Quantum theory predicts that Bose-Einstein condensation of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form, provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between the self-attractive forces and a repulsion that arises from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate is therefore punctuated by intermittent collapses that are triggered by either macroscopic quantum tunnelling or thermal fluctuation. Previous observations of growth and collapse dynamics have been hampered by the stochastic nature of these mechanisms. Here we report direct observations of the growth and subsequent collapse of a 7Li condensate with attractive interactions, using phase-contrast imaging. The success of the measurement lies in our ability to reduce the stochasticity in the dynamics by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state.

We demonstrate unambiguously that the field enhancement near the apex of a laser-illuminated silicon tip decays according to a power law that is moderated by a single parameter characterizing the tip sharpness. Oscillating the probe in intermittent contact with a semiconductor nanocrystal strongly modulates the fluorescence excitation rate, providing robust optical contrast and enabling excellent background rejection. Laterally encoded demodulation yields images with <10 nm spatial resolution, consistent with independent measurements of tip sharpness. DOI: 10.1103/PhysRevLett.93.180801 PACS numbers: 07.79.Fc, 42.50.Hz, 61.46.+w, 78.67.Bf The potential of near-field microscopy to optically resolve structure well below the diffraction limit has excited physicists, chemists, and biologists for almost 20 years. Conventional near-field scanning optical microscopy (NSOM) uses the light forced through a small metal aperture to locally excite or detect an optical response. The spatial resolution in NSOM is limited to 30 -50 nm by the penetration depth of light into the metal aperture. More recently, apertureless-NSOM (ANSOM) techniques were developed which leverage the strong enhancement of an externally applied optical field at the apex of a sharp tip for local excitation of the sample [1][2][3][4][5][6][7][8][9][10][11]. The promised advantage of ANSOM is that spatial resolution should be limited only by tip sharpness (typically 10 nm). The resolution in most previous ANSOM experiments, however, was at best marginally better than NSOM and was inferior to expectations based on tip sharpness alone. Further, the external field used to induce enhancement led to a substantial background signal and to assertions that one-photon fluorescence is not appropriate for ANSOM [12,13]. These experiments fell short of their potential because they maintained a tip-sample gap of several nanometers, and thus did not thoroughly exploit the tightly confined enhancement.Here, we demonstrate an ANSOM technique that fully exploits the available contrast and leads to spatial resolution that is limited only by tip sharpness. The problems associated with a tip-sample gap are overcome by oscillating the probe in intermittent contact with the sample. The detected signal is then composed of a modulated near-field portion that is superimposed on the far-field background. Subsequent demodulation decouples the two components and thus strongly elevates the near-field signal relative to the background. With this technique, we measured <10 nm lateral resolution via one-photon fluorescence imaging of isolated quantum dots, consistent with independent measurements of tip sharpness. The measured resolution is >3 times better than previous reports for quantum dots using one-photon fluorescence [8,9], and is 2 times better than previous measurements using higher-order optical processes (two-photon fluorescence [6], Raman scattering [4,5]) despite predictions to the contrary [12,13].To better understand the advantages of this technique and to facilitate ...

The occupation number of a magnetically trapped Bose-Einstein condensate is limited for atoms with attractive interactions. It has been predicted that, as this limit is approached, the condensate will collapse by a collective process. The measured spread in condensate number for samples of 7 Li atoms undergoing thermal equilibration is consistent with the occurrence of such collapses. [ S0031-9007(98) The attainment of Bose-Einstein condensation (BEC) in dilute atomic gases has provided a new domain for studying the nonlinear effects of interactions in thermodynamic systems. Among the gases in which BEC has been observed, 7 Li is unique in having a negative triplet s-wave scattering length a. Because a , 0, the effective interaction between atoms is attractive, and the BEC phenomenon is substantially altered. Attractive interactions were long believed to make a condensate unstable and thus prevent BEC [1,2], but it is now known that, for a confined gas, a metastable condensate can exist as long as its occupation number, N 0 , remains small [3]. Such condensates are predicted to be rich in physics, exhibiting properties such as solitonlike behavior [4] and macroscopic quantum tunneling [5]. In particular, complex dynamical behavior is expected as N 0 approaches its stability limit [6][7][8]. In this Letter, we describe experimental investigations of this behavior.Attractive interactions limit N 0 because, at a maximum number N m , the compressibility of the condensate becomes negative and it will implosively collapse. By equating the positive zero-point kinetic energy to the negative interaction energy, it is found that N m ϳ ᐉ͞jaj when the condensate is confined to volume ᐉ 3 . The stability limit is more precisely determined from numerical solution of the nonlinear Schrödinger equation (NLSE) [9]. For 7 Li in our magnetic trap, a 21.46 nm [10] and ᐉ ഠ 3 mm, which yield a stability limit of ϳ1250 atoms.As the gas is cooled below the critical temperature for BEC, N 0 grows until N m is reached. The condensate then collapses spontaneously if N 0 $ N m , or the collapse can be initiated by thermal fluctuations or quantum tunneling for N 0 & N m [5,7]. During the collapse, the condensate shrinks on the time scale of the trap oscillation period. As the density rises, the rates for inelastic collisions such as dipolar decay and three-body molecular recombination increase. These processes release sufficient energy to immediately eject the colliding atoms from the trap, thus reducing N 0 . The ejected atoms are very unlikely to further interact with the gas before leaving the trap, since the density of noncondensed atoms is low. As the collapse proceeds, the collision rate grows quickly enough that the density remains small compared to jaj 23 and the condensate remains a dilute gas [7,8].Both the collapse and the initial cooling process displace the gas from thermal equilibrium. As long as N 0 is smaller than its equilibrium value, as determined by the total number and average energy of the trapped atoms, the condensate...

The triplet s-wave scattering length of 6 Li is determined using two-photon photoassociative spectroscopy of the diatomic a 3 ⌺ u ϩ state of 6 Li 2 . The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be ͑Ϫ2160Ϯ250)a 0 , where a 0 is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving 6 Li and 7 Li determined from this and our previous spectroscopic investigations is given.

Excitonic transitions in organic semiconductors are associated with large oscillator strength that limits the excited-state lifetime and can in turn impede long-range exciton migration. We present perylene-based emissive H-aggregate nanowires where the lowest energy state is only weakly coupled to the ground state, thus dramatically enhancing lifetime. Exciton migration occurs by thermally activated hopping, leading to luminescence quenching on topological wire defects. An atomic force microscope tip can introduce local topological quenchers by distorting the H-aggregate structure, demonstrating long-range exciton migration at room temperature and offering a potential route to writing fluorescent "nanobarcodes" and excitonic circuits.