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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 looks like = + = + ( + ()) where and are the strengths of the environment and the oscillating fields respectively, and is the frequency at ...
The Rabi frequency is the frequency at which the probability amplitudes of two atomic energy levels fluctuate in an oscillating electromagnetic field. It is proportional to the transition dipole moment of the two levels and to the amplitude ( not intensity ) of the electromagnetic field .
A well known example of a two-state system is the spin of a spin-1/2 particle such as an electron, whose spin can have values +ħ/2 or −ħ/2, where ħ is the reduced Planck constant. The two-state system cannot be used as a description of absorption or decay, because such processes require coupling to a continuum.
A mathematical description of vacuum Rabi oscillation begins with the Jaynes–Cummings model, which describes the interaction between a single mode of a quantized field and a two level system inside an optical cavity. The Hamiltonian for this model in the rotating wave approximation is
A simplified version of the Rabi method consists of a beam of atoms, all having the same speed and the same direction, sent through one interaction zone of length .The atoms are two-level atoms with a transition energy of (this is defined by applying a field ‖ in an excitation direction ^, and thus = | ‖ |, the Larmor frequency), and with an interaction time of = / in the interaction zone.
The value of , depends on the initial condition of the system. An exact solution of spin-1/2 system in an oscillating magnetic field is solved by Rabi (1937). From their work, it is clear that the Rabi oscillation frequency is proportional to the magnitude of oscillation magnetic field.
If instead of a single two-level system, an ensemble of identical two level systems (such as a chain of identical atoms in an ion trap) is prepared and continuously addressed with a laser, all the atoms will coherently Rabi flop. [citation needed] All two level systems will initially have a defined relative phase and the system will be coherent ...
The existence of Rabi oscillations between the states of the two-level system as it interacts with the quantum field. This was originally believed to be a purely quantum mechanical effect, although a semi-classical explanation for it was later provided in terms of linear dispersion and absorption [ 5 ]