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Search Results: 1 - 10 of 282737 matches for " C. W. Gardiner "
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A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
C. W. Gardiner
Physics , 1997, DOI: 10.1103/PhysRevA.56.1414
Abstract: The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators as the product of an annihilation operator $A$ for the total number of particles and the sum of a ``condensate wavefunction'' $\xi(x)$ and a phonon field operator $\chi(x)$ in the form $\psi(x) \approx A\{\xi(x) + \chi(x)/\sqrt{N}\}$ when the field operator acts on the N particle subspace. It is then possible to expand the Hamiltonian in decreasing powers of $\sqrt{N}$, an thus obtain solutions for eigenvalues and eigenstates as an asymptotic expansion of the same kind. It is also possible to compute all matrix elements of field operators between states of different N.
Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields
C. W. Gardiner
Physics , 2003, DOI: 10.1016/j.optcom.2004.05.061
Abstract: A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which takes account of anticommutation relations between the Fermionic driving field and those system operators which can change the number of Fermions within the system.
Quantum Kinetic Theory I: A Quantum Kinetic Master Equation for Condensation of a weakly interacting Bose gas without a trapping potential
C. W. Gardiner,P. Zoller
Physics , 1996, DOI: 10.1103/PhysRevA.55.2902
Abstract: A Quantum Kinetic Master Equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the Quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.
Quantum Noise in Quantum Optics: the Stochastic Schr?dinger Equation
Peter Zoller,C. W. Gardiner
Physics , 1997,
Abstract: Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluctuations in July 1995 to appear in Elsevier Science Publishers B.V. 1997, edited by E. Giacobino and S. Reynaud.
Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems
C. W. Gardiner,P. Zoller
Physics , 1997, DOI: 10.1103/PhysRevA.58.536
Abstract: We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle number conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long range order, to the extent that this concept makes sense in a tightly trapped condensate.
A phase-space method for the Bose-Hubbard model
P. Jain,C. W. Gardiner
Physics , 2004,
Abstract: We present a phase-space method for the Bose-Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard "one site" model where quantum tunneling is approximated entirely using mean-field terms; the second "two site" model explicitly includes tunneling between two adjacent sites while treating tunneling with other neighbouring sites using the mean-field approximation. The ground state is determined by minimizing the classical energy functional subject to quantum mechanical constraints, which take the form of uncertainty relations. For each model Hamiltonian we compare the ground state results from the Q-function method with the exact numerical solution. The results from the Q-function method, which are easy to compute, give a good qualitative description of the main features of the Bose-Hubbard model including the superfluid to Mott insulator. We find the quantum mechanical constraints dominate the problem and show there are some limitations of the method particularly in the weak lattice regime.
Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
C. W. Gardiner,P. Zoller
Physics , 1999, DOI: 10.1103/PhysRevA.61.033601
Abstract: A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.
Quantum Kinetic Theory III: Simulation of the Quantum Boltzmann Master Equation
D. Jaksch,C. W. Gardiner,P. Zoller
Physics , 1997, DOI: 10.1103/PhysRevA.56.575
Abstract: We present results of simulations of a em quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equations derived in previous work. We consider two cases of trapping potentials: a 3D square well potential with periodic boundary conditions, and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.
The stochastic Gross-Pitaevskii equation II
C. W. Gardiner,M. J. Davis
Physics , 2003, DOI: 10.1088/0953-4075/36/23/010
Abstract: We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a Bose gas, which includes only modes below an energy cutoff E_R that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provide noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation, and by the feasibility of its numerical implementation.
Effective Field Theory for Atom-Molecule Systems I: Formulation of Effective Field Theory
Catarina E Sahlberg,C W Gardiner
Physics , 2011,
Abstract: We present a model of a coupled bosonic atom-molecule system, using the recently developed c-field methods as the basis in our formalism. We derive expressions for the s-wave scattering length and binding energy within this formalism, and by relating these to the corresponding experimental parameters, we can accurately determine the phenomenological parameters in our system.
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