Harper's Light Shift vs Detuning Calculator

Model light shift over broad detuning ranges. Include scattering, dressed frequency, and uncertainty checks quickly. Export neat calculation tables for laser physics notes today.

Calculator

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Example Data Table

Case Rabi MHz Linewidth MHz Detuning MHz Scale Factor Approx Shift MHz
Red far detuned 5 6.07 -100 1 -0.0625
Blue far detuned 5 6.07 100 1 0.0625
Higher coupling 8 6.07 100 1 0.16
Scaled transition 5 6.07 100 0.5 0.03125

Formula Used

Detuning: Δ = fL − f0

Light shift: δLS = C × Ω² / 4Δ

Optional counter term: δCR = C × Ω² / 4(2f0 + Δ)

Total shift: δTotal = δLS + δCR

Scattering estimate: Γsc = ΓΩ² / 4Δ²

Generalized Rabi frequency: Ωeff = √(Ω² + Δ²)

Intensity mode: I = P / πr², s = I / Isat, Ω = Γ√(s / 2)

How to Use This Calculator

Choose direct Rabi mode when spectroscopy already gives Ω. Choose intensity mode when you only know beam power and radius.

Enter linewidth, detuning center, detuning span, and the number of table points. Use negative detuning for red detuning.

Add a scale factor when polarization strength, transition strength, or calibration changes the ideal two-level shift.

Press Calculate. The result appears above the form and below the header. Use CSV or PDF buttons to export the same settings.

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.

FAQs

What is light shift?

Light shift is the frequency shift caused by an off-resonant optical field. It is also called the AC Stark shift in many atom and laser experiments.

What does detuning mean here?

Detuning is laser frequency minus resonance frequency. Positive values mean blue detuning. Negative values mean red detuning under this calculator convention.

Why does the result fail near zero detuning?

The simple far-detuned formula divides by detuning. Near resonance, absorption and coherent dynamics dominate. Use a full optical Bloch model there.

When should I use intensity mode?

Use intensity mode when you know power, beam radius, saturation intensity, and linewidth. The calculator estimates Rabi frequency from those values.

What is the Harper scale factor?

It is a user correction factor. Use it for transition strength, polarization, calibration, or model adjustments that change the ideal two-level estimate.

What does scattering rate show?

It estimates unwanted photon scattering. Lower scattering is usually better for coherent measurements, traps, and precision spectroscopy.

Is the counter-rotating option required?

No. It is usually very small for optical transitions. It is included for advanced comparisons and sensitive theoretical checks.

Can I use exported values in a report?

Yes. The CSV and PDF exports include calculated rows and key settings. Add your experimental notes and calibration details before final reporting.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.