A red-sideband drive uses the internal gap minus one motional packet, so it lowers the packet index by one when the packet is available. The subtraction is exact only for the stated gap, spacing, starting index, and ideal sideband address; real experiments add finite linewidth, laser detuning, heating, imperfect cooling, and readout uncertainty.
The red sideband spends 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
Red sideband subtracts one motional packet from the gap
The drive energy is 6 joules, taking packet 2 to packet 1.