# Bose-Einstein condensates in microgravity

The study of atomic systems freely evolving over long times has a number of interesting applications, including high-precision measurements based on long-time atom interferometry. Microgravity platforms (such as drop-tower facilities, sounding rockets, the International Space Station and dedicated satellite missions) offer a natural environment where such long times can be reached with compact setups in free fall. In order to prevent the size of the atomic cloud from growing excessively, very low expansion rates are required. It is, therefore, necessary to prepare atomic ensembles with very low temperatures making use of laser cooling techniques, which are capable of reaching regimes of a few microkelvin.

Fig. 1: The MAIUS 1 mission was successfully completed on 23 January 2017 and accomplished the generation of the first BEC in space ever. The sounding rocket was launched into a huge parabolic flight in the upper atmosphere, reaching a height of 243 km and providing 6 minutes for performing experiments with ultracold atoms in microgravity conditions. This is a short movie of the rocket launch.

Fig. 2: ZARM's drop tower in Bremen is 146 m high and provides 4.7 s of microgravity conditions (with residual accelerations as small as $$10^{-6} g$$ ) when operating in drop mode and 9.2 s when the capsule is launched in catapult mode.

The temperature can be further reduced through evaporative cooling of the magnetically trapped neutral atoms, and for bosonic species the dilute gas can eventually undergo Bose-Einstein condensation as the ground state becomes occupied by a substantial fraction of the atoms. With all its atoms in the same quantum state, a Bose-Einstein condensate (BEC) after release from the trap is the atomic analogue of a laser pulse, where all the photons are also in the same state. Thanks to that BECs exhibit excellent coherence properties and a narrow momentum distribution. However, the energy associated with the repulsive interaction between the atoms, which is typically the dominant contribution for trapped BECs, is converted into kinetic energy after being released from the trap and additional techniques, such as atomic lensing (briefly described below), need to be employed in order to attain particularly low expansion rates (i.e. low momentum widths of the atomic wave packet).

Besides the atom interferometry aspects, discussed here, in our group we have been developing suitable analytical and numerical tools for investigating (among others) the following topics.

• Release and evolution of BECs prepared with an atom chip:
Taking as an input the currents circulating through the wires of the atom chip and the external Helmholtz coils, the magnetic fields and the corresponding (time-dependent) trap potential felt by the neutral atoms are simulated. The evolution of the BEC both before and after switching off the trap has been studied semi-analytically making use of the time-dependent Thomas-Fermi approximation and compared with exact solutions of the Gross-Pitaevskii equation. The center-of-mass (COM) motion induced by the whole process has also been investigated in detail.
• Atomic lensing:
After release from the trap the energy associated with the repulsive interaction of the atoms, which is the dominant contribution for the trapped BEC, gets converted into kinetic energy. By switching on the trap potential again for a suitable short period of time, most of this kinetic energy becomes potential energy and is removed from the system after the trap is switched off. In this way small momentum widths corresponding to effective temperatures of hundreds of picokelvin or even lower can be achieved. For harmonic traps one can in principle prepare atomic clouds with a narrower momentum width but a larger size (as dictated by Heisenberg's uncertainty principle) by waiting for longer times until the lensing potential is applied. For realistic potentials, however, anharmonicities lead to distortions of the wave packet and this effect becomes more pronounced for larger sizes of the cloud when acted upon by the lensing potential.
In our group we have developed valuable tools for describing the generation of such distortions and exploited them to thoroughly investigate (together with numerical simulations) the effects of anharmonicites in atomic lensing, including also the coupling of the expansion dynamics to the COM motion due to the potential anharmonicities.
• Space atom laser:
An alternative way of out-coupling a trapped BEC (instead of switching off the trap potential) is to induce a resonant transition to a magnetically untrapped state by means of a suitable radio-frequency (RF) field. The atomic analog of a continuous-wave laser can be generated by employing a weak RF field and tuning its frequency so that the transition is resonant for the atoms within an outer shell of the BEC. Under normal laboratory conditions, gravity pulls away the atoms in the untrapped state, which propagate as a more or less narrow beam along the direction of the gravitational field. In contrast, in microgravity the atoms are continuously out-coupled in an expanding spherical shell. The properties of such a "space atom laser" have been extensively investigated in our group and our proposal for its experimental realization in the forthcoming Cold Atom Laboratory (CAL) on the International Space Station has been selected by NASA.
• Bosonic and Bose-Fermi mixtures:
There are plenty of interesting physical phenomena associated with quantum degenerate mixtures of dilute gases and microgravity environments offer excellent conditions for their study, such as the absence of gravitational sag (which would in general differ for different species) and long free evolution times. We have performed detailed analysis of the trapped ground state and its subsequent expansion dynamics for both purely bosonic and Bose-Fermi mixtures with spin polarized fermions. Our main focus has been their role in tests of the equivalence principle with atom interferometry. In that respect, we have been investigating strategies to maximize the overlap between the expanding clouds of the two species (leading to a better suppression of common unwanted contributions, such as those from wavefront distortions, in the differential measurement) as well as ways to control and minimize the differences in their central position and velocity at the beginning of the interferometer sequence, which mimic violations of the equivalence principle in the presence of gravity gradients.

Fig. 3: Absorption images taken after different times of flight (25, 50, 75 and 100 ms respectively) of four different expanding BECs successively created in a single catapult launch. [Credit: H. Ahlers and J. Rudolph (LUH)]

Fig. 4: Density plot of the expanding spherical shell for the space atom laser. By clicking on the image a movie visualizing the rf-outcoupling process predicted by numerical simulations is played (left: trapped BEC, right: space atom laser).

### Contributors

M. Meister, C. Ufrecht, W. Zeller, A. Roura, W.P. Schleich

### Collaborations

The QUANTUS collaboration:
Leibniz Universität Hannover, ZARM/Universität Bremen, Humboldt-Universität Berlin, Johannes Gutenberg Universität Mainz, TU Darmstadt

### Funding

Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Bundesministerium für Wirtschaft und Energie (BMWi) under Grant No. 50WM1556 (QUANTUS IV -- Fallturm)

### References

[1] Van Zoest et al. (the QUANTUS collaboration), Bose-Einstein Condensation in Microgravity, Science 328, 1540 (2010)
[2] Müntinga et al. (the QUANTUS collaboration), Interferometry with Bose-Einstein condensates in microgravity, Phys. Rev. Lett. 110, 093602 (2013)
[3] Aguilera et al. (the STE-QUEST consortium, including A. Roura and W. P. Schleich), STE-QUEST – Test of the Universality of Free Fall Using Cold Atom Interferometry, Class. Quant. Grav. 31, 115010 (2014)
[4] H. Ahlers, H. Müntinga, A. Wenzlawski, M. Krutzik, G. Tackmann, S. Abend, N. Gaaloul, E. Giese, A. Roura, R. Kuhl, C. Lämmerzahl, A. Peters, P. Windpassinger, K. Sengstock, W. P. Schleich, W. Ertmer, E. M. Rasel, Double Bragg interferometry, Phys. Rev. Lett. 116, 173601 (2016)
[5] C. Ufrecht, M. Meister, A. Roura, W. P. Schleich, Comprehensive classification for Bose–Fermi mixtures, New J. Phys. 19, 085001 (2017)