Bose-Einstein Condensation of Atoms in a Uniform Potential

Abstract

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.

Conical refraction: fundamentals and applications

“…Blue-detuned optical potentials are used in the manipulation of Rydberg states [183], atomic clocks [184], quantum information processing [185] or Bose-Einstein condensation in uniform potentials [186]. In the best ideal situation for blue-detuned optical traps, the local minimum where atoms are trapped has null intensity.…”

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

“…It is immediate to generalize them to any trapping potentials and boundary conditions. They open a way to solve the long-standing problem of the BEC and other phase transitions [1][2][3][4][5][6][7][8][9][10][11][12], including a restricted canonical ensemble problem [2], and describe numerous modern laboratory and numerical experiments on the critical phenomena in BEC of the mesoscopic systems [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…It becomes possible due to the newly developed methods of (a) the nonpolynomial averages and contraction superoperators [15,16], (b) the partial difference (recurrence) equations [17][18][19] (a discrete analog of the partial differential equations) for superoperators, and (c) a characteristic function and cumulant analysis for a joint distribution of the noncommutative observables. They allow us to take into account (I) the constraints in a many-body Hilbert space, which are the integrals of motion prescribed by a broken symmetry in virtue of a Noether's theorem, and constraintcutoff mechanism, responsible for the very existence of a phase transition and its nonanalytical features, [4,20,21] (II) an insufficiency of a grand-canonical-ensemble approximation, which is incorrect in the critical region [2,8] because of averaging over the systems with different numbers of particles, both below and above the critical point, i.e., over the condensed and noncondensed systems at the same time, that implies an error on the order of 100% for any critical function, (III) a necessity to solve the problem for a finite system with a mesoscopic (i.e., large, but finite) number of particles N in order to calculate correctly an anomalously large contribution of the lowest energy levels to the critical fluctuations and to avoid the infrared divergences of the standard thermodynamic-limit approach [5][6][7][8][9][10][11] as well as to resolve a fine structure of the λ-point, (IV) a fact that in the critical region the Dyson-type closed equations do not exist for true Green's functions, but do exist for the partial 1-and 2-contraction superoperators, which reproduce themselves under a contraction.The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidit...…”

Producing an efficient, collimated, and thin annular beam with a binary axicon

“…The measured profile and propagation are in excellent agreement with a numerical Fourier simulation we perform. Annular beams, characterized by a hollow ring cross section, are useful for a variety of applications, such as optical dipole traps for ultra-cold atoms [1][2][3][4][5][6], hollow optical tweezers for dielectric particles [7,8], imaging and super-resolution microscopy [9,10], long-ranged atmospheric optical communication [11,12] and material processing [13,14].…”

“…We propose and demonstrate a novel method to produce a thin and highly collimated annular beam that propagates as, and even outperforms in a way, an ideal Gaussian ring beam, with a simple optical configuration composed of a diffractive binary axicon, a circular binary phase element, and a lens. Albeit less versatile, the binary axicon is much cheaper and (being a passive element) more robust than spatial light modulators [4,18,23]. Furthermore, it is well suited for highpower lasers, displaying damage thresholds higher than those of the typical spatial light modulator by many orders of magnitude.…”