Engineering magnon lasing in full quantum regime

We develop an analytical approach for steady-state normal-ordered magnon moments (NOMMs) in a driven-dissipative magnon-qubit system with coherent and dissipative couplings, and further benchmark it against the full quantum master-equation simulations of mean magnon number and second-order intensity correlation function, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msup> <a:mi>g</a:mi> <a:mrow> <a:mo>(</a:mo> <a:mn>2</a:mn> <a:mo>)</a:mo> </a:mrow> </a:msup> <a:mrow> <a:mo>(</a:mo> <a:mn>0</a:mn> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> . Specifically, we first show that strong coherent coupling alone can produce an intermediate-pump magnon-lasing-like emission window, identified by a small-signal stability criterion and characterized by near-Poissonian statistics <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mo>[</b:mo> <b:msup> <b:mi>g</b:mi> <b:mrow> <b:mo>(</b:mo> <b:mn>2</b:mn> <b:mo>)</b:mo> </b:mrow> </b:msup> <b:mrow> <b:mo>(</b:mo> <b:mn>0</b:mn> <b:mo>)</b:mo> </b:mrow> <b:mo>≃</b:mo> <b:mn>1</b:mn> <b:mo>]</b:mo> </b:mrow> </b:math> and pronounced linewidth narrowing. For dissipative coupling alone, the magnon emission exhibits nonclassical antibunching <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>[</c:mo> <c:msup> <c:mi>g</c:mi> <c:mrow> <c:mo>(</c:mo> <c:mn>2</c:mn> <c:mo>)</c:mo> </c:mrow> </c:msup> <c:mrow> <c:mo>(</c:mo> <c:mn>0</c:mn> <c:mo>)</c:mo> </c:mrow> <c:mo>&lt;</c:mo> <c:mn>1</c:mn> <c:mo>]</c:mo> </c:mrow> </c:math> at the optimal mean magnon number and features a large pump-tunable spectral linewidth. In the hybrid dissipative and weak-coherent-coupling regime, the dissipative channel can substantially enhance the steady-state mean magnon number while simultaneously inducing strong magnon antibunching, with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msup> <d:mi>g</d:mi> <d:mrow> <d:mo>(</d:mo> <d:mn>2</d:mn> <d:mo>)</d:mo> </d:mrow> </d:msup> <d:mrow> <d:mo>(</d:mo> <d:mn>0</d:mn> <d:mo>)</d:mo> </d:mrow> <d:mo>≪</d:mo> <d:mn>1</d:mn> </d:mrow> </d:math> . The results obtained here may find potential applications in microwave-magnonic and related hybrid quantum platforms, and the analytical NOMM method could also provide a route to treating other driven open boson-fermion systems.