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 populations of the instantaneous initial and final levels invariant, but in a much shorter time. This may require that the harmonic trap becomes an expulsive parabolic potential in some time interval. The cooling times achieved are also shorter than previous minimal times using optimal-control bang-bang methods and real frequencies.PACS numbers: 37.10. De, 37.10.Vz A fast adiabatic expansion in a short finite time looks like a contradiction in terms. An "adiabatic" process in quantum mechanics is a slow process where the system follows at all times the instantaneous eigenvalues and eigenstates of the time-dependent Hamiltonian. This is in a sense maximally efficient as the populations do not change, i.e. there is no heating or friction, but the price to pay is that the long times needed may render the process useless or even impossible to implement. Thus, a highly desirable goal is to prepare the same final states and energies of the adiabatic process in a given finite time t f , without necessarily following the instantaneous eigenstates along the way. We would also like the process to be robust with respect to arbitrary initial states. If fulfilled, this old goal [1] has important implications. In particular, cooling without phase-space compression, which is all that is needed for many applications other than Bose Einstein condensation, could be performed in fast cycles increasing, for example, the flux of cold atoms produced and the signal to noise ratio in an atomic clock [2], or in cold-atom pulsed beam experiments and related technology [3]. This goal also includes as a particular case a long standing question in the fields of optimal control theory and finite time thermodynamics, namely, to optimize the passage between two thermal states of a system [4,5,6,7]. For time-dependent harmonic oscillators, minimal times have been established using "bang-bang" real-frequency processes believed up to now to be optimal [6], in which the frequencies are changed suddenly at certain instants but kept constant otherwise. In this letter we shall describe a robust solution to the stated general goal for atoms trapped in a time-dependent harmonic oscillator which applies both to equilibrium and non-equilibrium states. In particular we describe cooling processes performed in a time interval smaller than the minimal time of the bang-bang methods considered so far. We shall for simplicity describe our method for states representing single atoms of mass m, but the same results are immediately applicable to N -body non-interacting fermions or to a Tonks-Girardeau gas [8], and generalizations will be relevant for other driving processes, such as cold atom launching or the transport of ultracold atoms with optical tweezers [9].We consider an effectively one dimensional time dependent harmonic oscillator, H =p 2 /2m + mω(t) 2q2 /2, with an initial angular frequency ω(0) > 0 a...

arXiv:1212.6343International audienceQuantum adiabatic processes--that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian--are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects