Fig. 2

Experimental schedule and coherent state control. a Spin-dependent kicks (SDKs) are concatenated to generate cat states. The kicks are inserted between two Ramsey microwave π/2 pulses with a variable relative phase, and finally the interference of the motional states, after being separated for a time T, is measured on the qubit state. Counter-propagating pulses have linear orthogonal polarisations and are orthogonal to an applied magnetic field B. b Each SDK originates from position-dependent stimulated Raman transitions driven by counterpropagating laser beams near a wavelength of 355 nm. c A single SDK displaces a coherent state by ±2ħk in momentum space (or ±iη in natural units of ħ/x ₀), with the sign depending on the initial qubit state (red: \(\left| \uparrow \right\rangle\) or blue: \(\left| \downarrow \right\rangle\)), and splits a qubit superposition (purple: \(\left| \uparrow \right\rangle + \left| \downarrow \right\rangle\)). Each momentum transfer is accompanied by a spin flip. d SDKs are concatenated by changing the direction of the laser beams between each kick, with every pulse from a mode-locked laser used to increase the cat state separation. e Alternatively, SDKs are concatenated by timing the kicks to occur at each half-period of oscillation of the ion in the trap. (The arrows only track population initially in \(\left| \downarrow \right\rangle\), but the final state is still shown by including the blue \(\left| \downarrow \right\rangle\) component.) Free evolution appears in figures d, e as circular orbits