Frictionless atom cooling in harmonic traps: a time-optimal approach
نویسندگان
چکیده
In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for trasient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has “bang-bang” form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.
منابع مشابه
Minimum-Time Frictionless Atom Cooling in Harmonic Traps
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.
متن کاملFast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity.
A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the same populations of instantaneous levels in the initial and final traps, but in a much shorter time. This may require that the harmonic trap become transiently an expulsive parabolic potential. The cooling times achieved are shorter than those ...
متن کاملTime-optimal controls for frictionless cooling in harmonic traps
Fast adiabatic cooling procedures have important implications for the attainability of absolute zero. While traditionally adiabatically cooling a system is associated with slow thermal processes, for the parametric quantum harmonic oscillator fast frictionless processes are known, which transfer a system from an initial thermal equilibrium at one temperature into thermal equilibrium at another ...
متن کاملNonperturbative and perturbative treatments of parametric heating in atom traps
We study the quantum description of parametric heating in harmonic potentials both nonperturbatively and perturbatively, having in mind atom traps. The first approach establishes an explicit connection between classical and quantum descriptions; it also gives analytic expressions for properties such as the width of fractional frequency parametric resonances. The second approach gives an alterna...
متن کاملMomentum diffusion for coupled atom-cavity oscillators
It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps ind...
متن کامل