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Adiabatic radio frequency (RF) potentials are powerful tools for creating advanced trapping geometries for ultra-cold atoms. While the basic theory of RF trapping is well understood, studies of more complicated setups involving multiple resonant frequencies in the limit where their effects cannot be treated independently are rare. Here we present an approach based on Floquet theory and show that it offers significant corrections to existing models when two RF frequencies are near degenerate. Furthermore it has no restrictions on the dimension, the number of frequencies or the orientation of the RF fields. We show that the added degrees of freedom can, for example, be used to create a potential that allows for easy creation of ring vortex solitons.
Coherent transport by adiabatic passage has recently been suggested as a high-fidelity technique to engineer the centre-of-mass state of single atoms in inhomogenous environments. While the basic theory behind this process is well understood, several
Adiabatic techniques are well known tools in multi-level electron systems to transfer population between different states with high fidelity. Recently it has been realised that these ideas can also be used in ultra-cold atom systems to achieve cohere
We present a non-destructive method to probe a complex quantum system using multiple impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particula
In this chapter we review the field of radio-frequency dressed atom trapping. We emphasise the role of adiabatic potentials and give simple, but generic models of electromagnetic fields that currently produce traps for atoms at microkelvin temperatur
An analytically solvable model for quasi-static transformations across quantum critical points featuring Bosonic quasi-particle excitations is presented. The model proves that adiabaticity breakdown is a general feature of universal slow dynamics in