A blue-sideband drive uses the internal gap plus one motional packet, so the same trapped ion leaves with one more motion quantum in the ledger. The addition is exact only for the declared gap, spacing, starting index, and ideal shared mode; laboratory pulses add detuning drift, sideband-strength calibration, heating, off-resonant excitation, and detection uncertainty.
The blue sideband adds one motional packet. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The sideband cites the trap gap and packet spacing
The trap source has gap 8 joules and spacing 2 joules.
ΔE=8J,hνm=2J
Blue sideband adds one motional packet to the gap
The drive energy is 10 joules, taking packet 2 to packet 3.