Recebido em 6/12/2006; Aceito em 28/2/2007Neste trabalho apresentamos um modelo simples de resfriamento evaporativo para ´atomos ultrafrios aprisio-nados. Este processo objetiva a diminui¸c˜ao da temperatura da amostra gasosa a partir da retirada dos ´atomosmais quentes desta e conseq¨uente retermaliza¸c˜ao dos remanescentes em uma temperatura mais baixa. O modeloparte da distribui¸c˜ao de Maxwell-Boltzmann de velocidades para a amostra atˆomica e permite o c´alculo da tem-peratura e n´umero de ´atomos remanescentes nesta ap´os a retirada dos ´atomos mais quentes e retermaliza¸c˜ao. Apartir dessas express˜oes simulamos o processo de resfriamento evaporativo realizado usualmente em experimen-tos, onde s˜ao retirados ´atomos cada vez mais frios ap´os cada retermaliza¸c˜ao.Palavras-chave: ´atomos frios, evapora¸ c˜ao, distribui¸c˜ao de Maxwell-Boltzmann.In this work we present a simple model to describe evaporative cooling for ultracold trapped atoms. Thisprocess is used to achieve low temperatures of the gaseous sample by removing the hottest atoms and subse-quently rethermalizing the remaining atoms at a lower temperature. The model assumes a Maxwell-Boltzmanndistribution of velocities in the atomic sample and allows the calculation of the temperature and the number ofremaining atoms after the hottest atoms have been removed and the rethermalization has taken place. Usingthese expressions we simulate the process of evaporative cooling as it is usually carried out in experiments, wherecolder atoms are removed after each successive rethermalization.Keywords: cold atoms, evaporation, Maxwell-Boltzmann distribution.
We develop a semiclassical thermodynamic framework for the evaporative cooling of trapped atomic gases that treats Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics on equal footing across box, harmonic, mixed, and linear-quadrupole potentials. Using the global thermodynamic variables of inhomogeneous confinement, we show that all geometries are unified by a single parameter
s, which fixes the polylogarithm order, the density of states exponent, and the number of degrees of freedom
2s. Modeling evaporation as a recursive sequence of energy truncation and rethermalization, we derive closed-form recurrence relations for the particle number and internal energy that track the full thermodynamic state, with the classical energy budget set by a virial factor
Ctrap=1+3/(2s). Quantum degeneracy emerges not as a singularity in the global susceptibilities, but as a smooth, geometry-dependent crossover in which bosons and fermions display opposite thermodynamic signatures. The results provide a versatile theoretical tool for modeling evaporative cooling across experimentally relevant geometries and offer quantitative guidance for optimizing the cooling process in ultracold atomic systems.
We apply kinetic theory to the problem of evaporative cooling of a dilute collisional gas in a trap. Assuming ``sufficient ergodicity'' (phase-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms is derived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that during evaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at the trap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained for the thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. We give analytical expressions both for power-law traps and for a realistic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas. \textcopyright{} 1996 The American Physical Society.
A quantitative, analytic model of evaporative cooling covering both the small-
(<4) and large-
(>4) $\ensuremath{\eta}$ regimes is presented. $\ensuremath{\eta}$ is the dimensionless parameter defined as the trap depth divided by the temperature of the trapped sample. Although some of the same general properties present at large $\ensuremath{\eta}$ are also present at small $\ensuremath{\eta}$, there are significant quantitative differences. These differences must be taken into account in order to accurately extract from the trapping data quantitative measurements of, for example, collisional atomic cross sections.
We demonstrate experimentally the evaporative cooling of a few hundred rubidium-87 atoms in a single-beam microscopic dipole trap. Starting with 800 atoms at a temperature of 125 $\ensuremath{\mu}$K, we produce an unpolarized sample of 40 atoms at 110 nK, within 3 s. The phase-space density at the end of the evaporation reaches unity, close to quantum degeneracy. The gain in phase-space density after evaporation is
103. We find that the scaling laws used for much larger numbers of atoms are still valid despite the small number of atoms involved in the evaporative cooling process. We also compare our results to a simple kinetic model describing the evaporation process and find good agreement with the data.
A method is proposed that utilizes a Feshbach resonance to cool an atomic gas to temperatures of quantum degeneracy. Through application of a sequence of alternating adiabatic and nonadiabatic magnetic field ramps in the region of a Feshbach resonance, a large number of atom pairs in a trapped gas lose energy at the expense of a relatively small number of pairs which gain energy. After removal from the trap of the atom pairs which gain energy, the remaining reduced energy atoms will equilibrate to a lower temperature.