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physica status solidi (b)

Zero-Phonon Lines: The Effect of a Strong Softening of Elastic Springs in the Excited State

V. Hizhnyakov, Helle Kaasik, Ilmo Sildos

Published Nov 1, 2002• 53 citations
Publisher

Abstract

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.

DOI
10.1002/1521-3951(200211)234:2<644::aid-pssb644>3.0.co;2-e

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NV--NV+ pair centre in 1b diamond

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With the creation of nitrogen (NV) in 1b diamond it is common to find that the absorption and emission is predominantly of negatively charged NV centres. This occurs because electrons tunnel from the substitutional nitrogen atoms to NV to form NV−–N+ pairs. There can be a small percentage of neutral charge NV0 centres and a linear increase of this percentage can be obtained with optical intensity. Subsequent to excitation it is found that the line width of the NV− zero-phonon has been altered. The alteration arises from a change of the distribution of N+ ions and a modification of the average electric field at the NV− sites. The consequence is a change to the Stark shifts and splittings giving the change of the zero-phonon line (ZPL) width. Exciting the NV− centres enhances the density of close N+ ions and there is a broadening of the ZPL. Alternatively exciting and ionizing N0 in the lattice results in more distant distribution of N+ ions and a narrowing of the ZPL. The competition between NV− and N0 excitation results in a significant dependence on excitation wavelength and there is also a dependence on the concentration of the NV− and N0 in the samples. The present investigation involves extensive use of low temperature optical spectroscopy to monitor changes to the absorption and emission spectra particularly the widths of the ZPL. The studies lead to a good understanding of the properties of the NV−–N+ pairs in diamond. There is a critical dependence on pair separation. When the NV−–N+ pair separation is large the properties are as for single sites and a high degree of optically induced spin polarization is attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. With separations of <12 A0 there is even no emission. The deterioration occurs as a consequence of electron tunneling in the excited state from NV– to N+ and an optical cycle that involves NV0. The number of pairs with the smaller separations and poorer properties will increase with the number of nitrogen impurities and it follows that the degree of spin polarization that can be achieved for an ensemble of NV− in 1b diamond will be determined and limited by the concentration of single substitutional nitrogen. The information will be invaluable for obtaining optimal conditions when ensembles of NV− are required. As well as extensive measurements of the NV− optical ZPL observations of Stark effects associated with the infrared line at 1042 nm and the optically detected magnetic resonance at 2.87 GHz are also reported.

•Nov 1, 2018•0 citations
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.
We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.
The negatively charged nitrogen-vacancy $({\mathrm{NV}}^{\ensuremath{-}})$ center in diamond is a promising candidate for many quantum applications. Here, we examine the splitting and broadening of the center's infrared (IR) zero-phonon line (ZPL). We develop a model for these effects that accounts for the strain induced by photodependent microscopic distributions of defects. We apply this model to interpret observed variations of the IR ZPL shape with temperature and photoexcitation conditions. We identify an anomalous temperature-dependent broadening mechanism and that defects other than the substitutional nitrogen center significantly contribute to strain broadening. The former conclusion suggests the presence of a strong Jahn-Teller effect in the center's singlet levels and the latter indicates that major sources of broadening are yet to be identified. These conclusions have important implications for the understanding of the center and the engineering of diamond quantum devices. Finally, we propose that, once the major sources of broadening are identified, the IR ZPL has the potential to be a sensitive spectroscopic tool for probing microscopic strain fields and performing defect tomography.
With the creation of nitrogen (NV) in 1b diamond it is common to find that the absorption and emission is predominantly of negatively charged NV centres. This occurs because electrons tunnel from the substitutional nitrogen atoms to NV to form NV − –N + pairs. There can be a small percentage of neutral charge NV 0 centres and a linear increase of this percentage can be obtained with optical intensity. Subsequent to excitation it is found that the line width of the NV − zero-phonon has been altered. The alteration arises from a change of the distribution of N + ions and a modification of the average electric field at the NV − sites. The consequence is a change to the Stark shifts and splittings giving the change of the zero-phonon line (ZPL) width. Exciting the NV − centres enhances the density of close N + ions and there is a broadening of the ZPL. Alternatively exciting and ionizing N 0 in the lattice results in more distant distribution of N + ions and a narrowing of the ZPL. The competition between NV − and N 0 excitation results in a significant dependence on excitation wavelength and there is also a dependence on the concentration of the NV − and N 0 in the samples. The present investigation involves extensive use of low temperature optical spectroscopy to monitor changes to the absorption and emission spectra particularly the widths of the ZPL. The studies lead to a good understanding of the properties of the NV − –N + pairs in diamond. There is a critical dependence on pair separation. When the NV − –N + pair separation is large the properties are as for single sites and a high degree of optically induced spin polarization is attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. With separations of <12 A 0 there is even no emission. The deterioration occurs as a consequence of electron tunneling in the excited state from NV – to N + and an optical cycle that involves NV 0 . The number of pairs with the smaller separations and poorer properties will increase with the number of nitrogen impurities and it follows that the degree of spin polarization that can be achieved for an ensemble of NV − in 1b diamond will be determined and limited by the concentration of single substitutional nitrogen. The information will be invaluable for obtaining optimal conditions when ensembles of NV − are required. As well as extensive measurements of the NV − optical ZPL observations of Stark effects associated with the infrared line at 1042 nm and the optically detected magnetic resonance at 2.87 GHz are also reported.
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.
With the creation of nitrogen (NV) in 1b diamond it is common to find that the absorption and emission is predominantly of negatively charged NV centres. This occurs because electrons tunnel from the substitutional nitrogen atoms to NV to form NV−–N+ pairs. There can be a small percentage of neutral charge NV0 centres and a linear increase of this percentage can be obtained with optical intensity. Subsequent to excitation it is found that the line width of the NV− zero-phonon has been altered. The alteration arises from a change of the distribution of N+ ions and a modification of the average electric field at the NV− sites. The consequence is a change to the Stark shifts and splittings giving the change of the zero-phonon line (ZPL) width. Exciting the NV− centres enhances the density of close N+ ions and there is a broadening of the ZPL. Alternatively exciting and ionizing N0 in the lattice results in more distant distribution of N+ ions and a narrowing of the ZPL. The competition between NV− and N0 excitation results in a significant dependence on excitation wavelength and there is also a dependence on the concentration of the NV− and N0 in the samples. The present investigation involves extensive use of low temperature optical spectroscopy to monitor changes to the absorption and emission spectra particularly the widths of the ZPL. The studies lead to a good understanding of the properties of the NV−–N+ pairs in diamond. There is a critical dependence on pair separation. When the NV−–N+ pair separation is large the properties are as for single sites and a high degree of optically induced spin polarization is attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. With separations of <12 A0 there is even no emission. The deterioration occurs as a consequence of electron tunneling in the excited state from NV– to N+ and an optical cycle that involves NV0. The number of pairs with the smaller separations and poorer properties will increase with the number of nitrogen impurities and it follows that the degree of spin polarization that can be achieved for an ensemble of NV− in 1b diamond will be determined and limited by the concentration of single substitutional nitrogen. The information will be invaluable for obtaining optimal conditions when ensembles of NV− are required. As well as extensive measurements of the NV− optical ZPL observations of Stark effects associated with the infrared line at 1042 nm and the optically detected magnetic resonance at 2.87 GHz are also reported.