Bose-Einstein Condensation of Strontium

Figure 1: The SrBEC team. From left to right: Bo Huang, Meng Khoon Tey, Rudolf Grimm, Florian Schreck (Author), and Simon Stellmer



[This is an invited article based on the recently published work of the author and his collaborators -- 2Physics.com]




Author: Florian Schreck

Affiliation: Institut für Quantenoptik und Quanteninformation (IQOQI), Austria
Link to the 'Ultracold Atoms and Quantum Gases' Group >>

Atoms are particles as well as waves. The wave nature of atoms becomes evident when cooling a gas of bosonic atoms to extremely low temperatures. The de Broglie wavelength describing the atomic wave packets grows and as soon as it exceeds the interatomic spacing, the gas undergoes a phase-transition and enters a collective state of matter, known as Bose-Einstein condensate (BEC). This behavior was predicted in 1924 by Bose and Einstein and realized for the first time in 1995 in gases of alkali-metal atoms [1, 2, 3]. Research on these degenerate quantum gases has since grown strongly and has now connected to many other fields as, for example, condensed-matter physics, molecular physics and precision measurements.

Since then, ten elements have been Bose-condensed: all stable alkali-metal atoms and hydrogen, metastable helium, chromium, ytterbium [4] and very recently calcium [5]. Oftentimes new isotopes cooled to quantum degeneracy have, with their unique properties, opened the doors to the investigation of novel phenomena. Atoms with two electrons in their outer shell, as ytterbium and the alkaline-earth elements, have properties unlike any other of the condensed species: a non-magnetic ground-state (for bosonic isotopes), metastable states and a combination of broad and narrow linewidth optical transitions. This has made these elements, especially ytterbium and strontium, prime choices for neutral atom optical clocks. In addition, numerous proposals employ these properties to realize quantum simulation and computation schemes, mHz-linewidth lasers or to probe the time dependence of natural constants.

These applications either rely on or would benefit from the availability of quantum degenerate samples. Already ten years ago, strontium atoms have been cooled to near quantum degeneracy [6], but a BEC could not be reached. The problem resided in the last cooling stage used in all experiments that have produced degenerate quantum gases: evaporative cooling. This cooling process works by removing hot atoms from the sample and using elastic collisions to rethermalize the remaining gas at a lower temperature. For strontium evaporative cooling worked very badly: the most abundant isotope, ⁸⁸Sr with 83% abundance, essentially does not collide. ⁸⁶Sr with 10% abundance has the opposite problem: the atoms collide so strongly that often molecules are formed, releasing the molecular binding energy, which leads to heating and the loss of atoms. Sr has yet another bosonic isotope: ⁸⁴Sr with only 0.56% natural abundance. Apparently for this reason nobody had undertaken experiments using this isotope.

However, we had experience working with low abundance isotopes and took a closer look at ⁸⁴Sr. We asked Roman Ciuryło to calculate the scattering properties of ⁸⁴Sr by scaling the known properties of the abundant isotopes with the mass. Based on measurements by Thomas Killians group he deduced an elastic scattering cross section in the Goldilocks zone: neither too small nor too big. This was shortly afterwards confirmed by two other groups [7, 8]. Therefore we decided to make ⁸⁴Sr our main approach to Sr BEC.

To overcome the low natural abundance, a combination of Sr properties turned out to be very beneficial. To produce a sample of cold Sr atoms suitable for evaporative cooling, an atomic beam is slowed and then held and cooled in a magneto-optical trap (MOT) using laserlight near-resonant with a broad-linewidth transition. A small fraction of the atoms in the excited state of that transition will not decay back to the ground-state, but to a metastable state with a lifetime of several minutes. Atoms in this state are magnetic and can be trapped in the quadrupole magnetic field used for the MOT. Within 10 seconds we can accumulate about 100 million atoms in this state, overcoming the low natural abundance and giving us enough material for evaporative cooling.

Temperature and density achievable in a MOT depend on the linewidth of the transition used. Strontium has also a narrow-linewidth transition that is suitable for a MOT. It is too narrow to allow slowing of an atomic beam or capture of atoms from that beam, but it can be used to further cool the atoms accumulated in the metastable state (after optically pumping them back to the ground-state). The figure of merit for a cooling process with the goal to reach BEC is phase-space density, the product of density and the de Broglie wavelength cubed. The phase-transition to BEC will occur if the phase-space density exceeds 2.6. For alkali-metal atoms, only one MOT transition exists, which allows to obtain phase-space densities on the order of 10^-6. The combination of broad-linewidth and just perfectly sized narrow-linewidth transition in strontium allows to achieve remarkably high phase-space densities of 10^-2 already after the MOT stage. This means that only very little evaporative cooling is required to obtain quantum degeneracy.

For evaporative cooling, the atoms have to be held in a conservative potential. Atoms in the ground-state have no magnetic moment, so a magnetic trap can not be used. We confine them using a so-called optical dipole trap, which consists of two crossed infrared laser beams. About one million atoms are loaded into the crossing region after switching off the MOT. Evaporative cooling proceeds now by letting hot atoms escape from the trap and waiting for the remaining atoms to thermalize. To force evaporation to continue at ever lower temperatures, the potential depth is lowered over the course of a few seconds. We knew that the elastic scattering properties of ⁸⁴Sr would be ideal for evaporative cooling, but it was impossible to predict the inelastic scattering properties that can lead to detrimental atom loss and heating. To our great pleasure we discovered that inelastic processes were very weak. Evaporative cooling worked the first time we tested it and only minutes later we created the first Bose-Einstein condensate of strontium.

Figure 2: Density distribution of strontium atoms released from a trap. To the left a thermal sample is shown. Further cooling results in the appearance of a dense and cold Bose-Einstein condensate in the middle of the cloud. Finally the thermal component is too small to be detectable.

Figure 3: Expansion of a ⁸⁴Sr BEC from an elongated trap. The repulsion between the atoms leads to a faster expansion along the initially strongly confined directions. The sequence of images shows the temporal evolution in 5ms steps [Ref: Physical Review Letters, 103, 200401 (2009)]

Figure 2 shows images of the density distributions of clouds of ⁸⁴Sr atoms across the phase transition from a thermal cloud to a pure BEC. As soon as the phase-transition is crossed, a dense central peak appears, the BEC. Figure 3 highlights another property of the BEC: after release from the trap it expands fastest along the direction in which it was initially strongest confined leading to a disk-shaped density distribution, shown here from the side. Thermal atoms would expand isotropically and show a spherical density distribution.

About two weeks after we had achieved BEC of Sr [9], the group of Thomas Killian arrived at the same goal [10]. It is clear from both experiments that BEC of Sr is very robust. Simple scaling up of the volume of the optical dipole trap should result in BECs in excess of one million atoms. The two other species with two electrons in the outer shell that have been Bose-condensed, Yb and Ca, have so far only produced relatively small BECs of up to 6 X 10⁴ atoms. This puts Sr in a prime position for experiments with BECs of two-electron systems.

Using sympathetic cooling it should be possible to cool also the other Sr isotopes to quantum degeneracy. ⁸⁸Sr is nearly non-interacting, which would be useful for precision sensors, for example force sensors. The fermionic isotope ⁸⁷Sr has a nuclear magnetic moment, which can be used to store quantum information. It is at the heart of proposals for quantum computation and is the key to the study of a new class of many-body systems. Sr₂ molecules can be created and used to measure the stability of fundamental constants. Cooling of the alkali-metal rubidium is compatible with the scheme employed for Sr. SrRb ground-state molecules would possess both, an electric and a magnetic dipole moment. This can be used to design many-body systems with spin-dependent long range interactions.

It will be exciting to explore all the new possibilities opened up by the Bose-Einstein condensation of strontium.

References
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