal that forced evaporative cool- shown at three different final trap depths. Line profiles are ing produces Bose gases with extremely low temper- shown offset for clarity. A condensate obscures the momen- ature and entropy. At the lowest trap-depth setting tum distribution of the non-condensed fraction of the majority gas, especially at low temperatures. In contrast, the magnons (dashed circles, Fig. 2), we measure an average gas tem- can have have little to no condensed fraction, allowing non- perature of T = 1.04(3)stat(7)sys nK, corresponding to condensed magnons to be identified and the temperature de- T/Tc = 0.022(1)(2) where Tc is calculated using the mea- termined. sured atom number, N = 8.1 105, and optical trap fre- × quencies. For this gas, kBT/µ 0.07, with µ the chem- ical potential, meaning that thermal≈ excitations in the a large entropy and energy per particle. Furthermore, the high density region of the condensed gas (in the major- minority spins that we use—magnons within a ferromag- ity spin state) are predominantly phonons. Measurement netic spinor Bose-Einstein condensate—support a higher procedures, error estimates, and calculations of Tc and µ Nth than the majority spins because of their free-particle are detailed in Methods. density of states [19], increasing the signal of the temper- We observe that evaporative cooling is highly efficient ature measurement. Performing spin-selective measure- with respect to particle loss in the regime µ/kB < T < Tc ments on the minority spins allows the gas temperature [Fig. 2(b)]. When T < µ/kB, the cooling efficiency re- to be readily determined. duces, consistent with the fact that the chemical poten- Our procedure to measure temperatures is illustrated tial accounts for a non-negligible amount of the energy in Fig. 1(a). Experiments begin with spin-polarized 87Rb carried away by each atom lost to evaporation. The rele- in the F =1, m = 1 state confined in an anisotropic vance of the chemical potential in evaporation is also indi- | F − i optical dipole trap and cooled to just above quantum cated in Fig. 2(a) by the observation that η U/(kBT ), degeneracy by forced evaporation to an intermediate trap the ratio of trap depth to thermal energy,≡ increases at depth.
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