We report on the measurement of the Casimir force between conducting surfaces in a parallel configuration. The force is exerted between a silicon cantilever coated with chromium and a similar rigid surface and is detected looking at the shifts induced in the cantilever frequency when the latter is approached. The scaling of the force with the distance between the surfaces was tested in the 0.5 -3.0 µm range, and the related force coefficient was determined at the 15% precision level.

We have studied dissipation in a Bose-Einstein condensed gas by moving a blue detuned laser beam through the condensate at different velocities. Strong heating was observed only above a critical velocity.PACS 03.75.Fi, 67.40.Vs,67.57.De Macroscopic quantum coherence and collective excitations are key features in our understanding of the phenomenon of superfluidity. The superfluid velocity is proportional to the gradient of the phase of a macroscopic wavefunction. Collective excitations determine a critical velocity below which the flow is dissipationless. This velocity is given by Landau's criterion [1],where ε is the energy of an excitation with momentum p. [4]. Previous work has explored some aspects related to superfluidity such as the macroscopic phase [5] and the phonon nature of low-lying collective excitations [4,6]. In this Letter we report on the measurement of a critical velocity for the excitation of a trapped BoseEinstein condensate. In analogy with the well known argument by Landau and the vibrating wire experiments in superfluid helium [7], we study dissipation when an object is moved through the fluid. Instead of a massive macroscopic object we used a blue detuned laser beam which repels atoms from its focus to create a moving boundary condition.The experiment was conducted in a new apparatus for the production of Bose-Einstein condensates of sodium atoms. The cooling procedure is similar to previous work [8]-the new features have been described elsewhere [9]. Briefly, laser cooled atoms were transferred into a magnetic trap in the Ioffe-Pritchard configuration and further cooled by rf evaporative cooling for 20 seconds, resulting in condensates of between 3 and 12 ×10 6 atoms. After the condensate was formed, we reduced the radial trapping frequency to obtain condensates which were considerably wider than the laser beam used for stirring. This decompression was not perfectly adiabatic, and heated the cloud to a final condensate fraction of about 60%. The final trapping frequencies were ν r = 65 Hz in the radial and ν z = 18 Hz in the axial direction. The resulting condensate was cigar-shaped with Thomas-Fermi diameters of 45 and 150 µm in the radial and axial directions, respectively. The final chemical potential, transition temperature T c and peak density n 0 of the condensate were 110 nK, 510 nK and 1.5 × 10 14 cm −3 , respectively.The laser beam for stirring the condensate had a wavelength of 514 nm and was focused to a Gaussian 1/e 2 beam diameter of 2w = 13µm. The repulsive optical dipole force expelled the atoms from the region of highest laser intensity. A laser power of 400 µW created a 700 nK barrier resulting in a cylindrical hole ∼ 13µm in diameter within the condensate. The laser barrier created a soft boundary, since the Gaussian beam waist was more than 10 times wider than the healing length ξ = (8πan 0 ) −1/2 = 0.3µm, a being the two-body scattering length. The laser was focused on the center of the cloud. Using an acousto-optic deflector, it was scanned back and forth along t...

We have studied the hydrodynamic flow in a Bose-Einstein condensate stirred by a macroscopic object, a blue detuned laser beam, using nondestructive in situ phase contrast imaging. A critical velocity for the onset of a pressure gradient has been observed, and shown to be density dependent. The technique has been compared to a calorimetric method used previously to measure the heating induced by the motion of the laser beam.PACS 03.75.Fi, 67.40.Vs, 67.57.De Beginning with the London conjecture [1], BoseEinstein condensation has been considered crucial for the understanding of superfluidity. Since then, the weakly interacting Bose gas has served as an idealized model for a superfluid [2]. It has a phonon-like energy-momentum dispersion relation that does not allow for the generation of elementary excitations below a critical velocity, thus implying dissipationless flow at lower velocities. The onset of dissipation has been treated in the framework of the nonlinear Schrödinger equation [3][4][5][6][7] and shows an intriguing richness. Experiments on liquid helium could not test these theories, because superfluidity and dissipation are even more complex in this system due to the presence of strong interactions and surface effects [8].The creation of Bose-Einstein condensates in dilute gases has dramatically changed this situation, allowing for quantitative tests of microscopic theories using the tools and precision of atomic physics experiments [9]. A number of recent experiments have examined phenomenological features of superfluidity in gaseous BoseEinstein condensates. These include the observation of vortices [10,11], a non-classical moment of inertia [12], and suppression of collisions from microscopic impurities [13]. In previous work we found evidence for a critical velocity in a stirred condensate [14]. In this Letter we study the onset of dissipation with higher sensitivity using repeated in situ non-destructive imaging of the condensate. These images show the distortion of the density distribution around the moving object, thus directly probing the dynamics of the flow field that has been recently treated with different models [15][16][17][18][19][20]. The experimental setup was similar to the one used in our previous work [14]. Improvements in the evaporation strategy and decompression techniques allowed us to produce pure condensates with up to 5×10 7 sodium atoms, with densities ranging from 8.4×1013 to 3.5×10 14 cm −3 , corresponding to chemical potentials from 60 to 250 nK. We determined the Thomas-Fermi radius R z along the axial direction through in situ phase contrast imaging. The sound velocity at the center of the condensate was then evaluated through the relationship c s = 2πν z R z / √ 2, with ν z =20.1Hz being the axial trapping frequency. The macroscopic moving object was a 514 nm laser beam blue-detuned with respect to the sodium transitions, thereby creating an effective repulsive potential for the atoms. The beam is focused on the center of the condensate to a Gaussian 1/e 2 diameter o...

Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. [S0034-6861(96)00103-1] CONTENTS