The NV center in diamond is the archetypal quantum defect, with applications in quantum computing, cryptography, and ultra-precise sensors. To function properly, the NV center needs to acquire an extra electron, which can be supplied by nitrogen (N) atoms in the crystal. However, these N atoms hold onto their electrons so tightly that they cannot be released at room temperature. An international team of researchers has now revealed that the electron takes another route: it exploits a quantum phenomenon known as tunneling, allowing it to reach the NV center by passing through a barrier that it could not overcome under the laws of classical physics. This discovery explains the wide range of recovery times that have been observed after an NV center has lost its electron, and will enable strategies to increase NV stability.

A really useful “defect”
A diamond's most useful quantum properties come from defects, places where the regular arrangement of carbon atoms is broken. One of these, a nitrogen atom situated next to a vacancy caused by a missing carbon atom, has become a key component in quantum technology. Known widely as the NV center, short for nitrogen-vacancy, this defect can serve many roles. It can be a qubit that works at room temperature, a fundamental element in the construction of quantum computers and quantum networks, or a highly sensitive magnetic sensor that can be read using a laser in such a way that it is able to detect weak magnetic fields inside objects like living cells and microchips. Researchers from Germany, Lithuania, and the United States have now worked out how it returns to working order once it loses an electron. The explanation is that a replacement electron is supplied by a neighboring nitrogen atom through a quantum process called tunnelling.

A sensor that must borrow an electron
The NV center only works as a qubit or a sensor while it holds one extra electron, which it has to acquire from another defect in the crystal. While operating, it often loses that electron, and in some cases the center never acquires one at all. It has long been known that nitrogen atoms dispersed throughout the diamond provide the electrons, but nitrogen holds onto its electrons very tightly. In a semiconductor, heat is often sufficient to free an electron from a defect, even at room temperature; the electron then moves around through the crystal and is eventually captured by defects. In the case of nitrogen in diamond, this process does not take place: the electron is bound too strongly for heat to release it. The way in which an electron actually gets from a nitrogen atom to the NV center had remained a puzzle up to now. Tunneling had been suggested, but nobody had worked out how it could actually happen and how to prove it.

The electron takes a shortcut
Reported in the journal Physical Review Letters, a new study shows that no thermal release is needed and explains the mechanism by which the transfer takes place. The electron tunnels directly from the nitrogen atom to the NV center, passing through the energy barrier that holds it to the nitrogen atom, a barrier which, according to classical physics, it should never be able to surmount. 

Tunneling alone is not enough though. The electron transfer releases a burst of energy, and unless something absorbs it (obeying energy conservation), the jump cannot take place. Quantum-mechanical simulations found that the nitrogen atom is ideally suited for this role since it has one bond broken with its neighboring carbon atoms; when it donates its electron, the missing bond reforms, and the energy is released into vibrational motion of the crystal. 

The nitrogen atom plays a special role in this situation, Lukas Razinkovas, head of the Electronic Structure Theory Laboratory at the Center for Physical Sciences and Technology (FTMC) in Vilnius, points out. 

"When the electron tunnels, it releases a large quantity of energy and the nitrogen atom turns out to be remarkably efficient at absorbing that particular amount,” he said.

Razinkovas, together with Audrius Alkauskas of FTMC, and Chris Van de Walle, a distinguished professor in the Materials Department at UC Santa Barbara, performed the quantum-mechanical simulations and developed the theoretical model that explains the experimental observations.

From nanoseconds to hours: watching the electrons return
How fast tunneling occurs depends strongly on how far away the nitrogen is from the NV center, and the time it takes for an electron to tunnel could vary from nanoseconds, billionths of a second, to hours or longer. Typically, scientists use pump-probe experiments to measure such processes: one (pump) laser pulse disturbs the system (here: it removes an electron from NV), and a second, delayed (probe) pulse measures the response (here: the electron returns), usually focusing on timescales of just billionths of a second. To observe the slow recoveries, the group needed an experiment that could monitor the process a billion times longer.

Ronald Ulbricht, a group leader at the Max Planck Institute for Polymer Research, had created one; a pulsed red laser removes the electrons from the centers, while a continuous and very weak second laser goes through the diamond to the detector. As the centers start to regain their electrons, they begin to absorb that light once again, and the detector records the recovery.

"Most time-resolved optical studies of these centers stop a few nanoseconds after the laser pulse," said Ulbricht. "Following the signal from nanoseconds to seconds lets us separate the fast relaxation inside the NV center from the slow return of the charge, and that slow part is the tunneling."

The researchers looked at diamonds with different nitrogen content, and the amount of nitrogen made a large difference: in nitrogen-rich diamond, the NV centers recovered their lost electron much faster. In contrast, the temperature of the diamond made practically no difference. Heating the crystals from near absolute zero up to room temperature produced no measurable effect, just as the tunneling model predicts. If the process had been heat-activated, it would have sped up considerably.

The probability of tunneling decreases rapidly as distance increases, meaning small variations in spacing can cause large differences in timing. The team's calculations show that a nitrogen atom within about two nanometers, roughly a dozen atoms away, restores the center in a few billionths of a second. Beyond five nanometers, the time required becomes hours long. Since the nitrogen atoms are distributed randomly throughout the crystal, a real diamond should have centers recovering on all time scales between those values. In a diamond that has a large number of nitrogen atoms, essentially all of the NV centers regain their charge within a fraction of a second. However, in a diamond which has only one nitrogen atom for every million carbon atoms, the model predicts that most of the centers still have not recovered after one hour.

Since the NV center is out of action while it’s waiting for its electron to return, fluctuations on these time scales severely hamper the reliable operation of quantum devices. The insights provided by these new results allow developing strategies to help stabilize the NV centers, for instance by judicious placement of nitrogen or other impurity atoms.

Beyond diamond
"Diamond is the case we could measure, but the question is much bigger than one defect in one material," Van de Walle said. "Defects that hold their electrons tightly are everywhere: in the phosphors that make LEDs glow, in the crystals that detect radiation, in the insulating layers of electronic chips. Wherever such defects trade electrons without the help of heat, this is the mechanism to look at, and it helps us predict what the textbook picture simply could not." 

Funding for this research was provided by the Department of Energy Office of Science, Office of Basic Energy Sciences, through the Co-design Center for Quantum Advantage (C2QA), the Max Planck Society, the Lithuanian Research Council, and the European Union. 

The paper is dedicated to the memory of co-author Audrius Alkauskas of FTMC, who initiated the theoretical work and passed away before its completion.