Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3

Abstract

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy.

Measurement of the Yb IS01−P11transition frequency at 399 nm using an optical frequency comb

“…This effect has been measured in Li [24] and H [45]. It has been estimated in muonic hydrogenic atoms [43] and microwave transitions in He [41]. However it has not been previously measured in divalent atoms.…”

“…Quantum interference that arises from this structure can adversely influence the determination of the transition frequencies if not properly addressed [24,[41][42][43][44][45]. The magnitude of this interference effect depends on laser intensity and polarization as well as measurement geometry.…”

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

“…Recently, the effect of quantum-mechanical interference on precision measurements has been investigated by the present authors [1][2][3][4][5][6] and by others [7][8][9][10][11][12][13][14][15][16]. These investigations indicate that interference with a neighboring resonance, even if it is very distant, can lead to significant shifts for precision measurements.…”

Two-photon processes based on quantum commutators

“…When considering molecules, this summation is even harder to perform due to either the complexity of obtaining states for complex potentials or the summation requiring a huge amount of vibrational and rotational states for a reliable evaluation, even for harmonic potentials [19]. Because of these reasons, simpler methods -such as the Thomson or the Form Factor (FF) approximations [43,44] -are very much used when calculating, for instance, light scattering by manyelectron atoms or crystallographic specimens [8,9,45], although they are unable to capture quantum mechanical effects that are given by the target bound spectrum, such as quantum interference [46,47] or resonance effects [29], among others.…”