User:BonPhire/NV centers

Energy level structure and its manipulation by external fields
The energy level structure of the N-V− center was established by combining optical, electron paramagnetic resonance and theoretical results, as shown in the figure. In particular, several theoretical works have been done, using the Linear Combination of Atomic Orbitals (LCAO) approach, to build the electronic orbitals to describe the possible quantum states, looking at the N-V center as a molecule. Moreover, group theory results are used, to take into account the symmetry of the diamond crystal, and so the symmetry of the N-V itself. The energy levels are labeled according to the group theory, and in particular are labelled after the irreducible representations of the C3V symmetry group of the defect center, A1, A2 and E. The numbers 3 in 3A and 1 in 1A represent the number of allowable ms spin states, or the spin multiplicity, which range from –S to S for a total of 2S+1 possible states. If S = 1, ms can be −1, 0, or 1. The 1A level is predicted by theory but not directly observed in the experiment, and it is believed to play an important role in the quenching of photoluminescence.

In the absence of an external magnetic field, the ground and excited states are split by the magnetic interaction between the two unpaired electrons at the N-V− center (see microscopic model): when two electrons have parallel spins (ms=±1), their energy is higher than when spins are antiparallel (ms=0). The farther apart the electrons are, the weaker their interaction energy D (roughly D ~1/r3). Thus the smaller splitting in the excited state can be viewed in terms of larger electron-electron separation in the excited state. When an external magnetic field is applied to the N-V− center, it does not affect the ms=0 states nor the 1A state (because it has S = 0), but it splits the ms = ±1 levels. If a magnetic field is oriented along the defect axis and reaches about 1027 G (or 508 G) then the ms = –1 and ms = 0 states in the ground (or excited) state become equal in energy; they strongly interact resulting in so-called spin polarization, which strongly affects the intensity of optical absorption and luminescence transitions involving those states.

This happens because transitions between electronic states are mediated by a photon which cannot change overall spin. Thus optical transitions must preserve the total spin and occur between levels of the same total spin. For this reason, transitions 3E↔1A and 1A ↔ 3A are non-radiative and quench the luminescence. Whereas ms = −1 (excited state) ↔ ms = 0 (ground state) transition was forbidden in the absence of an external magnetic field, it becomes allowed when a magnetic field mixes the ms = −1 and ms = 0 levels in the ground state. As a measurable outcome of this phenomenon, luminescence intensity can be strongly modulated by magnetic field.

An important property of the non-radiative transition between 3E and 1A is that it is stronger for ms = ±1 and weaker for ms = 0. This property results in a very useful manipulation of N-V center, which is called optical spin-polarization. First, consider an off-resonance excitation which has a higher frequency (typically 2.32 eV (532 nm)) than the frequencies of all transitions and thus lays in the vibronic bands for all transitions. By using a pulse of this wavelength, people can excite all spin states and create phonons as well. For a spin state with ms = 0, due to conservation of spin in transition, it will be excited to the corresponding ms = 0 state in 3E and then go back to the original state. However, for a spin state with ms = ±1 in 3A, after the excitation, it has a relatively high probability to jump to the intermediate state 1A by non-radiative transition and go to the ground state with ms = 0. After sufficient cycles, the state of the N-V center can be regarded as in the ms = 0 state. Such a process can be used in the initialization of quantum state in quantum information processing.

There is an additional level splitting in the excited 3E state due to the orbital degeneracy and spin-orbit interaction. Importantly, this splitting can be modulated by applying a static electric field, in a similar fashion to the magnetic field mechanism outlined above, though the physics of the splitting is somewhat more complex. Nevertheless, an important practical outcome is that the intensity and position of the luminescence lines can be modulated by applying electric or/and magnetic fields.

The energy difference between the ms = 0 and ms = ±1 states corresponds to the microwave region. Thus by irradiating the N-V centers with microwave radiation, one can change the relative population of those levels, thereby again modulating the luminescence intensity.

There is an additional splitting of the ms = ±1 energy levels, which originates from the "hyperfine" interaction between the nuclear and electron spins. Thus finally, the optical absorption and luminescence from the N-V− center consists of roughly a dozen sharp lines with a separation in the MHz-GHz range, and all those lines can be resolved, given proper sample preparation. The intensity and position of those lines can be modulated using the following tools:


 * 1) Amplitude and orientation of magnetic field, which splits the ms = ±1 levels in the ground and excited states.
 * 2) Amplitude and orientation of elastic field (strain), which can be applied by, e.g., squeezing the diamond. Similar effects can be induced by applying an electric field,  and the electric field can be controlled with much higher precision.
 * 3) Continuous-wave microwave radiation, which changes the population of the sublevels within the ground and excited state.
 * 4) Tunable laser, which can selectively excite certain sublevels of the ground and excited state.
 * 5) In addition to those static perturbations, numerous dynamic effects (spin echo, Rabi oscillations, etc.) can be exploited by applying a carefully designed sequence of microwave pulses.     The first pulse coherently excites the electron spins, and this coherence is then manipulated and probed by the subsequent pulses. Those dynamic effects are rather important for the practical realization of quantum computers, which ought to work at high frequency.

The above-described energy structure is by no means exceptional for a defect in diamond or other semiconductor. It was not this structure alone, but a combination of several favorable factors (previous knowledge, easy production and excitation, etc.) which suggested the use of the N-V− center.