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

Abstract

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.

Shortcuts to adiabaticity using flow fields

“…We then define a velocity flow field 5 4 The dynamical phase α is generically accompanied by a geometric phase [75], but the latter vanishes for a kinetic-plus-potential Hamiltonian in one degree of freedom. 5 The quantity v q t , -( ) was identified as a 'hydrodynamic velocity' in [25], equation (6). ,…”

“…Using the identity m m 0 t á ¶ ñ = | , which holds for H 0 given by equation (4), we rewrite the equality in equation (25) as follows:…”

“…Shortcuts to adiabaticity [16] are protocols that suppress these excitations, often by means of an auxiliary Hamiltonian H t 1 ( ), which is added to H t 0 ( ) to achieve the desired evolution. A variety of shortcut protocols have been developed including invariant-based inverse engineering [17,18], transitionless counterdiabatic driving [19][20][21][22], fast-forward methods [23][24][25] and methods based on unitary [26][27][28][29][30] or gauge [31] transformations. Quantum shortcuts to adiabaticity have been extended to non-Hermitian Hamiltonians [32,33], open quantum systems [34][35][36][37] and Dirac-dynamics [38][39][40].…”

Fast forward of the adiabatic spin dynamics of entangled states

“…The corresponding Hamiltonian is given by: 27) which can generate an entangled state from the product state. In Eq.…”

Shortcut to adiabaticity in a Stern-Gerlach apparatus

“…These methods enable one to guarantee a transitionless evolution faster than the time scale imposed by the adiabatic regime. The STA approach has been shown experimentally to efficently speed up the transport or manipulation of wave functions [10][11][12][13][14][15][16][17] and even thermodynamical transformations [18][19][20]. Concerning the transfer of quantum states, recent impressive implementations have been reported in cold atoms experiments [21], solid-state architectures [22] or in optomechanical systems [23].…”