Rabi cycle

Key takeaways

Rabi cycle belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Rabi cycle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Rabi cycle from memory before moving on to harder problems.

Reference excerpt

In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particle physics can be conveniently studied in terms of two-level quantum mechanical systems, and exhibit Rabi flopping when coupled to an optical driving field. The effect is important in quantum optics, magnetic resonance, and quantum computing, and is named after Isidor Isaac Rabi. A two-level system is one that has a Hilbert space spanned by two possible orthogonal states. These states may have two possible energy levels. One level can be a ground state with lower energy, and the other can be an excited state with higher energy. If the energy levels are not degenerate (i.e. don't have equal energies), the system can absorb or emit a quantum of energy and transition from the ground state to the excited state or vice versa. When an atom (or some other two-level system) is illuminated by a coherent beam of photons, it will cyclically absorb photons and emit them by stimulated emission. One such cycle is called a Rabi cycle, and the inverse of its duration is the Rabi frequency of the system. The effect can be modeled using the Jaynes–Cummings model and the Bloch vector formalism. More generally, the introduction of an oscillatory driving field to a two-level system can be viewed as a perturbation which couples the previously uncoupled states. The time evolution under this perturbed Hamiltonian therefore results in oscillations, called Rabi cycles, between the two unperturbed states. In the strong coupling limit, a complete oscillation between the unperturbed states is observed.

Mathematical description of spin flipping One example of Rabi flopping is the spin flipping within a quantum system containing a spin-1/2 particle and an oscillating magnetic field. We split the magnetic field into a constant 'environment' field, and the oscillating part, so that our field may be written as B = B e n v + B o s c = B 0 k + B 1 ( cos ⁡ ( ω t ) i + sin ⁡ ( ω t ) j ) , {\displaystyle \mathbf {B} =\mathbf {B} _{env}+\mathbf {B} _{osc}=B_{0}\mathbf {k} +B_{1}(\cos(\omega t)\mathbf {i} +\sin(\omega t)\mathbf {j} ),} where B 0 {\displaystyle B_{0}} and B 1 {\displaystyle B_{1}} are the strengths of the environment and the oscillating fields respectively, and ω {\displaystyle \omega } is the frequency at which the oscillating field oscillates. We can then write a Hamiltonian describing this field, yielding H = − μ → ⋅ B = ω 0 S z + ω 1 ( cos ⁡ ( ω t ) S x + sin ⁡ ( ω t ) S y ) {\displaystyle H=-{\vec {\mu }}\cdot \mathbf {B} =\omega _{0}S_{z}+\omega _{1}(\cos(\omega t)S_{x}+\sin(\omega t)S_{y})} where the magnetic moment is μ ^ = − γ S = − γ ( S x ^ i + S y ^ j + S z ^ k ) , {\displaystyle {\hat {\mathbf {\mu } }}=-\gamma \mathbf {S} =-\gamma ({\hat {S_{x}}}\mathbf {i} +{\hat {S_{y}}}\mathbf {j} +{\hat {S_{z}}}\mathbf {k} ),}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Rabi cycle

Start with the simplest possible case. Write down what Rabi cycle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rabi cycle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rabi cycle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rabi cycle

In research: Rabi cycle appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Rabi cycle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Rabi cycle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Atomic physics, Quantum optics, so understanding it makes those chapters shorter.
In everyday life: Look for Rabi cycle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Rabi cycle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Rabi cycle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Rabi cycle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rabi cycle in simple terms?

In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, atomic and molecular physics, and nuclear and particl…

Why does Rabi cycle matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rabi cycle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rabi cycle.