58 research outputs found
Scaling dynamics of the ultracold Bose gas
The large-scale expansion dynamics of quantum gases is a central tool for
ultracold gas experiments and poses a significant challenge for theory. In this
work we provide an exact reformulation of the Gross-Pitaevskii equation for the
ultracold Bose gas in a coordinate frame that adaptively scales with the system
size during evolution, enabling simulations of long evolution times during
expansion or similar large-scale manipulation. Our approach makes no
hydrodynamic approximations, is not restricted to a scaling ansatz, harmonic
potentials, or energy eigenstates, and can be generalized readily to
non-contact interactions via the appropriate stress tensor of the quantum
fluid. As applications, we simulate the expansion of the ideal gas, a
cigar-shaped condensate in the Thomas-Fermi regime, and a linear superposition
of counter propagating Gaussian wavepackets. We recover known scaling for the
ideal gas and Thomas-Fermi regimes, and identify a linear regime of
aspect-ratio preserving free expansion; analysis of the scaling dynamics
equations shows that an exact, aspect-ratio invariant, free expansion does not
exist for nonlinear evolution. Our treatment enables exploration of nonlinear
effects in matter-wave dynamics over large scale-changing evolution.Comment: 12 pages, 3 figures, 2 appendice
Probing the degree of coherence through the full 1D to 3D crossover
We experimentally study a gas of quantum degenerate 87Rb atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system’s dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential μ controls the departure of the system from 3D and that the fluctuations are dependent on both μ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations
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