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...

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Transition temperature data obtained as a function of particle density in the 4 He-Vycor system are compared with recent theoretical calculations for 3D Bose condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form ∆T /T0 = γ(na 3 ) 1/3 . At higher densities a maximum is found in the ratio of Tc/T0 for a value of the interaction parameter, na 3 , that is in agreement with path-integral Monte Carlo calculations.PACS numbers: 03.75. Fi, 05.30.Jp, The role of interparticle interactions in the determination of the properties of low density Bose-Einstein condensed (BEC) systems has been a topic of interest for many years. In spite of a long history of theoretical investigation [1] dating back to the 1950s, elementary questions such as the possible shift in the transition temperature, T c , with density and interaction strength have remained unsettled until the recent past. In the case of the repulsive interactions in the dilute Bose gas, there has now emerged a consensus [2] [3] [4] that T c will be an increasing function of the interaction parameter, na 3 , where a is the hard sphere diameter and n the particle density. This may seem a surprising result, since it is well known that in the case of liquid 4 He the superfluid transition occurs at a temperature well below the transition temperature, T 0 , for an ideal Bose gas with the same particle mass and number density. Moreover, a number of the earlier calculations [5] had found that the transition temperature would be reduced as a consequence of interparticle interaction.Motivated by the recent theoretical work in this area, we have examined the dependence of the transition temperature on superfluid particle number for the 4 He-Vycor system. In our early work with this system we demonstrated, for the first time in 1983 [6], an experimental realization of the weakly interacting or "dilute" Bose gas. The lowest density achieved in these experiments was on the order of 2 × 10 18 per cm 3 . This is sufficiently low to provide a region of overlap, in terms of the interaction parameter, with the values of na 3 , currently accessible to the BEC systems realized with 87 Rb [7] or 23 Na [8] atoms confined within magnetic or optical traps. In the case of Bose condensed atomic hydrogen [9] the small swave scattering length and limits on the particle density, set by recombination, restrict this system to values of na 3 several orders of magnitude below the values that can be achieved with Bose-condensed Na, Rb or He.For questions such as the effect on T c of increasing the interaction parameter, the 4 He-Vycor system offers advantages over the BEC systems of trapped atomic gases, because in the Vycor case, the interaction parameter can be varied continuously from the low-density, weakly interacting limit to the strongly interacting regime currently inaccessible with the alkali vapor systems. Further, working with the 4 He-Vycor system allows much larger sample sizes, on the order...

We report the first measurements of the superfluid density of thin 3 He films for a broad range of thicknesses. In contrast to previous experiments, we find good agreement with the predictions of the general theory for the suppression of the superfluid transition temperature 7 C . In addition, we find evidence for a new phase of the superfluid in films thinner than 2750 A.

We have performed both ac susceptibility and dc magnetization measurements on the diluted magnetic semiconductor Zn 1Ϫx Mn x Te. The measurements clearly indicate spin-glass behavior. For samples with concentrations xϭ0.51 and xϭ0.41, the data for the imaginary part of the complex susceptibility (Љ) were analyzed according to conventional power-law dynamics and good scaling was obtained with the critical exponent values zϭ10Ϯ2 and ␤ϭ1.0Ϯ0.2. These values of z and ␤ are consistent with results obtained in other insulating spin-glass systems with short-range interactions. Because of the presence of significant Dzyaloshinsky-Moriya anisotropy in these materials, an attempt was also made to fit the data using an activated dynamics model. However, the scaling of the Љ data was less satisfactory in this case. Magnetization measurements on the xϭ0.51 sample also showed a spin-glass-like transition. Scaling of the nonlinear magnetization just above the transition gave T c ϭ20.8Ϯ0.2 K, and the critical exponent values ␥ϭ4.0Ϯ1.0 and ␤ ϭ0.8Ϯ0.2. The value of T c obtained from the static magnetization measurements is in good agreement with the value T c ϭ20.7Ϯ0.05 K obtained from the dynamic scaling analysis. Further, the value for the critical exponent ␥ obtained in this work is in fair agreement with values reported for other spin-glass materials. These results represent convincing evidence that diluted magnetic semiconductors are a subset of the class of insulating spin-glass materials with short-range interactions.