Optimal quantum control of Bose-Einstein condensates in magnetic microtraps

Abstract

Transport of Bose-Einstein condensates in magnetic microtraps, controllable by external parameters such as wire currents or radio-frequency fields, is studied within the framework of optimal control theory (OCT). We derive from the Gross-Pitaevskii equation the optimality system for the OCT fields that allow to efficiently channel the condensate between given initial and desired states. For a variety of magnetic confinement potentials we study transport and wavefunction splitting of the condensate, and demonstrate that OCT allows to drastically outperfrom more simple schemes for the time variation of the microtrap control parameters.

OCTBEC—A Matlab toolbox for optimal quantum control of Bose–Einstein condensates

“…Such splitting has been described in some length in Ref. [22], and details of the demo program will be presented in Sec. 5.1.…”

“…Our computational approach is based on a Runge-Kutta or Crank-Nicolson solution of the dynamic equations, together with an optimal control framework using conjugate gradient or quasi-Newton minimization techniques [22,23,28,36,37]. Despite the large diversity of problems studied in the past, the simulations are similar in many aspects, and at some point we realized that we were wasting a significant amount of time copying code from one program to another one.…”

“…The OCTBEC toolbox considers situations where the confinement potential for atoms can be controlled by some external control parameters λ(t) [22]. A typical example are the magnetic fields of an atom chip, where the potential can be modified by changing the currents running through the wires of the chip.…”

“…In addition, in the Matlab window the progress of the optimal control loop is reported Here, it gives the iteration number of the optimization loop, f is the cost function value [22], and ||g|| is the norm of the gradient which should become zero for the optimal control. Figs.…”

“…In the past, we have successfully developed and implemented an optimal quantum control approach for Bose-Einstein condensates in magnetic microtraps within the framework of the Gross-Pitaevskii equation [22,23]. More recently, this approach has been generalized to more sophisticated description schemes, such as the two-mode model [24,25] or the multi-configurational Hartree method for bosons (MCTDHB) [26], which allow to additonally describe condensate fragmentations and excitations.…”