[Paper Review] Coherence and entanglement of inherently long-lived spin pairs in diamond

H. P. Bartling, M. H. Abobeih+8 more|arXiv (Cornell University)|Mar 14, 2021

Diamond and Carbon-based Materials Research14 references4 citations

TL;DR

This paper demonstrates that pairs of identical 13C nuclear spins in diamond form inherently long-lived quantum systems due to a combination of clock transitions, decoherence-free subspaces, and motional narrowing. Using a nearby nitrogen-vacancy (NV) center, the authors achieve a record T₂* coherence time of 1.9(3) minutes for individually controlled spin-pair qubits and realize high-fidelity entanglement via projective parity measurements.

ABSTRACT

Understanding and protecting the coherence of individual quantum systems is a central challenge in quantum science and technology. Over the last decades, a rich variety of methods to extend coherence have been developed. A complementary approach is to look for naturally occurring systems that are inherently protected against decoherence. Here, we show that pairs of identical nuclear spins in solids form intrinsically long-lived quantum systems. We study three carbon-13 pairs in diamond and realize high-fidelity measurements of their quantum states using a single NV center in their vicinity. We then reveal that the spin pairs are robust to external perturbations due to a unique combination of three phenomena: a clock transition, a decoherence-free subspace, and a variant on motional narrowing. The resulting inhomogeneous dephasing time is $T_2^* = 1.9(3)$ minutes, the longest reported for individually controlled qubits. Finally, we develop complete control and realize an entangled state between two spin-pair qubits through projective parity measurements. These long-lived qubits are abundantly present in diamond and other solids, and provide new opportunities for quantum sensing, quantum information processing, and quantum networks.

Motivation & Objective

• To investigate whether pairs of identical nuclear spins in solids can serve as intrinsically protected quantum systems with long coherence times.
• To overcome the traditional view of such spin pairs as sources of decoherence by demonstrating their potential as robust, individually controllable qubits.
• To achieve high-fidelity initialization, control, and readout of spin-pair pseudo-spin states using a nearby NV center as a quantum sensor and controller.
• To demonstrate entanglement between two such spin-pair qubits using projective parity measurements.
• To establish that these long-lived qubits are naturally abundant in diamond and other solids, enabling new applications in quantum technologies.

Proposed method

• The study uses a nitrogen-vacancy (NV) center in diamond to sense and control three distinct 13C nuclear spin pairs (A, B, C) at 3.7 K, leveraging the NV's long coherence and optical addressability.
• The spin pairs are modeled as pseudo-spins in the antiparallel subspace (|↑↓⟩ and |↓↑⟩), with dynamics governed by a Hamiltonian H = X·Iₓ + mₛZ·I_z, where X is the dipolar coupling and Z is the hyperfine splitting difference.
• High-fidelity state preparation and measurement are achieved using a sequence of resonant π pulses and NV spin readout, with timing optimized to avoid decoherence during measurement.
• For pairs with X ≫ Z (A and B), universal single-qubit control is implemented via free evolution and dynamical decoupling; for Z ≫ X (C), control is achieved through NV spin-state-dependent evolution (mₛ = 0 for X-rotation, mₛ = -1 for approximate Z-rotation).
• Entanglement between two spin-pair qubits is created using projective parity measurements that distinguish between symmetric and antisymmetric Bell states.
• The entire Hilbert space of pair C is accessed via RF driving of single-spin-flip transitions, enabling selective initialization and control of individual 13C spins with negligible NV coupling.

Experimental results

Research questions

• RQ1 Can pairs of identical nuclear spins in diamond function as intrinsically long-lived quantum systems due to inherent protection mechanisms?
• RQ2 To what extent do clock transitions, decoherence-free subspaces, and motional narrowing collectively suppress dephasing in 13C spin pairs?
• RQ3 Can a single NV center be used to achieve high-fidelity, individually addressable control of multiple 13C spin-pair qubits in the same diamond sample?
• RQ4 What is the maximum achievable coherence time for such spin-pair qubits under ambient conditions, and how does it compare to other solid-state qubits?
• RQ5 Is it possible to generate and verify entanglement between two such long-lived spin-pair qubits using projective measurements?

Key findings

• The inhomogeneous dephasing time T₂* for the 13C spin pairs reaches 1.9(3) minutes, the longest reported for individually controlled qubits in any solid-state system.
• The spin pairs exhibit robustness against external perturbations due to the simultaneous presence of a clock transition, a decoherence-free subspace, and a variant of motional narrowing.
• High-fidelity initialization and readout of pseudo-spin states are achieved through repeated projective measurements using the NV center, with NV readout time minimized to ~5 μs.
• Entanglement is successfully generated between two spin-pair qubits using projective parity measurements, demonstrating scalable quantum control of multiple long-lived qubits.
• The entire Hilbert space of a 13C pair (including symmetric states) is accessible via RF driving of single-spin transitions, enabling selective control of individual 13C spins with negligible NV coupling.
• The measured hyperfine coupling strengths (e.g., A∥^(1) = 2π·2826(5) Hz and A∥^(2) = 2π·18(7) Hz) are consistent with 13C-13C pair assignments, confirming the origin of the observed signals.