In physics, quantum beats are simple examples of phenomena that cannot be described by semiclassical theory, but can be described by fully quantized calculation, especially quantum electrodynamics. In semiclassical theory (SCT), there is an interference or beat note term for both V-type and
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Historical overview
The observation of quantum beats was first reported by A.T. Forrester, R.A. Gudmunsen and P.O. Johnson in 1955, in an experiment that was performed on the basis of an earlier proposal by A.T. Forrester, W.E. Parkins and E. Gerjuoy. This experiment involved the mixing of the Zeeman components of ordinary incoherent light, that is, the mixing of different components resulting from a split of the spectral line into several components in the presence of a magnetic field due to the Zeeman effect. These light components were mixed at a photoelectric surface, and the electrons emitted from that surface then excited a microwave cavity, which allowed the output signal to be measured in dependence on the magnetic field.
Since the invention of the laser, quantum beats can be demonstrated by using light originating from two different laser sources.
V-type and Λ {displaystyle Lambda } -type atoms
There is a figure in Quantum Optics that describes V-type and
Simply, V-type atoms have 3 states:
In
The derivation below follows the reference Quantum Optics
Calculation based on semiclassical theory
In the semiclassical picture, the state vector of electrons is
If the nonvanishing dipole matrix elements are described by
then each atom has two microscopic oscillating dipoles
In the semiclassical picture, the field radiated will be a sum of these two terms
so it is clear that there is an interference or beat note term in a square law detector
Calculation based on quantum electrodynamics
For quantum electrodynamical calculation, we should introduce the creation and annihilation operators from second quantization of quantum mechanics.
Let
Then the beat note becomes
when the state vector for each type is
The beat note term becomes
By orthogonality of eigenstates, however
Therefore, there is a beat note term for V-type atoms, but not for
Conclusion
As a result of calculation, V-type atoms have quantum beats but
The calculation by QED is correct in accordance with the most fundamental principle of quantum mechanics, the uncertainty principle. Quantum beats phenomena are good examples of such that can be described by QED but not by SCT.