Fast quasi-adiabatic dynamics

We work out the theory and applications of a fast quasi-adiabatic approach to speed up slow adiabatic manipulations of quantum systems by driving a control parameter as near to the adiabatic limit as possible over the entire protocol duration. Specifically, we show that the population inversion in a two-level system, the splitting and cotunneling of two-interacting bosons, and the stirring of a Tonks-Girardeau gas on a ring to achieve mesoscopic superpositions of many-body rotating and non-rotating states, can be significantly speeded up.Comment: 5 pages, 6 figure

Fast bias inversion of a double well without residual particle excitation

We design fast bias inversions of an asymmetric double well so that the lowest states in each well remain so and free from residual motional excitation. This cannot be done adiabatically, and a sudden bias switch produces in general motional excitation. The residual excitation is suppressed by complementing a predetermined fast bias change with a linear ramp whose time-dependent slope compensates for the displacement of the wells. The process, combined with vibrational multiplexing and demultiplexing, can produce vibrational state inversion without exciting internal states, just by deforming the trap.Comment: 7 pages, 6 figure

Fast driving between arbitrary states of a quantum particle by trap deformation

By performing a slow adiabatic change between two traps of a quantum particle, it is possible to transform an eigenstate of the original trap into the corresponding eigenstate of the final trap. If no level crossings are involved, the process can be made faster than adiabatic by setting first the interpolated evolution of the wave function from its initial to its final form and inferring from this evolution the trap deformation. We find a simple and compact formula which gives the trap shape at any time for any interpolation scheme. It is applicable even in complicated scenarios where there is no adiabatic process for the desired state-transformation, e.g., if the state changes its topological properties. We illustrate its use for the expansion of a harmonic trap, for the transformation of a harmonic trap into a linear trap and into an arbitrary number of traps of a periodic structure. Finally, we study the creation of a node exemplified by the passage from the ground state to the first excited state of a harmonic oscillator.Comment: 6 pages, 5 figure

Engineering fast and stable splitting of matter waves

When attempting to split coherent cold atom clouds or a Bose-Einstein condensate (BEC) by bifurcation of the trap into a double well, slow adiabatic following is unstable with respect to any slight asymmetry, and the wave "collapses" to the lower well, whereas a generic fast chopping splits the wave but it also excites it. Shortcuts to adiabaticity engineered to speed up the adiabatic process through non-adiabatic transients, provide instead quiet and robust fast splitting. The non-linearity of the BEC makes the proposed shortcut even more stable

Hamiltonian engineering via invariants and dynamical algebra

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations as slow, adiabatic ones. As application examples, we design families of shortcut Hamiltonians that drive two- and three-level systems between initial and final configurations, imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.We are grateful to K. Takahashi and R. Kosloff for stimulating discussions. We acknowledge funding by Grants No. IT472-10 and No. FIS2009-12773-C02-01, and theUPV/EHU Program No. UFI 11/55. E.T. is supported by the Basque Government postdoctoral program. S.M.-G. acknowledges support from a UPV/EHU fellowship.Publicad