Extended Data Fig. 1: Calibration techniques in phase space.

Here we show how the required properties of the tickling pulse are determined (‘calibrated’) and the use of the tickling pulse for motional frequency calibrations. a, Matching of the tickling pulse to the SDF pulse (see Methods for nomenclature). The squeezed ion motional state (dashed state labelled 0) is displaced using an SDF together with two π/2 internal state rotations (SDFz). This realizes the displaced squeezed state 1. A subsequent tickling pulse is calibrated in order to revert the displacement implemented by the laser. After this shift the oscillator is in state 2. Whether or not the squeezed state returns to the squeezed vacuum can be probed using the squeezed basis analogue of the red sideband²². Shown is the case of a laser displacement along the squeezed axis, which enhances sensitivity for the tickling coupling strength. b, Similarly, a laser displacement perpendicular to the squeezed axis is used to calibrate the direction of the tickling pulse. c, Motional frequency calibration. The ion is ground state cooled (0), then a coherent state (1) is created by a first tickling pulse. The state evolves freely during the wait time T and rotates by an angle Tδ, with δ the detuning from the angular motional frequency ω_m. A second tickling pulse inverts the first displacement. Because of the detuning, the final state (3) does not return to the ground state, which can be detected applying a red sideband probe pulse.