First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

Facilitating soil-and plant-water research through the use of TDR

The development of TDR for measurement of soil water content and electrical conductivity has resulted in a large shift in measurement methods for a breadth of soil and hydrological characterization efforts. TDR has also opened new possibilities for soil and plant research. Five examples show how TDR has enhanced our ability to conduct our soil- and plant-water research. (i) Oxygen is necessary for healthy root growth and plant development but quantitative evaluation of the factors controlling oxygen supply in soil depends on knowledge of the soil water content by TDR. With water content information we have modeled successfully some impact of tillage methods on oxygen supply to roots and their growth response. (ii) For field assessment of soil mechanical properties influencing crop growth, water content capability was added to two portable soil strength measuring devices; (a) A TDT (Time Domain Transmittivity)-equipped soil cone penetrometer was used to evaluate seasonal soil strengthwater content relationships. In conventional tillage systems the relationships are dynamic and achieve the more stable no-tillage relationships only relatively late in each growing season; (b) A small TDR transmission line was added to a modified sheargraph that allowed shear strength and water content to be measured simultaneously on the same sample. In addition, the conventional graphing procedure for data acquisition was converted to datalogging using strain gauges. Data acquisition rate was improved by more than a factor of three with improved data quality. (iii) How do drought tolerant plants maintain leaf water content? Non-destructive measurement of TDR water content using a flat serpentine triple wire transmission line replaces more lengthy procedures of measuring relative water content. Two challenges remain: drought-stressed leaves alter salt content, changing electrical conductivity, and drought induced changes in leaf morphology affect TDR measurements. (iv) Remote radar signals are reflected from within the first 2 cm of soil. Appropriate calibration of radar imaging for soil water content can be achieved by a parallel pair of blades separated by 8 cm, reaching 1.7 cm into soil and forming a 20 cm TDR transmission line. The correlation between apparent relative permittivity from TDR and synthetic aperture radar (SAR) backscatter coefficient was 0.57 from an airborne flyover. These five examples highlight the diversity in the application of TDR in soil and plant research.