Quantum beats

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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 -type atoms.[clarification needed] However, in the quantum electrodynamic (QED) calculation, V-type atoms have a beat term but -types do not. This is strong evidence in support of quantum electrodynamics.

Historical overview[edit]

The observation of quantum beats was first reported by A.T. Forrester, R.A. Gudmundsen and P.O. Johnson in 1955,[1] in an experiment that was performed on the basis of an earlier proposal by A.T. Forrester, W.E. Parkins and E. Gerjuoy.[2] 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.[3][4]

Since the invention of the laser, quantum beats can be demonstrated by using light originating from two different laser sources. In 2017 quantum beats in single photon emission from the atomic collective excitation have been observed.[5] Observed collective beats were not due to superposition of excitation between two different energy levels of the atoms, as in usual single-atom quantum beats in -type atoms.[6] Instead, single photon was stored as excitation of the same atomic energy level, but this time two groups of atoms with different velocities have been coherently excited. These collective beats originate from motion between entangled pairs of atoms,[6] that acquire relative phase due to Doppler effect.

V-type and -type atoms[edit]

There is a figure in Quantum Optics[7] that describes -type and -type atoms clearly.

Simply, V-type atoms have 3 states: , , and . The energy levels of and are higher than that of . When electrons in states and : subsequently decay to state , two kinds of emission are radiated.

In -type atoms, there are also 3 states: , , and :. However, in this type, is at the highest energy level, while and : are at lower levels. When two electrons in state decay to states and :, respectively, two kinds of emission are also radiated.

The derivation below follows the reference Quantum Optics.[7]

Calculation based on semiclassical theory[edit]

In the semiclassical picture, the state vector of electrons is


If the nonvanishing dipole matrix elements are described by

for V-type atoms,
for -type atoms,

then each atom has two microscopic oscillating dipoles

for V-type, when ,
for -type, when .

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[edit]

For quantum electrodynamical calculation, we should introduce the creation and annihilation operators from second quantization of quantum mechanics.


is an annihilation operator and
is a creation operator.

Then the beat note becomes

for V-type and
for -type,

when the state vector for each type is


The beat note term becomes

for V-type and
for -type.

By orthogonality of eigenstates, however and .

Therefore, there is a beat note term for V-type atoms, but not for -type atoms.


As a result of calculation, V-type atoms have quantum beats but -type atoms do not. This difference is caused by quantum mechanical uncertainty. A V-type atom decays to state via the emission with and . Since both transitions decayed to the same state, one cannot determine along which path each decayed, similar to Young's double-slit experiment. However, -type atoms decay to two different states. Therefore, in this case we can recognize the path, even if it decays via two emissions as does V-type. Simply, we already know the path of the emission and decay.

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.

See also[edit]


  1. ^ A.T. Forrester, R.A. Gudmunsen, P.O. Johnson, Physical Review, vol. 99, pp. 1691–1700, 1955 (abstract)
  2. ^ A.T. Forrester, W.E. Parkins, E. Gerjuoy: On the possibility of observing beat frequencies between lines in the visible spectrum, Physical Review, vol. 72, pp. 241–243, 1947
  3. ^ Edward Gerjuoy: Atomic physics, In: H. Henry Stroke (ed.): The Physical Review—the First Hundred Years: A Selection of Seminal Papers and Commentaries, Springer, 1995, ISBN 978-1-56396-188-5, pp. 83–102, p. 97
  4. ^ Paul Hartman: A Memoir on The Physical Review: A History of the First Hundred Years, Springer, 2008, ISBN 978-1-56396-282-0, p. 193
  5. ^ Whiting, D. J.; Šibalić, N.; Keaveney, J.; Adams, C. S.; Hughes, I. G. (2017-06-22). "Single-Photon Interference due to Motion in an Atomic Collective Excitation". Physical Review Letters. 118 (25): 253601. arXiv:1612.05467. doi:10.1103/PhysRevLett.118.253601. PMID 28696754. S2CID 5126428.
  6. ^ a b Haroche, S. (1976), "Quantum beats and time-resolved fluorescence spectroscopy", High-Resolution Laser Spectroscopy, Topics in Applied Physics, vol. 13, Springer Berlin Heidelberg, pp. 253–313, doi:10.1007/3540077197_23, ISBN 9783540077190
  7. ^ a b Marlan Orvil Scully & Muhammad Suhail Zubairy (1997). Quantum optics. Cambridge UK: Cambridge University Press. p. 18. ISBN 978-0-521-43595-6.

Further reading[edit]