Correlations in a BEC collision: First-principles quantum dynamics with 150 000 atoms

The quantum dynamics of colliding Bose-Einstein condensates with 150 000 atoms are simulated directly from the Hamiltonian using the stochastic positive-P method. Two-body correlations between the scattered atoms and their velocity distribution are found for experimentally accessible parameters. Hanbury Brown-Twiss or thermal-like correlations are seen for copropagating atoms, while number correlations for counterpropagating atoms are even stronger than thermal correlations at short times. The coherent phase grains grow in size as the collision progresses with the onset of growth coinciding with the beginning of stimulated scattering. The method is versatile and usable for a range of cold atom systems.Comment: 4 pages, 4 figures. v2: Rewording and style changes, minor except for rewrite of background on the positive-P representation. Original research unchange

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations, which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented.Comment: 4 pages, 2 figure

Many-body quantum dynamics of polarisation squeezing in optical fibre

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.Comment: 4 pages, 4 figure

First-principles quantum dynamics in interacting Bose gases I: The positive P representation

The performance of the positive P phase-space representation for exact many-body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made to other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.Comment: 21 pages, 7 figures, 2 tables, IOP styl

Quantum theory of dispersive electromagnetic modes

A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (plane-wave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group-velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one, two or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (I.R.) and one exciton (U.V.) mode, in order to accurately represent dispersion in transparent solid media. Our method of diagonalization does not require an explicit solution of the dispersion relation, but relies instead on the analytic properties of Cauchy contour integrals over all possible mode frequencies. When there is longitudinal phonon dispersion, the relevant group-velocity term is modified so that it only includes the purely electromagnetic part of the group velocity

Gaussian quantum Monte Carlo methods for fermions

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application, we calculate finite-temperature properties of the two dimensional Hubbard model.Comment: 4 pages, 3 figures, Revised version has expanded discussion, simplified mathematical presentation, and application to 2D Hubbard mode

Cost effectiveness of photodynamic therapy with verteporfin for age related macular degeneration: the UK case

AIM: To estimate the potential cost effectiveness of photodynamic therapy (PDT) with verteporfin in the UK setting. METHODS: Using data from a variety of sources a Markov model was built to produce estimates of the cost effectiveness (incremental cost per quality adjusted life year (QALY) and incremental cost per vision year gained) of PDT for two cohorts of patients (one with starting visual acuity (VA) of 20/40 and one at 20/100) with predominantly classic choroidal neovascular disease over a 2 year and 5 year time horizon. A government perspective and a treatment cost only perspective were considered. Probabilistic and one way sensitivity analyses were undertaken. RESULTS: From the government perspective, over the 2 year period, the expected incremental cost effectiveness ratios range from £286 000 (starting VA 20/100) to £76 000 (starting VA 20/40) per QALY gained and from £14 000 (20/100) to £34 000 (20/40) per vision year gained. A 5 year perspective yields incremental ratios less than £5000 for vision years gained and from £9000 (20/40) to £30 000 (20/100) for QALYs gained. Without societal or NHS cost offsets included, the 2 year incremental cost per vision year gained ranges from £20 000 (20/100) to £40 000 (20/40), and the 2 year incremental cost per QALY gained ranges from £412 000 (20/100) to £90 000 (20/40). The 5 year time frame shows expected costs of £7000 (20/40) to £10 000 (20/100) per vision year gained and from £38 000 (20/40) to £69 000 (20/100) per QALY gained. CONCLUSION: This evaluation suggests that early treatment (that is, treating eyes at less severe stages of disease) with PDT leads to increased efficiency. When considering only the cost of therapy, treating people at lower levels of visual acuity would probably not be considered cost effective. However, a broad perspective that incorporates other NHS treatment costs and social care costs suggests that over a long period of time, PDT may yield reasonable value for money

Manipulating Majorana fermions in one-dimensional spin-orbit coupled atomic Fermi gases

Majorana fermions are promising candidates for storing and processing information in topological quantum computation. The ability to control such individual information carriers in trapped ultracold atomic Fermi gases is a novel theme in quantum information science. However, fermionic atoms are neutral and thus are difficult to manipulate. Here, we theoretically investigate the control of emergent Majorana fermions in one-dimensional spin-orbit coupled atomic Fermi gases. We discuss (i) how to move Majorana fermions by increasing or decreasing an effective Zeeman field, which acts like a solid state control voltage gate; and (ii) how to create a pair of Majorana fermions by adding a magnetic impurity potential. We discuss the experimental realization of our control scheme in an ultracold Fermi gas of $^{40}$K atoms.Comment: 4 papges, 6 figure

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus enables first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness and positivity of the basis, and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anti-commuting Grassmann variables

Codimension zero superembeddings

Superembeddings which have bosonic codimension zero are studied in 3,4 and 6 dimensions. The worldvolume multiplets of these branes are off-shell vector multiplets in these dimensions, and their self-interactions include a Born-Infeld term. It is shown how they can be written in terms of standard vector multiplets in flat superspace by working in the static gauge. The action formula is used to determine both Green-Schwarz type actions and superfield actions.Comment: Improved spelling, one reference adde