A red sideband removes one motional packet while changing the ion state, so the drive is rejected when the packet index is already zero. That boundary is exact only in the stated ideal ladder; real ion traps add heating, detuning, pulse-area error, spectator modes, and state-preparation uncertainty.
A red sideband cannot step below packet zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
At packet zero there is no lower motional packet
The checked packet index is 0, so a red sideband cannot remove one packet.
n=0⇒lower packet is out
The rejected red sideband still matches the energy relation
The drive energy is still 6 joules, but the accepted bit is 0.