Coherence and instability in a driven Bose-Einstein condensate: a fully dynamical number-conserving approach |

T. P. Billam and S. A. Gardiner |

New J. Phys. **14**, 013038 (2012) |

We consider a Bose–Einstein condensate driven by periodic δ-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion in our fully time-dependent, second-order description acts to damp this growth, leading to oscillations in the (non)condensate population and the coherence of the system. |

Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps |

T. P. Billam, S. A. Wrathmall, and S. A. Gardiner |

Physical Review A **85**, 013627 (2012) |

We consider the ground state of an attractively interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground state takes the form of a bright soliton solution of the nonlinear Schrödinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation, we systematically and quantitatively assess how solitonlike this ground state is, over a wide range of trap and interaction strengths. Our analysis reveals that the regime in which the ground state is highly solitonlike is significantly restricted and occurs only for experimentally challenging trap anisotropies. This result and our broader identification of regimes in which the ground state is well approximated by our simple analytic variational solution are relevant to a range of potential experiments involving attractively interacting Bose-Einstein condensates. |

Realizing bright-matter-wave-soliton collisions with controlled relative phase |

T. P. Billam, S. L. Cornish, and S. A. Gardiner |

Physical Review A **83**, 041602(R) (2011) |

We propose a method to split the ground state of an attractively interacting atomic Bose-Einstein condensate into two bright solitary waves with controlled relative phase and velocity. We analyze the stability of these waves against their subsequent recollisions at the center of a cylindrically symmetric, prolate harmonic trap as a function of relative phase, velocity, and trap anisotropy. We show that the collisional stability is strongly dependent on relative phase at low velocity, and we identify previously unobserved oscillations in the collisional stability as a function of the trap anisotropy. An experimental implementation of our method would determine the validity of the mean-field description of bright solitary waves and could prove to be an important step toward atom interferometry experiments involving bright solitary waves. |

Quantum resonances in an atom-optical *δ*-kicked harmonic oscillator |

T. P. Billam and S. A. Gardiner |

Physical Review A **80**, 023414 (2009) |

Under certain conditions, the quantum *δ*-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the *δ*-kicked harmonic oscillator and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite two-dimensional set of coefficients from which we derive an analytic expression for the evolution of a coherent state at quantum resonance. |