Sideband Energy Ladder Cross-Scan - Ion-Trap Qubits: Sidebands, Shared Modes, and Fluorescence Readout Step by Step

Use the same trap gap and packet spacing in three rows so the changing drive role is easy to see. With an 8 joule gap and 2 joule packet spacing, the carrier stays at 8 joules, the red sideband lands at 6 joules, and the blue sideband lands at 10 joules; real sideband checks need calibrated lasers, prepared motional modes, and uncertainty on the frequency and packet model.

Carrier, red, and blue drives use the same gap and packet spacing with different signs. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Carrier drive uses only the internal gap

With gap 8 joules and packet spacing 2 joules, the carrier drive is 8 joules and keeps packet 2 unchanged.

E_{\text{drive}}=8\ \text{J},\quad n:2\to2

Red sideband subtracts one motional packet

The red row keeps the same gap and spacing, but spends one packet: 8 minus 2 gives 6 joules.

8\ \text{J}\mathbin{-}2\ \text{J}=6\ \text{J},\quad n:2\to1

Blue sideband adds one motional packet

The blue row uses the same source, but adds one packet: 8 plus 2 gives 10 joules.

8\ \text{J}\mathbin{+}2\ \text{J}=10\ \text{J},\quad n:2\to3

The sign of the motional packet selects six, eight, or ten joules

The three-row scan isolates the relation: gap stays eight joules, spacing stays two joules, and only the drive role changes the packet update.

\begin{array}{c|c|c|c|c}\text{drive}&E_{\text{drive}}&n_{\text{start}}&n_{\text{end}}&a\\\text{carrier}&8\ \text{J}&2&2&1\\\text{red}&6\ \text{J}&2&1&1\\\text{blue}&10\ \text{J}&2&3&1\\\end{array}