Interference between two resonant transitions with distinct initial and final states connected by radiative decay

Abstract

The resonant line shape from driving a transition between two states, |a and |b , can be distorted due to a quantum-mechanical interference effect involving a resonance between two different states, |c and |d , if |c has a decay path to |a and |d has a decay path to |b . This interference can cause a shift of the measured resonance, despite the fact that the two resonances do not have a common initial or final state. As an example, we demonstrate that such a shift affects measurements of the atomic hydrogen 2S 1/2 -to-2P 1/2 Lamb-shift transition due to 3S-to-3P transitions if the 3S 1/2 state has some initial population.

Systematic effects important to separated-oscillatory-field measurements of the n=2 Lamb shift in atomic hydrogen

“…[7] and [8]. Such interference effects have been investigated by the present authors [9][10][11][12][13][14][15] and by others [16][17][18][19][20][21][22][23][24][25][26]. These investigations indicate that interference with a neighboring resonance, even if it is very distant, can lead to significant shifts for precision measurements.…”

“…When added in quadrature, the uncertainty from these three sources gives 20 kHz, and is dominated by the standard deviation of the 8 configurations. A final consideration is found in our previous work [15], in which we showed that the effect of higher-n states could be of the order of 10 kHz. Since the 20 kHz uncertainty assigned here is larger than the this 10-kHz scale, and since, as discussed in Ref.…”

“…Since the 20 kHz uncertainty assigned here is larger than the this 10-kHz scale, and since, as discussed in Ref. [15], we cannot calculate the actual shift caused by higher-n, we do not assess any additional uncertainty due to the possible effect from these states.…”

A measurement of the atomic hydrogen Lamb shift and the proton charge radius

“…One concern for the present measurement is the effect of other hyperfine transitions and transitions involving states with n ≥ 3. This concern is heightened by our analysis of unexpectedly large shifts from n = 3 states for Lamb shift measurements (15). It is also heightened because we still see 0.3% of our Lyman-a signal, even when we employ all six of the rf cavities shown in Fig.…”

Observation of asymmetric line shapes in precision microwave spectroscopy of the positronium 2S13→2PJ3

“…Hessels and co-workers have made significant contributions toward understanding these effects [47,[56][57][58][59], and they have shown that measurements performed with an uncertainty comparable to the square of the linewidth divided by (twice) the separation of the main resonance and a neighboring (offresonant) transition may well be affected by them [55]. This "rule of thumb" [47], which has also been obtained analytically by other researchers using perturbation theory [60], gives an approximate value for the error one would obtain fitting a Lorentzian profile to a line shape distorted by QI effects.…”