We explore how the size and shape of the microscopic confinement potential affects the nonradiative Auger decay rate of confined carriers. Calculations conducted in the two-band, effective mass Kane model unambiguously show that smoothing out the confinement potential could reduce the rate by more than 3 orders of magnitude relative to the rate in structures with abruptly terminating boundaries. As the confinement potential width is increased, the calculated rate decreases overall, exhibiting very deep minima at regular widths. Such minima suggest that nanocrystals of "magic sizes" can exist for which nonradiative Auger processes are strongly suppressed.

The photoluminescence from a variety of individual molecules and nanometre-sized crystallites is defined by large intensity fluctuations, known as 'blinking', whereby their photoluminescence turns 'on' and 'off' intermittently, even under continuous photoexcitation. For semiconductor nanocrystals, it was originally proposed that these 'off' periods corresponded to a nanocrystal with an extra charge. A charged nanocrystal could have its photoluminescence temporarily quenched owing to the high efficiency of non-radiative (for example, Auger) recombination processes between the extra charge and a subsequently excited electron-hole pair; photoluminescence would resume only after the nanocrystal becomes neutralized again. Despite over a decade of research, completely non-blinking nanocrystals have not been synthesized and an understanding of the blinking phenomenon remains elusive. Here we report ternary core/shell CdZnSe/ZnSe semiconductor nanocrystals that individually exhibit continuous, non-blinking photoluminescence. Unexpectedly, these nanocrystals strongly photoluminesce despite being charged, as indicated by a multi-peaked photoluminescence spectral shape and short lifetime. To model the unusual photoluminescence properties of the CdZnSe/ZnSe nanocrystals, we softened the abrupt confinement potential of a typical core/shell nanocrystal, suggesting that the structure is a radially graded alloy of CdZnSe into ZnSe. As photoluminescence blinking severely limits the usefulness of nanocrystals in applications requiring a continuous output of single photons, these non-blinking nanocrystals may enable substantial advances in fields ranging from single-molecule biological labelling to low-threshold lasers.

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A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM). By use of a total-internal-reflection geometry, standing evanescent waves are generated that spatially modulate the excitation of the sample. An enhanced two-dimensional image is formed from a weighted sum of images taken at different phases and directions of the standing wave. The performance of such a system is examined through theoretical calculations of both the point-spread function and the optical transfer function.

In this Letter, we reported the unusual non-blinking characteristics of the fluorescence from individual CdZnSe/ZnSe alloyed quantum dots. However, it has recently come to our attention that similar fluorescence behaviour was seen by Celso de Mello Donega, Daniel Vanmaekelbergh and co-workers from a single fluorophore on bare silica glass. In particular, individual fluorescence spots from single molecules were found to be non-blinking, and fluorescence spectra looked similar to what we reported in our Letter. We corroborated their findings by conducting experiments of our own on bare quartz coverslips, and on quartz coverslips coated with polymethyl methacrylate (PMMA). Although these same control experiments were performed by us before publication, this time we clearly observed non-blinking fluorescence from isolated spots on the coverslip. Furthermore, the fluorescence spectra from these spots were in all practical respects identical to what we reported in our Letter. Subsequent investigations by us have revealed that the surprising origins of the unusual fluorescence come from individual, molecular defects in silica glasses, brightened by the polymer coating. The details of these new findings will be the subject of future publications 1 . After examining the data of de Mello Donega and colleagues, and determining that we were both observing the same phenomena, we concluded that we cannot attribute the fluorescence we observed to CdZnSe/ZnSe quantum dots. In view of these new results, we therefore wish to retract the paper and sincerely apologize for our error. All authors agree with the decision to retract the paper with the exception of X.R., who was unable to be contacted.

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We explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasi-bound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce an underlying decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density (∼ ρ 3/2 ) and on scattering length (∼ a 5/2 ) can be measured in experimental tests of this theory.Since the production of atomic Bose-Einstein condensates (BEC) in the laboratory [1, 2], many schemes have been proposed whereby the experimentalist may control the interatomic interactions governing the behavior of these gases [3]. One such proposal involves a Feshbach resonance in which two atoms combine to form a quasibound molecule [4,5]. This molecule is described as the intermediate state or closed channel of the scattering reaction as the constituent atoms in general have different spin configurations in the bound state than in the scattering state. Due to its dependence on the internal spin states, the energy difference, or detuning between the scattered and bound states can thus be tuned using the Zeeman effect in an external magnetic field. As the binding energy of the molecular state is brought close to the energy of the colliding atoms, the appearance of these loosely bound molecules increases. Consequently, the coupling between atoms and molecules acts to modify the effective interatomic interactions. Near zero energy, these interactions are described by the s-wave scattering length, which in turn can be tuned by varying the external magnetic field. This degree of control suggests that the negative scattering length of initially unstable condensates may be tuned to positive values thereby rendering the condensate stable. We provide a many-body variational description of such a scenario, specifically using the case of 85 Rb to compare our results with experiment [6,7]. For a uniform system our findings reveal a collapsing ground state and a decaying excited state, where the latter fits the behavior seen from experiment. In the excited state, a complex chemical potential is obtained in which the imaginary part determines the inverse decay time.Before embarking on the many-body analysis of the coupled atom-molecule BEC, it is first necessary to review the relevant two-body physics underlying the interatomic interactions. It can be seen that the two-body formalism provides a means by which the many-body equations can be renormalized by replacing the interaction strength by the s-wave scattering length as the relevant parameter. In two-atom scattering, there are a number of different channels or outcomes of the scatter...

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