Light Shift and Detuning Overview
Harper’s light-shift versus detuning calculator models how an off-resonant laser changes an atomic transition. The tool uses a two-level approximation. It also lets you add a scale factor for polarization, Clebsch-Gordan strength, or a local calibration. The result is useful when planning laser cooling, optical pumping, spectroscopy, and atom trapping work.
Why Detuning Matters
Detuning is the difference between laser frequency and the atomic resonance. A red detuning gives a negative shift in this convention. A blue detuning gives a positive shift. Near zero detuning, the simple formula grows very large. Real systems then need full optical Bloch equations. For safe estimates, keep detuning much larger than linewidth and Rabi coupling.
What This Calculator Adds
The calculator accepts direct Rabi frequency or derives it from beam power, radius, and saturation intensity. It reports light shift, scattering rate, generalized Rabi frequency, and an uncertainty estimate. The optional counter-rotating term gives a small Bloch-Siegert style correction. It is normally tiny for optical transitions, yet it helps advanced comparisons.
Practical Interpretation
A large detuning reduces scattering quickly. It also reduces the desired shift. This creates a design tradeoff. More laser power can restore the shift, but it may heat optics or broaden nearby transitions. The table shows each detuning point, so you can find a useful operating region. Export the data when comparing several laser settings.
Limits of the Model
This page is an engineering calculator, not a full atomic solver. It does not include multilevel hyperfine structure, Doppler averaging, tensor polarizability, magnetic fields, coherent population trapping, or open decay channels. Use the scale factor for known corrections. Use laboratory data when available. Treat very small detuning warnings seriously.
Workflow Tips
Start with measured beam values. Then switch to direct Rabi input if spectroscopy has already calibrated the transition. Use positive and negative detuning runs to check sign errors. Keep the same unit choices across experiments. Review the warning column before trusting exported values.
Lab Reporting Use
The exported files help document assumptions. They include input settings and computed rows. That makes notebook review easier. It also helps students compare theory with measured frequency shifts. Repeat the calculation after every major alignment change. Record temperature when it matters.