Fast atomic transport without vibrational heating

Abstract

We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven non-adiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies and accelerations involved are analyzed, as well as the relation to previous approaches (based on classical trajectories or "fast-forward" and "bang-bang" methods) which can be integrated in the invariant-based framework.

Shortcuts to adiabaticity: Fast-forward approach

“…Performing now the unitary transformation [3,4] ψ n (x, t) = e im [ρ|x| 2 /2ρ+(αρ−αρ)·x/ρ] 1 ρ 3/2 χ n (σ), (23) the state ψ n is easily obtained from the solution χ n (σ) (normalized in σ-space) of the auxiliary stationary Schrödinger equation…”

“…Among other approaches let us mention (i) a transitionless tracking algorithm or "counterdiabatic" approach that adds to the original Hamiltonian extra terms to cancel transitions in the adiabatic or superadiabatic bases [8][9][10][11][12][13]; (ii) inverse engineering of the external driving [3,4,6,[21][22][23][24][25][26] based on Lewis-Riesenfeldt invariants [27], which has been applied in several expansion experiments [25,26]; (iii) optimal control (OC) methods [5,7,14,16], sometimes combined with other methods to enhance their performance [4,5,7]; (iv) the fast-forward (FF) approach advocated by Masuda and Nakamura [19,28]; (v) parallel adiabatic passage [29][30][31][32].…”

“…Motivated by the practical need to accelerate quantum adiabatic processes in different contexts (transport [1][2][3][4][5], expansions [6,7], population inversion and control [8][9][10][11][12][13], cooling cycles [6,14,15], wavefunction splitting [16][17][18][19]), and by related fundamental questions (about the quantum limits to the speed of processes, the viability of adiabatic computing [20], or the third principle of thermodynamics [14,21]), a flurry of theoretical and experimental activity has been triggered by the proposal of several approaches to design "shortcuts to adiabaticity". Among other approaches let us mention (i) a transitionless tracking algorithm or "counterdiabatic" approach that adds to the original Hamiltonian extra terms to cancel transitions in the adiabatic or superadiabatic bases [8][9][10][11][12][13]; (ii) inverse engineering of the external driving [3,4,6,[21][22][23][24][25][26] based on Lewis-Riesenfeldt invariants [27], which has been applied in several expansion experiments [25,26]; (iii) optimal control (OC) methods [5,...…”

Two-Qubit Gate Operation on Selected Nearest-Neighbor Neutral Atom Qubits

“…We might also use nonadiabatic transport of an atom with shorter execution time compared to adiabatic transfer and improve the fidelity. This is realized by employing the Lewies-Riesenefeld invariant [26] associated with the Hamiltonian for example [27,28]. Application of nonadiabatic atom transport to the current problem will discuss in other paper.…”

Ehrenfest dynamics and frictionless cooling methods

“…However, these techniques do reduce the temperature, with all the associated benefits in terms of state preparation [6]. Examples include efficient fast decompression of 87 Rb atoms in normal [7] and Bose-condensed [8] states, which have been experimentally demonstrated, and detailed proposals for efficient fast atomic transport [9] and optimized sympathetic cooling [10].…”