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Le Journal de Physique Colloques

HOMOGENEOUS BROADENING OF ZERO-PHONON LINES FOR A MULTILEVEL SYSTEM IN A CRYSTAL : THE ROLE OF THE ELECTRON-PHONON INTERACTIONS

Alberto Barchielli, E. Mulazzi

Published Dec 1, 1981• 0 citations
Publisher

Abstract

We present the evaluation of the homogeneous broadening for a Jahn Teller centre in a crystal when interactions which cause interlevel mixing are present. Contributions coming out from one and two-phonon processes are taken in to account. The special case in which the mixing is due to the presence of spin-orbit interaction is also treated.

DOI
10.1051/jphyscol:19816138

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We present the evaluation of the homogeneous broadening for a Jahn Teller centre in a crystal when interactions which cause interlevel mixing are present. Contributions coming out from one and two-phonon processes are taken in to account. The special case in which the mixing is due to the presence of spin-orbit interaction is also treated.
Fano's theory of configuration interaction has been extended to Jahn-Teller systems. Homogeneous broadening and shift of the zero-phonon lines are directly connected with interlevel spin-orbit interaction and with the density of states of the interacting continuum. Application to MgO: V2+{\mathrm{V}}^{2+}V2+ and Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​: Cr3+{\mathrm{Cr}}^{3+}Cr3+ gives excellent agreement between theory and experiment.
A recursive method is developed to treat electrons coupled to phonons. It is applied to small systems with $E\ensuremath{\bigotimes}\ensuremath{\beta}$ Jahn-Teller coupling. Two cases are considered, a model with one electron and two orbitals on a single site (related to the Rabi Hamiltonian) and a model with two electrons on two sites. The corresponding Green's functions are represented by rational functions. It is found that the spectra change substantially when one phonon couples to the electron but are relatively robust under an increasing number of phonons.
Applications of the negatively charged nitrogen-vacancy center in diamond exploit the center's unique optical and spin properties, which at ambient temperature are predominately governed by electron-phonon interactions. Here, we investigate these interactions at ambient and elevated temperatures by observing the motional narrowing of the center's excited-state spin resonances. We determine that the center's Jahn-Teller dynamics are much slower than currently believed and that they do not solely account for the broadening of the center's optical resonance above cryogenic temperatures. We show that the inclusion of interactions with symmetric phonon modes can explain the observed broadening and resolve the current inconsistencies in the literature. However, our model also reveals unexpected features of the electron-phonon processes that coincide with other poorly understood vibronic features of the center and require further investigation.
The optical dephasing, caused by a quadratic interaction with acoustic phonons, is studied on the basis of the nonperturbative theory. The effect of a strong weakening of the elastic springs on the electronic transition is studied. It is found that, if the weakening brings the system close to the dynamical instability, then the usual ∝ T7 dependence of the homogeneous width of a zero-phonon line (ZPL) is replaced by the ∝ T3 dependence in a broad temperature interval. An equation is derived which describes the additional broadening of a ZPL caused by the dynamical instability of the final state. The model explains the temperature broadening and shift of the zero-phonon lines of some nitrogen-containing centers in diamond crystals.
The nitrogen-vacancy centre in diamond has shown to be a promising solid-state spin-qubit for applications in quantum information processing. NV centres can be used as nodes in quantum communication networks by remote controlled entanglement. The success of such entanglement schemes depends on the probability of photons being emitted in the zero-phonon line. To increase this probability, NV centres in thin diamond membranes are placed in optical cavities. However, NV centres in thin diamond membranes often show much larger strain splitting. In this thesis, the effect of such strain interactions on the population dynamics and homogeneous broadening of the zero-phonon line of the excited state is determined.
Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.