

Bright Soliton Theory: Publications 
Coherence and instability in a driven BoseEinstein condensate: a fully dynamical numberconserving approach 
T. P. Billam and S. A. Gardiner 
New J. Phys. 14, 013038 (2012) 
We consider a Bose–Einstein condensate driven by periodic δkicks. In contrast to firstorder descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion in our fully timedependent, secondorder 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 matterwave 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 BoseEinstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasionedimensional 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 GrossPitaevskii 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 BoseEinstein condensates. 
Realizing brightmatterwavesoliton 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 BoseEinstein 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 meanfield description of bright solitary waves and could prove to be an important step toward atom interferometry experiments involving bright solitary waves. 
Numberconserving approach to a minimal selfconsistent treatment of condensate and noncondensate dynamics in a degenerate Bose gas 
S.A. Gardiner and S.A. Morgan 
Physical Review A 75, 043621 (2007) 
We describe a numberconserving approach to the dynamics of BoseEinstein condensed dilute atomic gases. This builds upon the works of Gardiner [Phys. Rev. A 56, 1414 (1997)] and Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of noncondensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a secondorder treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and noncondensate number dynamics for a finite total number of particles, and show that such a secondorder treatment is provided by a suitably generalized GrossPitaevskii equation, coupled to the CastinDum numberconserving formulation of the Bogoliubovde Gennes equations. The necessary equations of motion can be generated from an approximate thirdorder Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics occurring at finite temperature, where there is a significant noncondensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant noncondensate fraction, even if the noncondensate fraction is initially negligible. 
Many excellent articles relating to bright solitons can also be found on our links page.
