Robust dynamical exchange cooling with trapped ions

Abstract

We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions’ equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to 6.3 motional cycles, comprising 14.2 μs for ions with a 0.44 MHz trap frequency. This is considerably faster than can be achieved using laser cooling in the weak coupling regime, which makes this an attractive scheme in the context of quantum computing.

Time-dependent harmonic potentials for momentum or position scaling

“…Shortcuts to adiabaticity techniques can be made very robust with respect to initial conditions or protocol imperfections. This feature and the possibility to choose and shorten the process time make them powerful tools to design cooling [13,21,22], even for open systems [23][24][25][26], launching [27], or compression and expansion protocols [9,10]. This work, in particular, demonstrates that, making use of linear invariants, momentum or position scaling, irrespective of initial conditions of the particle, can be achieved.…”

Shortcuts to adiabatic rotation of a two-ion chain

“…If we wish to approach θ = 0 smoothly at the time boundaries, then k → 0 there, which implies a vanishing trapping potential and d → ∞. A way out is explored in Appendix B making use of a more complex external trap potential with linear and quartic terms added, as in reference [31]. In the main text we stay within the harmonic trap configuration with constant k and renounce to separate the modes.…”

“…Specifically we consider a tilted double well potential, which combines a repulsive harmonic potential with the confinement provided by the quartic term and a linear term [31], V = γ(t)(s 1 + s 2 ) + 1 2 u 1 (t)s…”

“…Motional control operations, and rotations in particular, need in most applications to be fast, relative to adiabatic dynamics, but also gentle, avoiding final excitations, two requirements met with shortcut to adiabaticity (STA) driving protocols [22]. There are different STA techniques but, for trapped ion driving, STA invariant-based inverse engineering has proven useful [1,3,4,21,23,24,25,26,27,28,29,30,31], also to design trap rotations for a single ion [20].…”

Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators

“…The two oscillators have to be driven simultaneously with common controls but, among the plethora of parameter trajectories, it is possible to find the ones that satisfy simultaneously the boundary conditions imposed on both oscillators. This strategy has been successfully applied to design the driving of different operations on two trapped ions such as transport or expansions [9,10], separation of two equal ions in double wells [13], phase gates [14], or dynamical exchange cooling [15].…”