Formal structure of phase-space path integrals based on different types of operator orderings is ... more Formal structure of phase-space path integrals based on different types of operator orderings is analysed.
We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bos... more We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.
Technical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236), 2000
ABSTRACT Experimental techniques for the production and manipulation of Bose-Einstein condensates... more ABSTRACT Experimental techniques for the production and manipulation of Bose-Einstein condensates have now advanced to the stage where macroscopic coherence effects have been observed. The usual method for theoretical investigation of the bulk properties of a Bose-Einstein condensate with collisions is to use the Gross-Pitaevski equation, which ignores any contribution made by quantum noise within a condensate
We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in... more We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a "ferromagnetic" state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.
We investigate the dynamical and statistical effects of different input states of the electromagn... more We investigate the dynamical and statistical effects of different input states of the electromagnetic field in the travelling wave parametric processes of second harmonic generation and nondegenerate downconversion. Using the phase space techniques of stochastic integration in the positive-P representation, equivalent to a fully quantum mechanical analysis, we consider different input states and show that the effects on the mean field solutions can be quite drastic. We also investigate the effects of the input statistics on the quantum properties of the output fields, finding that a thermal input can actually cause the value of some quantum correlations to increase. Ó
We show that stochastic electrodynamics and quantum mechanics give quantitatively dierent predict... more We show that stochastic electrodynamics and quantum mechanics give quantitatively dierent predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are dierent in the regions where the system performs best in relation to the QND criteria, and that they signi®cantly overestimate the performance in these regions. Ó 2001 Published by Elsevier Science B.V.
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and i... more Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit → 0. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wavepacket in momentum space. This way, if the electronic wavepacket produced by optical tunneling in strong infrared fiels is localised both in coordinate and momentum, its motion after tunneling ipso facto cannot be described with purely classical trajectories -in contrast to popular models in the literature.
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is... more A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the measure in Feynman path integrals in terms of stochastic differential equations for the paths.
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number... more We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation,
We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy a... more We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy and a light atom in the Born-Oppenheimer approximation. We focus on the situation where the heavy atoms are bosons, which was realized in several experiments. The elastic and inelastic cross sections for the atom-molecular scattering exhibit a series of resonances corresponding to three-body Efimov
Collisional damping of the excitations in a Bose-condensed gas is investigated over the wide rang... more Collisional damping of the excitations in a Bose-condensed gas is investigated over the wide range of energies and temperatures. Numerical results for the damping rate are presented and a number of asymptotic and interpolating expressions for it are derived.
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body syst... more We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and longrange, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.
Formal structure of phase-space path integrals based on different types of operator orderings is ... more Formal structure of phase-space path integrals based on different types of operator orderings is analysed.
We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bos... more We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.
Technical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236), 2000
ABSTRACT Experimental techniques for the production and manipulation of Bose-Einstein condensates... more ABSTRACT Experimental techniques for the production and manipulation of Bose-Einstein condensates have now advanced to the stage where macroscopic coherence effects have been observed. The usual method for theoretical investigation of the bulk properties of a Bose-Einstein condensate with collisions is to use the Gross-Pitaevski equation, which ignores any contribution made by quantum noise within a condensate
We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in... more We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a "ferromagnetic" state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.
We investigate the dynamical and statistical effects of different input states of the electromagn... more We investigate the dynamical and statistical effects of different input states of the electromagnetic field in the travelling wave parametric processes of second harmonic generation and nondegenerate downconversion. Using the phase space techniques of stochastic integration in the positive-P representation, equivalent to a fully quantum mechanical analysis, we consider different input states and show that the effects on the mean field solutions can be quite drastic. We also investigate the effects of the input statistics on the quantum properties of the output fields, finding that a thermal input can actually cause the value of some quantum correlations to increase. Ó
We show that stochastic electrodynamics and quantum mechanics give quantitatively dierent predict... more We show that stochastic electrodynamics and quantum mechanics give quantitatively dierent predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are dierent in the regions where the system performs best in relation to the QND criteria, and that they signi®cantly overestimate the performance in these regions. Ó 2001 Published by Elsevier Science B.V.
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and i... more Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are distinctly quantum features of these trajectories, such as the complex-valued coordinates, physically relevant in the classically allowed region of phase space, and what is their origin? First, we argue that solutions of classical equations of motion can account for quantum effects. To this end, we construct an exact solution to the classical Hamilton-Jacobi equation which accounts for dynamics of the wave packet, and show that this solution is physically correct in the limit → 0. Second, we show that imaginary components of classical trajectories are directly linked to the finite size of the initial wavepacket in momentum space. This way, if the electronic wavepacket produced by optical tunneling in strong infrared fiels is localised both in coordinate and momentum, its motion after tunneling ipso facto cannot be described with purely classical trajectories -in contrast to popular models in the literature.
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is... more A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the measure in Feynman path integrals in terms of stochastic differential equations for the paths.
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number... more We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation,
We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy a... more We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy and a light atom in the Born-Oppenheimer approximation. We focus on the situation where the heavy atoms are bosons, which was realized in several experiments. The elastic and inelastic cross sections for the atom-molecular scattering exhibit a series of resonances corresponding to three-body Efimov
Collisional damping of the excitations in a Bose-condensed gas is investigated over the wide rang... more Collisional damping of the excitations in a Bose-condensed gas is investigated over the wide range of energies and temperatures. Numerical results for the damping rate are presented and a number of asymptotic and interpolating expressions for it are derived.
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body syst... more We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and longrange, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.
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Papers by L. Plimak