Motion Uses Packet Indexes - Ion-Trap Qubits: Sidebands, Shared Modes, and Fluorescence Readout Step by Step

The shared motional mode is modeled as a ladder of equally spaced packets, so a packet index becomes a compact energy ledger. The row arithmetic is exact only for the declared packet spacing, index, and finite ladder bookkeeping; real traps add anharmonicity, heating, mode-frequency calibration error, sideband linewidth, and imperfect state preparation or readout.

The motional mode is a finite packet ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Motion is counted by packets on a finite ladder

The mode spacing is 2 joules per packet.

E_{\text{packet}}=2\ \text{J}

Packet index two carries four joules of motion

At packet index 2, the motional energy is 4 joules.

2\cdot 2=4\ \text{J}