Stabilizing a single-magnon state by optimizing magnon blockade

A stable and high-quality single-magnon state is desired by the single-magnon source for quantum-information application with a macroscopic spin system. We consider a hybrid system where a magnon mode is directly coupled to a nonresonant superconducting qubit via the exchange interaction. The magnon and qubit are under the driving and probing fields with the same frequency, respectively. We find that the single-magnon probability ${P}_{1}$ can be maximized when the product of the magnon-driving field detuning and the qubit-probing field detuning is equivalent to the square of the magnon-qubit coupling strength, ${\mathrm{\ensuremath{\Delta}}}_{q}{\mathrm{\ensuremath{\Delta}}}_{m}\ensuremath{\approx}{J}^{2}$. Then, the double-magnon probability ${P}_{2}$ can be minimized by tuning the ratio of the probing intensity to the driving intensity and the relative phase between the two fields. Under these optimized conditions with accessible strong driving intensity and low decay rate, strong magnon blockade gives rise to a stable single-magnon state with a high quality. It features a large brightness (the single-magnon probability) ${P}_{1}\ensuremath{\approx}0.40$ and a high purity (the equal-time second-order correlation function) ${g}^{(2)}(0)\ensuremath{\sim}{10}^{\ensuremath{-}5}$. The two indicators as a whole prevail over the existing results for photon, phonon, and magnon modes with respect to a stable single-quantum state. The optimized conditions with a scalable modification ${\mathrm{\ensuremath{\Delta}}}_{q}{\mathrm{\ensuremath{\Delta}}}_{m}\ensuremath{\approx}N{J}^{2}$ apply to the situation when one focuses on any one of the $N$ magnon modes that are simultaneously coupled to a common qubit.