We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasi-homogeneous atomic gas, prepared in an optical-box trap. We characterise the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein's textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient µJT > 10 9 K/bar, about ten orders of magnitude larger than observed in classical gases. [3]. However, they are traditionally produced in harmonic traps, which makes them spatially inhomogeneous and thus different both from other correlated systems, that they often aim to emulate, and from textbook models. This difference can often be addressed using local density approximation (LDA), and is in some cases even beneficial [4][5][6][7][8][9][10]. However, spatial inhomogeneity is also often problematic. Integrating over the varying density can smear or even qualitatively change experimental signatures (see, e.g., [11][12][13][14][15]). Moreover, LDA breaks down close to phase transitions, where the correlation length diverges [16]. Recently, a Bose-Einstein condensate (BEC) of atoms in an essentially uniform potential was achieved [17], opening new possibilities for studies of both quantum-statistical and interaction effects in many-body systems.In this Letter, we explore the thermodynamics of a weakly interacting quasi-homogeneous Bose gas, prepared in an optical-box trap (see Fig. 1). We characterise the critical point for condensation and demonstrate two purely quantumstatistical phenomena that are, despite weak interactions, obscured in harmonically trapped gases. First, we observe saturation of the thermal component in a partially condensed gas, in agreement with Einstein's textbook picture of condensation as a purely statistical phase transition. Second, we observe and quantitatively explain cooling of partially condensed clouds through isoenthalpic rarefaction, driven by collisions with the background gas in the vacuum chamber. This phenomenon is the quantum version of the Joule-Thomson (JT) effect, exploited in thermal machines such as refrigerators and heat pumps. In the classical JT process, isoenthalpic cooling occurs only due to interactions, whereas a quantum Bose gas is expected to show it even in their absence. This phenomenon was predicted as early as 1937 [18], and was at the time proposed as a way to experimentally observe the quantum statistics obeyed by a gas, the effect being opposite for fermions (see also [19]). However, to our knowledge, JT cooling has never before been experimentally observed in the regime where quantum-statistical effects dominate over the interaction ones. Outside the realm of ultracold atomic gases, the quantum JT effect is ma...

We study the properties of an atomic Bose-Einstein condensate produced in an optical-box potential, using high-resolution Bragg spectroscopy. For a range of box sizes, up to 70 µm, we directly observe Heisenberglimited momentum uncertainty of the condensed atoms. We measure the condensate interaction energy with a precision of kB × 100 pK and study, both experimentally and numerically, the dynamics of its free expansion upon release from the box potential. All our measurements are in good agreement with theoretical expectations for a perfectly homogeneous condensate of spatial extent equal to the size of the box, which also establishes the uniformity of our optical-box system on a sub-nK energy scale. 03.75.Hh, 03.75.Kk, 67.85.Hj Ultracold atomic gases produced in harmonic traps are widely used for fundamental studies of many-body quantum mechanics in a flexible experimental setting [1][2][3][4]. Recently, it also became possible to produce a Bose-Einstein condensate (BEC) in an essentially homogeneous atomic gas, held in the quasi-uniform potential of an optical-box trap [5]. This has opened new possibilities for closer connections with other many-body systems and theories that rely on the translational symmetry of the system (see, e.g., [6][7][8][9][10][11][12][13][14][15][16]).The first experimental studies of a Bose gas in a box potential focused on the critical point for condensation and the thermodynamics of the gas close to the critical temperature [5,17]. Here, we investigate a box-trapped Bose gas in the low-temperature regime of a quasi-pure condensate. While previous experiments [5,17] established the effective uniformity of the thermal gas from which the BEC forms, here we directly probe and prove the uniformity of the condensate itself, which requires measurements on a two orders of magnitude lower energy scale. We study its coherence, energy, and free expansion from the box trap, employing twophoton Bragg spectroscopy [18][19][20][21][22][23][24][25] to obtain high resolution measurements of the momentum distribution and interaction energy. For a wide range of box sizes, extending up to 70 µm, we directly observe Heisenberg-limited momentum uncertainty of the condensed atoms, corresponding to a fully coherent macroscopic BEC wavefunction spanning the whole box trap. From the interaction shift of the Bragg resonance we deduce the BEC ground-state energy (per atom) with a precision of k B × 100 pK, and find good agreement with meanfield theory for a perfectly uniform condensate. Finally, we study the free time-of-flight (ToF) expansion of a BEC from the box trap. We follow the evolution of the cloud shape and the gradual conversion of the interaction energy into the width of the momentum distribution, and reproduce our observations in numerical simulations based on the Gross-Pitaevskii (GP) equation.Our apparatus is described in Refs. [5,26]. We trap 87 Rb atoms in a cylindrical optical box of radius R ≈ 16 µm and a tuneable length L = 15 − 70 µm [see Fig. 1(a)]. Our box is formed by 532 nm repul...

We present first experimental results of our investigation of non-collinear high harmonic generation (NCHHG) with a chirped pulse amplification system. Collimated high harmonic radiation of higher than 9th order is observed along the bisector of two fundamental beams crossing in a xenon gas target. The obtained results show that cavity-assisted non-collinear high harmonic generation is a promising candidate for efficient generation and outcoupling of extreme ultraviolet (XUV) radiation.