Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure

Coupled dynamics of RNA folding and nanopore translocation

The translocation of structured RNA or DNA molecules through narrow pores necessitates the opening of all base pairs. Here, we study the interplay between the dynamics of translocation and base-pairing theoretically, using kinetic Monte Carlo simulations and analytical methods. We find that the transient formation of basepairs that do not occur in the ground state can significantly speed up translocation.Comment: 4 pages, 3 figures, to appear in Physical Review Letter

Disruption of reflecting Bose-Einstein condensates due to inter-atomic interactions and quantum noise

We perform fully three-dimensional simulations, using the truncated Wigner method, to investigate the reflection of Bose-Einstein condensates from abrupt potential barriers. We show that the inter-atomic interactions can disrupt the internal structure of a cigar-shaped cloud with a high atom density at low approach velocities, damping the center-of-mass motion and generating vortices. Furthermore, by incorporating quantum noise we show that scattering halos form at high approach velocities, causing an associated condensate depletion. We compare our results to recent experimental observations.Comment: 5 figure

The Morphologies of the Small Magellanic Cloud

We compare the distribution of stars of different spectral types, and hence mean age, within the central SMC and find that the asymmetric structures are almost exclusively composed of young main sequence stars. Because of the relative lack of older stars in these features, and the extremely regular distribution of red giant and clump stars in the SMC central body, we conclude that tides alone are not responsible for the irregular appearance of the central SMC. The dominant physical mechanism in determining the current-day appearance of the SMC must be star formation triggered by a hydrodynamic interaction between gaseous components. These results extend the results of population studies (cf. Gardiner and Hatzidimitriou) inward in radius and also confirm the suggestion of the spheroidal nature of the central SMC based on kinematic arguments (Dopita et al; Hardy, Suntzeff & Azzopardi). Finally, we find no evidence in the underlying older stellar population for a ``bar'' or ``outer arm'', again supporting our classification of the central SMC as a spheroidal body with highly irregular recent star formation.Comment: 8 pages, accepted for publication in ApJ Letters (higher quality figures available at http://ngala.as.arizona.edu/dennis/mcsurvey.html

Non-degenerate, three-wave mixing with the Josephson ring modulator

The Josephson ring modulator (JRM) is a device, based on Josephson tunnel junctions, capable of performing non-degenerate mixing in the microwave regime without losses. The generic scattering matrix of the device is calculated by solving coupled quantum Langevin equations. Its form shows that the device can achieve quantum-limited noise performance both as an amplifier and a mixer. Fundamental limitations on simultaneous optimization of performance metrics like gain, bandwidth and dynamic range (including the effect of pump depletion) are discussed. We also present three possible integrations of the JRM as the active medium in a different electromagnetic environment. The resulting circuits, named Josephson parametric converters (JPC), are discussed in detail, and experimental data on their dynamic range are found to be in good agreement with theoretical predictions. We also discuss future prospects and requisite optimization of JPC as a preamplifier for qubit readout applications.Comment: 21 pages, 16 figures, 4 table

Non-destructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms

We describe a scheme for probing a gas of ultracold atoms trapped in an optical lattice and moving in the presence of an external potential. The probe is non-destructive and uses the existing lattice fields as the measurement device. Two counter-propagating cavity fields simultaneously set up a conservative lattice potential and a weak quantum probe of the atomic motion. Balanced heterodyne detection of the probe field at the cavity output along with integration in time and across the atomic cloud yield information about the atomic dynamics in a single run. The scheme is applied to a measurement of the Bloch oscillation frequency for atoms moving in the presence of the local gravitational potential. Signal-to-noise ratios are estimated to be as high as $10^4$.Comment: 8 pages, 6 figures, submitted to Phys. Rev.

Isospin fluctuations in spinodal decomposition

We study the isospin dynamics in fragment formation within the framework of an analytical model based on the spinodal decomposition scenario. We calculate the probability to obtain fragments with given charge and neutron number, focussing on the derivation of the width of the isotopic distributions. Within our approach this is determined by the dispersion of N/Z among the leading unstable modes, due to the competition between Coulomb and symmetry energy effects, and by isovector-like fluctuations present in the matter that undergoes the spinodal decomposition. Hence the widths exhibit a clear dependence on the properties of the Equation of State. By comparing two systems with different values of the charge asymmetry we find that the isotopic distributions reproduce an isoscaling relationship.Comment: 18 RevTex4 pages, 6 eps figure

Quantum-limited force measurement with an optomechanical device

We study the detection of weak coherent forces by means of an optomechanical device formed by a highly reflecting isolated mirror shined by an intense and highly monochromatic laser field. Radiation pressure excites a vibrational mode of the mirror, inducing sidebands of the incident field, which are then measured by heterodyne detection. We determine the sensitivity of such a scheme and show that the use of an entangled input state of the two sideband modes improves the detection, even in the presence of damping and noise acting on the mechanical mode.Comment: 8 pages, 4 figure

Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback

We apply quantum filtering and control to a particle in a harmonic trap under continuous position measurement, and show that a simple static feedback law can be used to cool the system. The final steady state is Gaussian and dependent on the feedback strength and coupling between the system and probe. In the limit of weak coupling this final state becomes the ground state. An earlier model by Haine et. al. (PRA 69, 2004) without measurement back-action showed dark states: states that did not display error signals, thus remaining unaffected by the control. This paper shows that for a realistic measurement process this is not true, which indicates that a Bose-Einstein condensate may be driven towards the ground state from any arbitrary initial state.Comment: 1 Tex, 4 PS pictures, 1 bbl fil

Anharmonic effects on a phonon number measurement of a quantum mesoscopic mechanical oscillator

We generalize a proposal for detecting single phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the readout oscillator.Comment: 13 pages, 2 figure