Superfluidity in a Dilute Bose Gas

Abstract

Superfluid 4 He films adsorbed on porous Vycor glass have been studied in the low-density limit where the superfluid interparticle spacing is more than an order of magnitude greater than the atomic hard-core diameter. For the lowest transition temperatures observed, the influence of critical fluctuations near T c is much reduced and a range of crossover to behavior more characteristic of the dilute Bose gas is observed.PACS numbers: 67.40.-w, 67.70.+n Stimulated by recent theoretical and experimental advances in the study of low-density, spin-polarized hydrogen, 1 there has been renewed interest in the phenomenon of Bose condensation and the possibility of observing superfluidity in a dilute weakly interacting Bose gas. In this Letter we report new results from a different approach to the experimental realization of a dilute Bose gas, one that utilizes a low-density 4 He system.Our approach has been to make systematic observations of the temperature dependence of the superfluid mass of low-density 4 He films adsorbed on porous Vycor glass. Earlier work on the 4 He-Vycor system 2 " 4 has demonstrated superfluidity for a range of transition temperatures varying over nearly two orders of magnitude. For the lowest transition temperatures previously observed, 3 the effective superfluid coverage was only a few percent of a monolayer, and the average spacing between mobile superfluid particles was considerably greater than the atomic scattering length. We wished to test the proposition that, if the superfluid coverage were sufficiently reduced, superfluid behavior characteristic of the dilute Bose gas might be observed. The data that we report in this Letter give, for the first time, a definite indication that a crossover to a regime of dilute Bose gas behavior has been seen.The dense three-dimensional (3D) superfluids, bulk 4 He, liquid 3 He-4 He mixtures, and higher coverage superfluid films adsorbed on Vycor, all show superfluid behavior that is strongly influenced by order-parameter fluctuations. The temperature variation for the superfluid mass obeys the well known "two-thirds" power law in the neighborhood of the transition temperature. In contrast, fluctuations are usually assumed to be unimportant in the case of the dilute, weakly interacting Bose gas. For the dilute gas, the superfluid mass is expected to follow a temperature dependence close to that of the condensate density in the ideal Bose gas and thus to vary linearly with T c -T as the transition temperature, T c , is approached.In the present experiment we have determined the temperature dependence of the superfluid mass for an extended range of 4 He coverages adsorbed on Vycor glass. As the density of the superfluid was systematically reduced, we have looked for indications of a crossover from the "two-thirds" power-law behavior seen for the dense superfluids to the more linear temperature variation of the superfluid mass expected for the dilute, weakly interacting Bose gas.The experimental technique employed in the present work is similar to that re...

Onset of superfluidity inHe4films adsorbed on disordered substrates

“…These data, taken with the magnetization thermometer, show a cusp at 20 mK, which is a signature of the superfluid transition. 28,29 (Since we did not take a BET isotherm for this sample, the surface area was determined by comparing our measured superfluid transition temperatures as a function of 4 He dosage with those of Crooker et al 13 ) The ordinary low-temperature limit of our measurements was 10 mK. This was determined by the internal heat leak of the calorimeter, which decayed from approximately 0.8 to 0.4 nW over the course of three months.…”

“…This observation has to led to some variations on the inert-layer model, including the suggestion that the compression of the film as it becomes thicker leads to an increase in the density of the inert layer. 13 A more rigorous approach is difficult, and, although outlined almost twenty years ago, 9 has been pursued in detail only in the last several years. It is quite natural to draw an analogy between the metal-insulator transition in Fermi systems and the onset transition in a 4 He film, which is a Bose system.…”

“…2 The two limiting forms, however, suggest another way of testing for crossover to Bose gas-like behavior. 13 The quantity lim T →Tc ρ s (T )/(T c − T ) diverges in the strongly interacting limit but remains finite for the dilute Bose gas. In Fig.…”

Bogoliubov theory of dipolar Bose gas in a weak random potential

“…Now we investigate how the validity range of the Bogoliubov theory depends on the gas parameter γ and the relative temperature t for different values of the relative dipolar interaction strength ǫ dd and the disorder strength R 0 . To this end we restrict the condensate depletion ∆n = n − n 0 in equation (19) to be limited maximally by half of the particle number density n. Inserting the critical temperature for the non-interacting Bose gas T 0 c and the gas parameter γ in the condensate depletion due to quantum fluctuation (28) …”

“…In addition, in order to make quantum gas simulators even more realistic, various experimental and theoretical methods for controlling the effect of disorder have been designed. Using superfluid helium in vycor glass, which represents some kind of porous media, the random distribution of pores represents a random environment [19]. Laser speckles are produced by focusing the laser beam on a glass plate, where the resulting random interference pattern is reflected to a BEC cell [20][21][22][23].…”