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arXiv:1006.1495 · Physical Review A

Fast optimal transition between two equilibrium states

Jean-François Schaff, Xiao-Li Song, Patrizia Vignolo, G. Labeyrie

Published Sep 24, 2010• 170 citations
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Abstract

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of $^{87}\mathrm{Rb}$ atoms held in a harmonic magnetic trap in the presence of gravity. We are able to decompress the trap by a factor of $15$ within $35$ ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of $37$ on the transition time.

DOI
10.1103/physreva.82.033430

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We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of 87Rb^{87}\mathrm{Rb}87Rb atoms held in a harmonic magnetic trap in the presence of gravity. We are able to decompress the trap by a factor of 151515 within 353535 ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of 373737 on the transition time.
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We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven nonadiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies, and accelerations involved are analyzed along with the relation to previous approaches based on classical trajectories or ``fast-forward'' and ``bang-bang'' methods, which can be integrated in the invariant-based framework.
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Shortcuts to adiabaticity are techniques allowing rapid variation of the system Hamiltonian without inducing excess heating.Fast optical transfer of atoms between different locations is an important application of shortcuts to adiabaticity.We show that the common boundary conditions on the atomic position, which are imposed to find the driving trajectory, lead to highly non-practical boundary conditions for the optical trap.Our experimental results demonstrate that, as a result, previously suggested trajectories are likely to fall short of the expectation.We develop two complementary methods that solve this boundary conditions problem by adding more degrees of freedom to the trajectory parameter space.In the first method, this is achieved by the addition of a spectral component at the trapping frequency, while in the second we use a polynomial trajectory of an order high enough to account for the new boundary conditions.We experimentally demonstrate that this approach allows us to construct highly non-adiabatic movements with no residual sloshing.Our techniques can also account for non-harmonic terms in the confining potential.