Although the ground-state spin of NV centers has been understood for over a decade, the spin of the orbital excited state has not been addressed until recently. Understanding of the excited-state spin Hamiltonian is critical to enacting ultra-fast, all-optical methods of spin control. Below is a diagram of the orbital energy levels of a NV center along with the spin-splitting of those levels. Due to the presence of a spin-selective and non-radiative relaxation through a S=0 state, The spin of NV centers can be read-out by measuring the brightness of the photoluminescence.
Like the ground-state, the excited-state also has total spin-1, but with a different Hamiltonian. In order to probe the spin levels in the excited state we simultaneously apply a microwave manipulation field and an optical excitation. Although the excited-state is relatively short-lived (about 10 ns) we are sensitive to excited state transitions, even at room temperature, if the microwave field is strong enough to cause a substantial transition probability within that lifetime. Below on the left is a diagram of the spin levels of the ground and excited states. On the right is a measurement of the photoluminescence as a function of frequency showing the resonances that occur in both the ground state and the excited state.
By repeating these measurements as a function of magnetic field we can map out the entire spin Hamiltonian for the excited state. Below is that data, plotted as a relief map and inverted so that the dips appear as peaks, which makes the data easier to follow. In this data, as above, the sharp resonances are the ground-state spin transitions while the lower, broad transitions are the excited-state transitions. There are several features that are immediately apparent:
- The resonances in the excited state shift with magnetic field the same way they do in the ground state, indicating they have similar g-factors.
- The intercept at zero magnetic field (B=0) has a value around half that of the ground state.
- There is a level-crossing at B=500 G that explains the observation made by Epstein et al.
Higher resolution measurement of the excited-state resonances, shown below, also reveals that they are each split into two dips. The NV centers used in this study were made with nitrogen-15, which has a nuclear spin-1/2. The hyperfine interaction of the nitrogen nuclear spin with the electronic spin of the NV center causes this splitting. Moreover, this interaction in the excited-state is about 20x larger than that of the ground-state. We also see that at magnetic fields near the excited-state spin level-crossing, there is a dynamic nuclear polarization effect that changes the relative intensity of the two resonances by polarizing the nuclear spin of the nitrogen. This effect can be exploited to simultaneously initialize the NV electronic spin and the nitrogen nuclear spin for experiments with coupled spins in diamond.
Putting these observations together we can find all the terms of the excited state spin Hamiltonian including the hyperfine term. Below is the form of the excited-state spin Hamiltonian along with fits of its eigenvalues to the observed transition frequencies which allows us to determine the coefficients.
The Ees term, the transverse anisotropy splitting, is essentially zero in the ground-state spin Hamiltonian, but plays an important role in the excited state. This term is sensitive to the strain of the diamond and determines the splitting between the two excited-state transitions at zero magnetic field. Since the local strain can vary considerably within the same sample, we can observe this effect simply by looking at different NV centers. Below is shown low-field measurements of the NV center (NV1) that has been described throughout plotted with a similar measurement of another NV center (NV2) less than two microns away in the sample. They have a dramatically different value of transverse splitting, indicating a different value of local strain. This offers the ability to control a term of the spin Hamiltonian by controlling strain within the material.
To learn more about our studies, please refer to “Excited-State Spectroscopy Using Single Spin Manipulation in Diamond”, G. D. Fuchs, V. V. Dobrovitski, R. Hanson, A. Batra, C. D. Weis, T. Schenkel, and D. D. Awschalom, Phys. Rev. Lett. 101, 117601 (2008).