ATM-24

Rabi frequency

Ω = μ E / ħ. Coherent driving rate of a two-level atom.

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StructureRabi

Governing equation

\Omega=\mu\mathcal{E}/\hbar

$\mathcal{E} \in \left[0.001, 100\right]$

where

\mu: Dipole (D)
\mathcal{E}: Field amplitude (V/cm)
\Omega: Rabi frequency (MHz)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Omega=\mu\mathcal{E}/\hbar

$\mathcal{E} \in \left[0.001, 100\right]$

$\mathcal{E} = 0.001$ $\Omega = 0.003$

Along the curve

②

Domain of the variable — blue

\mathcal{E}_{\min} = 0.001,\quad \mathcal{E}_{\max} = 100

$\mathcal{E} \in \left[0.001, 100\right]$

$\mathcal{E} = 0.001$ $\mathcal{E} = 0.001$

Along the curve

③

Response curve — green

\Omega=\mu\mathcal{E}/\hbar

$\mathcal{E} \in \left[0.001, 100\right]$

$\mathcal{E} = 0.001$ $\Omega = 0.003$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Omega}{\mathrm{d}\mathcal{E}}

$\mathcal{E} \in \left[0.001, 100\right]$

$\mathcal{E} = 0.63$ $\Omega^{\prime} = 3.163$

Along the curve

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-24 — Rabi frequency) is the form associated with Rabi. Working symbols: $\mu$ , $\mathcal{E}$ $\rightarrow$ $\Omega$ . π-pulse time is π/Ω. Rabi flopping is the textbook of atomic clocks and qubits.

Purpose

Purpose: compute

\Omega

from

\mu

\mathcal{E}

in Atomic physics via

\Omega=\mu\mathcal{E}/\hbar

Ω = μ E / ħ. Coherent driving rate of a two-level atom. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 1.000\,\mathrm{D}

\mathcal{E} = 1.000\,\mathrm{V/cm}

, the governing relation

\Omega=\mu\mathcal{E}/\hbar

yields

\Omega = 3.163\,\mathrm{MHz}

. A two-level, a driving field, a flopping population. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Dipole \mu1 DField amplitude \mathcal{E}1 V/cm

Outputs

Rabi frequency \Omega3.163 MHz

Reading speed

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Narration of this film

A two-level, a driving field, a flopping population.

π-pulse time is π/Ω. Rabi flopping is the textbook of atomic clocks and qubits.

Reading speed

Watch on YouTube