Nitrogen-Vacancy Centers in Diamond

Nitrogen-Vacancy Centers in Diamond#

Room-temperature quantum systems using defects in diamond. Quantum sensing, long coherence times, and networked quantum computing prospects.

The nitrogen-vacancy (NV) center in diamond is a point defect that traps electrons with spin, creating a qubit that can operate at room temperature. While NV centers may not compete with superconducting or trapped-ion systems for raw qubit count, they excel in quantum sensing and quantum networking.

The NV Center Structure#

An NV center consists of a substitutional nitrogen atom adjacent to a vacant lattice site in the diamond crystal. The negatively charged state (NV\(^-\)) hosts an electron spin triplet (\(S = 1\)) in its ground state, with the \(m_s = 0\) and \(m_s = \pm 1\) levels split by 2.87 GHz even at zero magnetic field. This zero-field splitting arises from spin-spin interaction within the defect.

To use the NV center as a qubit, two of the three spin levels are selected, typically \(|0\rangle = |m_s = 0\rangle\) and \(|1\rangle = |m_s = -1\rangle\). An external magnetic field lifts the degeneracy between \(m_s = +1\) and \(m_s = -1\), enabling selective addressing.

Control and Readout#

Initialization is achieved by optical pumping. A green laser (532 nm) excites the NV center. Through spin-dependent intersystem crossing via a metastable singlet state, the system preferentially relaxes into \(m_s = 0\) after a few optical cycles. This provides >90% polarization into the \(|0\rangle\) state.

Single-qubit gates are driven by microwave pulses at the spin resonance frequency (~2.87 GHz \(\pm\) the Zeeman shift). A microwave stripline fabricated on the diamond surface delivers the control field. Rabi oscillations between \(|0\rangle\) and \(|1\rangle\) are routine, with gate fidelities above 99%.

Readout exploits spin-dependent fluorescence. The \(m_s = 0\) state fluoresces brightly under green illumination, while \(m_s = \pm 1\) states are dimmer due to the intersystem crossing that diverts population into the non-radiative singlet pathway. Counting photons over a short window (~300 ns) discriminates the spin state. The contrast is typically 20-30%, limited by photon collection efficiency.

To improve photon collection, solid immersion lenses are sculpted directly into the diamond surface. The high refractive index of diamond (\(n = 2.4\)) causes strong total internal reflection at flat surfaces; a hemispherical lens increases photon extraction by 10-20x.

Coherence Properties#

NV centers in high-purity, isotopically engineered diamond (\(^{12}\)C, removing \(^{13}\)C nuclear spins) achieve remarkable coherence:

  • \(T_1\) (spin relaxation): seconds to minutes at cryogenic temperatures

  • \(T_2\) (Hahn echo): 1-2 ms at room temperature

  • \(T_2\) (dynamical decoupling): up to 1 second at low temperature

The primary decoherence source is the bath of \(^{13}\)C nuclear spins (1.1% natural abundance). Using isotopically purified \(^{12}\)C diamond reduces this bath dramatically.

Multi-Qubit Registers#

The NV electron spin couples to nearby nuclear spins through hyperfine interaction:

  • Nitrogen nuclear spin (\(^{14}\)N, \(I = 1\) or \(^{15}\)N, \(I = 1/2\)): Always present, strongly coupled. Used as an additional qubit.

  • Carbon-13 nuclear spins: Weakly coupled spins in the lattice. Individual \(^{13}\)C nuclei within ~2 nm can be selectively addressed using dynamical decoupling sequences. Each provides an additional qubit with extremely long coherence (\(T_2 > 10\) s).

This gives a multi-qubit register at a single NV center: 1 electron spin + the nitrogen nuclear spin + several \(^{13}\)C nuclear spins. Registers of 10+ qubits have been demonstrated.

The electron spin serves as a bus: it mediates initialization, gates, and readout of the nuclear spins. During computation, the nuclear spins store quantum information while the electron handles communication.

Quantum Networking#

The NV center’s optical transitions connect the spin qubit to photons, enabling quantum networking. The protocol:

  1. Excite the NV center and collect a spin-entangled photon

  2. Send photons from two distant NV centers to a beamsplitter

  3. A joint photon detection (Bell-state measurement) heralds entanglement between the two remote spins

This approach was used to demonstrate loophole-free Bell inequality violation (Delft, 2015) and the first multi-node quantum network (Delft, 2021), distributing entanglement across three nodes separated by tens of meters.

Quantum sensing

NV centers are among the most sensitive magnetic field sensors, detecting fields at the nanotesla level with nanometer spatial resolution. Applications include imaging magnetic domains in materials, detecting neural activity, and NMR spectroscopy of single molecules. This sensing capability operates at room temperature, making NV centers commercially relevant today.

Further Reading#

  • Doherty, M. W. et al., “The nitrogen-vacancy colour centre in diamond,” Phys. Rep. 528, 1 (2013). doi:10.1016/j.physrep.2013.02.001

  • Pompili, M. et al., “Realization of a multinode quantum network of remote solid-state qubits,” Science 372, 259 (2021). doi:10.1126/science.abg1919

  • Bradley, C. E. et al., “A ten-qubit solid-state spin register with quantum memory up to one minute,” Phys. Rev. X 9, 031045 (2019). doi:10.1103/PhysRevX.9.031045