Non-Hermitian Dynamics of Spin Chains with Loss and Gain

Understanding the joint dynamics of electron and nuclear spins is central to core concepts in solid-state magnetic resonance - such as spin-lattice relaxation and DNP - but a generalization that capitalizes on competing polarization loss and gain channels is still lacking. In this work, we theoretically study the non-Hermitian dynamics of hybrid electron/nuclear spin systems in the simultaneous presence of electron spin pumping and spin-lattice relaxation. We consider chain-like arrays where the nuclear spin coupling is mediated by pairs of interacting electron spins, one of which spin-polarizes under laser excitation. Setting an externally applied magnetic field to allow inter-electronic spin flips, we show that when the spin pumping rate reaches a critical threshold, nuclear spin polarization flows selectively in one direction but not in the other. The dynamics that ensues lead to asymmetric, site-selective nuclear spin polarization along the chain. In ring-like arrays, we identify a different final regime, featuring uniform polarization distributions and persistent nuclear spin currents, even in the absence of net nuclear polarization. Finally, we show that these processes can be made robust to defects in the chain through the periodic modulation of the applied magnetic field.