Quantum State Control of a Bose-Einstein Condensate in an Optical Lattice

Abstract

We report on the efficient design of quantum optimal control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our protocols operate on the momentum comb associated with the lattice. In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position. With this technique, we experimentally demonstrate a precise, robust and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components. This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…Also, a shaken-lattice interferometer has been experimentally realized through a specific phase modulation of the lattice [605]. Recent extensions include remote control of a BEC [278,360] and state preparation of a BEC in an optical lattice [205] as highlighted in Fig. 1 in Sec.…”

“…A recent and striking example of the power of quantum optimal control techniques is illustrated in Fig. 1 showing the realization of a Bose-Einstein condensate (BEC) printer [205]. In this experiment, a BEC of ultra-cold 87 Rb atoms was loaded into a one-dimensional optical lattice formed by two counter-propagating laser beams with the same wavelength, but a different phase.…”

“…1. This approach to preparing states of a BEC in an optical lattice is also practically useful in many areas from quantum simulation to quantum metrology [205]. We review further highlights of experimental implementations of quantum optimal control in Sec.…”

Weber number and the outcome of binary collisions between quantum droplets

“…Subsequently, the potential barrier was turned off and the two droplets migrate towards the center of a harmonic confining potential. After a controlled time interval ∆t the latter potential was also turned off, and the droplets collided in a potential free environment; ∆t is used to tune the initial relative speed of the droplets [28]. If that speed were higher than a critical value v c as a result of the collision the droplets coalesced; v c depends in a non monotonic way on the number of atoms in each initial droplet.…”

Weber number and the outcome of binary collisions between quantum droplets

“…Subsequently, the potential barrier was turned off and the two droplets migrate towards the center of a harmonic confining potential. After a controlled time interval the potential was turned off, and the droplets collided in a potential free environment; was used to tune the initial relative speed of the droplets 32 . The analysis of experimental data in Ref.…”