Abstract
Using Optimal Control Theory (OCT), we design fast ramps for the controlled transport of Bose-Einstein condensates with atom chips’ magnetic traps. These ramps are engineered in the context of precision atom interferometry experiments and support transport over large distances, typically of the order of 1 mm, i.e. about 1,000 times the size of the atomic clouds, yet with durations not exceeding 200 ms. We show that with such transport durations of the order of the trap period, one can recover the ground state of the final trap at the end of the transport. The performance of the OCT procedure is compared to that of a Shortcut-To-Adiabaticity (STA) protocol and the respective advantages/disadvantages of the OCT treatment over the STA one are discussed.
Highlights
The measurement’s outcome of a phase-sensitive sensor probing forces exerted on neutral atoms by inertial, material or electromagnetic sources depends dramatically on the initial conditions, i.e. on the position, velocity and size of the input matter-wave
This approach based on the reverse engineering technique allows for a full control of the translational degrees of freedom of the Bose-Einstein Condensates (BEC). It is exciting several collective modes of the quantum gas, an effect which could eventually compromise the expected metrological gain if such a source is used without any precaution as an input of an atom interferometer. It is in this context that the use of optimal control theory (OCT) can reveal an unchallenged potential of targeting a given final state in timescales shorter than the trivial adiabatic manipulation, which is of no practical use in the metrology context since it is associated with poor cycling rates
A first conclusion of this study is that, if one is mainly interested in the control of the average translational degree of freedom of the BEC, the STA approach, whose numerical implementation is much simpler than OCT, is sufficient
Summary
We consider the case of a Z-shaped chip configuration used to trap and manipulate cold Rb atoms in micro-gravity (See reference[15] for a detailed description of the numerical model and reference[44] for the description of an experimental implementation). The physical parameters which govern the trap potential are the chip intensity Iw and the bias magnetic field Bbias. The size of the BEC is defined by the three time-dependent radii rx(t), ry(t) and rz(t) of the paraboloid associated with the BEC wave function, with rx(t) = rx(0) λx(t), ry(t) = ry(0) λy(t) and rz(t) = rz(0) λz(t) It was shown[46,47] that the time-dependent scaling factors λx(t), λy(t) and λz(t) obey the three coupled second order differential equations λx. To be compatible with metrology applications with an integration over thousands of experimental cycles, we want this transport to be realized quickly, i.e. in a duration of the order of the largest time scale associated with the trap, that is of the order of 100 ms with the present chip configuration
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