Nuclear Magnetic Resonance in TmVO₄ as a Probe of Entanglement at a Quantum Critical Point

Understanding the mechanisms of decoherence is a key problem for quantum computing, and the behavior of a central spin coupled to a well-controlled environment is an important and widely studied theoretical model. This problem can be investigated experimentally in the model transverse field Ising system TmVO₄ and offers a new approach to understanding decoherence in terms of the quantum fidelity of the environment. Our experiments show that low frequency quantum fluctuations at the quantum critical point have a very different effect on ⁵¹V nuclear spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point because NMR spin echoes filter out the latter but not the former. This distinction allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO₄ to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence. Our findings also offer new insights and connections between NMR and quantum information theory, particularly in the context of NMR wipeout effects observed in cuprates, pnictides, and other complex systems and their relation to quantum entanglement and fidelity in those systems.