By Vasant Natarajan

Metrology size platforms common devices and basic constants Atomic devices Preliminaries Classical harmonic oscillator Quantum harmonic oscillator Coherent states Squeezed states Radiation Atoms Spectroscopic notation strength degrees of 1 electron atoms interplay with magnetic fields Atoms in static electrical fields-Stark impression everlasting atomic electrical dipole second (EDM) Atoms in oscillating electric Read more...

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**Example text**

Its dimensions are M 1/2 L3/2 T −1 . (c) There are two issues with using the Coulomb force analogy to deﬁne mass. (i) The Coulomb force already has a mass term in it because the force is mass times the acceleration (from Newton’s second law of motion). This mass is called the “inertial” mass. ” The equality is actually an empirical fact (subject to experimental veriﬁcation), which was used by Einstein in formulating the general theory of relativity. If we accept this as a true fact, then mass can indeed be deﬁned using the gravitational force equation m1 m2 F = r2 The deﬁnition would be that two unit masses placed one meter apart have an acceleration of 1 m/s2 .

Radiation We start by describing radiation in a classical electromagnetic ﬁeld, and take up quantization∗ later. This approach of treating the radiation classically while treating the atom quantum mechanically is called semiclassical. Although fundamentally inconsistent, it provides a natural and intuitive approach to the study of interaction of EM radiation with atomic systems. e. there are many photons in each mode, as for example in the case of microwave or laser spectroscopy. The chief disadvantage is that this treatment does not predict spontaneous emission, thus forcing us to use complex eigenvalues to mimic the presence of this decay in excited states.

2 n = e−|α| 2 n −iω(n+ 12 )t α e /2 √ n! n = e−iωt/2 e−|α| 2 /2 n =e −iωt/2 |αe |n (αe−iωt )n |n √ n! −iωt The last line shows that the time evolved coherent state is just the original state with a time varying argument whose phase evolves like the classical phase. From Eq. 4), we know that a a 0 = α. Therefore a t = αe−iωt =⇒ t a† = a t t e−iωt . For a coherent state = α∗ eiωt Using this we can show that X and Y classical variables. X 0 evolve like the corresponding = α(t)|(a† + a)|α(t) /2 = [ a† t+ ∗ iωt = [α e a t ]/2 + αe−iωt ]/2 = Re{αe−iωt } Y t = i[α∗ eiωt − αe−iωt ]/2 = Im{αe−iωt } Thus both X t and Y t are real oscillating functions.