Ultracold atoms are neutral atoms cooled to nanokelvin temperatures, as Bose–Einstein condensates or degenerate Fermi gases, and held in magnetic traps, atom chips or optical lattices [1]. The controls are the trapping potentials themselves: their depth, position, shape and time dependence, plus laser and radio-frequency couplings between internal states. Control tasks include moving and splitting clouds, preparing motional and many-body states, and building the beam splitters and mirrors of atom interferometers.

Transport, compression and splitting

  • Moving atoms. Transport with optical tweezers on the timescale of a trap period leaves no centre-of-mass excitation for a discrete set of durations, set by the Fourier transform of the velocity profile [2].
  • Shortcuts to adiabaticity. Engineered trap trajectories based on invariants of motion decompressed a cold cloud by a factor of 15 in 35 ms, 37 times faster than a linear ramp [3]. They also worked for an interacting, finite-temperature condensate [4]. See Shortcuts to adiabaticity.
  • Splitting condensates. Optimal control of the splitting of a condensate in a double well increases number squeezing, which helps interferometry [5]. On an atom chip, optimally controlled excitation of a condensate’s vibrational state produced correlated twin-atom beams [6].

Mean-field and many-body control

For condensates, the Gross–Pitaevskii equation is a tractable model for gradient-based optimization. It has been used to design control of condensates in microtraps that remains good when the computed controls are distorted by filters [7], and to compare GRAPE and Krotov [8]. In optical lattices, the superfluid–Mott-insulator transition [9] is the standard control target. Optimal crossings were first designed with tensor networks [10]. Experimentally, closed-loop optimization sped up loading and crossing more than threefold [11]. Optimal transformations proved robust to temperature and atom-number fluctuations [12]. See Many-body optimal control and CRAB & dCRAB.

Motional states and interferometry

Shaking an optical lattice in position turns the lattice into a control knob for momentum states. Optimal control transferred a condensate into single or multiple momentum states with controlled relative phases [13]. Closed-loop dCRAB optimization of the shaking built a beam splitter and complete interferometers [14]. In light-pulse atom interferometry [15], GRAPE-designed mirror pulses are robust to the spread of velocities, intensities and Zeeman states in the cloud [16]. See Control for sensing & metrology and Robust & ensemble optimal control.

Learning and citizen science

Cold-atom experiments are slow to simulate but quick to repeat, which makes them natural targets for optimization on the experiment. Machine learning has optimized the production of condensates [17], and experts and citizen scientists have optimized it remotely [18]. See Closed-loop & in-situ optimization and Reinforcement & machine learning for control.

Limitations

  • Interactions, finite temperature and imperfect potentials make accurate models hard. Mean-field descriptions fail for strongly correlated states.
  • Each experimental run takes seconds, and the measurements are usually destructive, which limits how many cost evaluations closed-loop optimization can afford.
  • Calibration of potentials (atom-chip currents, lattice depths) drifts between runs.