Optical initialization and readout of NV spins

Introduction

The magnetic moment of an electron is called 'spin'. Just like a bar magnet, a spin wants to align itself with a magnetic field in order to lower its energy. The energy difference between the spin being aligned or anti-aligned with the field is called the Zeeman energy. How the electron Zeeman energy varies with magnetic field is known to a very large precision. Therefore, a measurement of this energy difference allows us to determine the magnetic field, which is the central concept of this lab course.

How can one measure the Zeeman energy of an electron spin? Firstly, it is important to realize that, at room temperature, the Zeeman energy is very small compared to the thermal energy $k_BT$. This implies that a spin in a material at room temperature continuously gets 'scrambled' through the contact with its hot environment, making it hard to determine its Zeeman energy.

Fortunately, the electron spin of the NV center has the advantageous property that it can be 'initialized' (polarized) using simple green laser excitation. In addition, laser excitation will make the NV center fluoresce (emit red photons), with a brightness that depends on its spin state. These properties allow us to use the NV center as a magnetometer.

Initialization and readout of the NV spin

The NV center has an $S=1$ electron spin. Therefore, it has 3 possible spin states, which we will label $m_S=0,−1,+1$. We will now describe the mechanism by which the NV spin state polarizes into $m_S=0$ under optical excitation, and how the NV fluorescence depends on the spin state. On the following page, we will describe in detail how the energies of the NV spin states depend on the applied magnetic field.

The optical initialization and read out of the NV spin can be understood from the following simplified energy level structure of the NV center:

The level structure shows the electronic (orbital) ground and excited state of the NV center. Both of these have a splitting between their $m_S=0$ and $m_S=\pm1$ spin states that is present even at zero magnetic field (the 'zero-field splitting'). Optical excitation (green arrows) preserves the spin state. The subsequent decay back to the ground state mostly occurs radiatively, emitting a red photon. However, decay can also occur non-radiatively via a metastable state, and this non-radiative decay is more likely to occur for the $m_s=\pm1$ states. As a result, the strength of the NV photoluminescence will be different depending on the spin state, with $m_S = 0$ being the "bright" state and $m_S = \pm 1$ being the "dark" states. And the decay from the metastable no longer preserves the spin, only ending up in $m_S=0$. This will allow us to polarize the NV spin into the $m_S=0$ state (refered to as "optical pumping").

Exercise 2 - Optical spin readout

1. Explain in your own words the principle of the NV center's spin-dependent photoluminescence. In particular, discuss how the decay via the metastable state causes optical spin contrast (i.e., a difference in the photoluminescence for the $m_S=0$ and the $m_S=\pm1$ states.)
2. Discuss the excitation and decay process under continuous green laser excitation, and how this process eventually polarizes the NV spin into the $m_S=0$ state.