Free-fall expansion of finite-temperature Bose-Einstein condensed gas in the non Thomas-Fermi regime

We report on our study of the free-fall expansion of a finite-temperature BoseEinstein condensed cloud of Rb. The experiments are performed with a variable total number of atoms while keeping constant the number of atoms in the condensate. The results provide evidence that the BEC dynamics depends on the interaction with thermal fraction. In particular, they provide experimental evidence that thermal cloud compresses the condensate. PACS numbers: 03.75.Hh, 03.75.Kk Submitted to: J. Phys. B: At. Mol. Phys. Anisotropic expansion of a condensate after its release from a trap is a well known feature of the Bose-Einstein condensed state [1, 2] and is also observed in non-condensed Bose gases [3, 4] and in degenerate Fermi gases [5, 6]. At low but finite temperatures, after switching off the trap potential, free expansion of a diluted Bose-Einstein condensed gas results in spatial separation of the thermal and condensed phases [7]. This behavior allows identification of the condensed and thermal fractions through absorption imaging. So far, most of the experimental work on the condensed gases was concentrated on samples with large number of atoms at very low temperatures, in the so-called ThomasFermi (TF) regime. The number of atoms in the condensed fraction in temperatures close to TC is usually small, hence the internal energy of the condensate fraction is Expansion of finite-temperature BEC in non-TF regime 2 also small compared to its kinetic energy. On the other hand, in the TF regime, i.e. for condensates with large number of atoms in temperatures much lower than Tc, the internal energy is large compared to the kinetic one. The condensate dynamics depends on the number of condensed atoms: the TF condensates behave hydrodynamically [8] but for smaller number of condensed atoms, the effective potential formed from the intrinsic self-interaction due to ground-state collisions vanishes and the TF approach ceases to be a good approximation of the BEC [9]. Consequently, the condensate dynamics can depart from the familiar hydrodynamic behaviour of TF condensates. The need for determination and interpretation of this modified dynamics justifies considerable interest in the region of higher temperatures, less than, but comparable to TC . Various properties of finite-temperature Bose-Einstein condensates and density distributions of their thermal and condensed parts were studied by several groups both theoretically [10, 11, 12, 13, 14, 15] and experimentally. The experiments on the BEC dynamics were largely devoted to spectroscopy of collective oscillation modes of the condensate described in references [16, 17, 18] which demonstrated that the mutual interaction of the condensate and noncondensate components affects the dynamics of the condensate. In other experiments, Busch et al. [19] reported observation of repulsion of non-condensed gas from the condensate and Gerbier et al. [20] studied the thermodynamics of an interacting trapped Bose-Einstein gas below TC . With an assumption that the condensate is in the TF regime, they showed a temperature dependent deviation from the predicted expansion. In this report we focus on getting further insight into interaction between the thermal and condensate fractions of the condensate which is not in the TF regime. In the first part of our paper we study a pure but small BEC while in the second part we focus on a mixture of a BEC with thermal fraction. Both cases are studied in a free expansion of an atomic sample released from a trap. In the first case with a pure condensate the departure from the TF predictions is caused by an intrinsic kinetic energy of a small sample, but in the second case it also reflects interaction of an expanding Bose-Einstein condensed cloud with thermal atoms. Our measurements show that the behavior of the condensate part depends on both the number of condensed atoms, N0, and on its interactions with thermal component. Thus, to study the effect of BEC interaction with thermal cloud, the BEC atom number needs to be kept constant when varying the N0/N ratio (N being the total atom number). These measurements confirm that the BEC dynamics strongly depends on interaction with thermal fraction and provide clear evidence of the compression effect. Our experimental setup uses magnetic trap with longitudinal and axial frequencies, ωz/2π = 12.(07)± 0.38 Hz and ωr/2π = 13(7.4)± 5.8 Hz, respectively. We create BEC of up to 300 000 Rb atoms in the |F = 2, mF = 2〉 hfs component of their ground state. This sample is analyzed by absorptive imaging with the imaging beam resonant with the |F = 2, mF = 2〉 |F = 3, mF = 3〉 hfs component of the Rb D2 line. More experimental details can be found in Ref. [21]. All pictures are taken after releasing atoms from the MT with a delay which can be Expansion of finite-temperature BEC in non-TF regime 3 varied between 2 and 30 ms in our setup. The images of a finite-temperature condensates reveal two fractions, the BEC and the thermal fraction. Their accurate identification is essential for proper analysis of the experimental results [22]. Our method of such identification will be described elsewhere [23].