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arXiv:2606.22753

Wigner-Negative Magnon Steady States from Incoherent Qubit Pumping

Yan Liu, Jiahua Li

quant-phSubmitted Jun 22, 2026• Announced Jun 23, 2026• 0 citations
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Abstract

We show that incoherently pumped qubits can realize a cascaded dissipative mechanism for stabilizing Wigner-negative magnon steady states. The mechanism combines qubit pumping with dispersive magnon-number selectivity to direct the steady-state population toward selected magnon Fock states. In the single-qubit case, the single-magnon population can approach unity, accompanied by strong antibunching and pronounced Wigner negativity. Extending the same principle to multiple qubits yields Wigner-negative steady states dominated by higher magnon Fock components. We further derive an analytical birth--death model that captures the mechanism and agrees with numerical results. These results establish incoherent qubit pumping as a controllable dissipative resource for generating nonclassical magnon states in hybrid quantum systems.

Comments
41 pages, 13 figures, including Supplemental Material

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We show that incoherently pumped qubits can realize a cascaded dissipative mechanism for stabilizing Wigner-negative magnon steady states. The mechanism combines qubit pumping with dispersive magnon-number selectivity to direct the steady-state population toward selected magnon Fock states. In the single-qubit case, the single-magnon population can approach unity, accompanied by strong antibunching and pronounced Wigner negativity. Extending the same principle to multiple qubits yields Wigner-negative steady states dominated by higher magnon Fock components. We further derive an analytical birth--death model that captures the mechanism and agrees with numerical results. These results establish incoherent qubit pumping as a controllable dissipative resource for generating nonclassical magnon states in hybrid quantum systems.
We show that a Kerr-nonlinear cavity coupled to an incoherently pumped two-level qubit can stabilize a nonclassical steady state with pronounced Wigner negativity. Without the qubit, two-photon drive and dissipation preserve photon-number parity and confine vacuum-initiated dynamics to the even-parity Fock subspace, preventing the emergence of odd-parity-induced central Wigner negativity. The qubit opens a frequency-selective injection channel into the odd-parity Fock subspace, while Kerr nonlinearity suppresses unwanted higher-order transitions, driving the system toward a steady state dominated by the single-photon Fock state that can approach a nearly pure state in the optimal regime. The resulting Wigner negativity remains robust over broad experimentally relevant loss and dephasing regimes, providing a route to the dissipative stabilization of nonclassical light in cavity quantum electrodynamics platforms.
We propose an autonomous scheme for stabilizing prescribed Fock states in a Kerr cavity by rectifying anti-Jaynes--Cummings interactions with auxiliary-qubit relaxation. Full Lindblad simulations demonstrate steady states dominated by the Fock states ∣1⟩|1\rangle∣1⟩ through ∣4⟩|4\rangle∣4⟩, accompanied by pronounced Wigner negativity. An analytical birth--death model captures the steady-state populations and identifies the operating regime for stabilization. These results establish auxiliary-qubit relaxation as a resource for autonomous reservoir engineering and provide a route to nonclassical bosonic-state preparation in a single Kerr cavity and, through a boundary reservoir, in a Kerr-cavity chain.
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, g ( 2 ) ( 0 ) . 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 [ g ( 2 ) ( 0 ) ≃ 1 ] and pronounced linewidth narrowing. For dissipative coupling alone, the magnon emission exhibits nonclassical antibunching [ g ( 2 ) ( 0 ) < 1 ] 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 g ( 2 ) ( 0 ) ≪ 1 . 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.
Driven-dissipative Kerr cavities serve as a versatile platform for generating nonclassical states, such as quantum cat states and high-photon-number Fock states, which are essential for quantum information processing. Building on the quantized Lugiato-Lefever equation (QLLE), which predicts steady-state coherent state superpositions in multi-mode Kerr resonators, and the framework for engineering Kerr nonlinearity ratios to mitigate spectral crowding in coupled oscillators, we propose an integrated approach for precise quantum control. By engineering the Kerr ratio K1/K2 to approximate an incommensurate value using complex rational approximations, we eliminate parasitic degeneracies and enable selective addressing of transitions in the QLLE steady state. Employing a Magnus expansion, we derive an effective Hamiltonian that incorporates Stark-shift corrections, facilitating deterministic synthesis of entangled cat states and Fock states with fidelities exceeding 99.9%. Numerical simulations using QuTiP validate robustness against dissipation and thermal noise, demonstrating quantum hysteresis and Wigner negativity in multi-mode configurations. This synthesis bridges dissipative phase transitions with architectural control, offering a blueprint for scalable bosonic quantum processors in circuit QED. The Wigner function plays a pivotal role in characterizing these nonclassical states, providing a phase-space representation that reveals quantum interference effects. In our framework, the emergence of negative values in the Wigner function for the central mode confirms the non-Gaussian nature of the cat states, as dictated by Hudson’s theorem, which states that only Gaussian pure states have non-negative Wigner functions everywhere [21]. This negativity arises from the interference term in the cat-state Wigner expression, quantifying macroscopic quantum coherence and serving as a witness for entanglement in multi-mode systems.For instance, our simulations at F = 2.0 yield a minimum Wigner value of approximately -0.006, highlighting the system’s departure from classical behavior and its utility for bosonic error correction, where cat codes leverage phase-space separation to suppress bit-flip errors exponentially with cat size. Furthermore, the relation to Wigner functions extends to dynamical properties: the steady-state Wigner negativity is robust against thermal noise due to the dissipative stabilization mechanism, aligning with results from driven Bose-Hubbard models where two-mode cat states maintain negativity under loss [46]. In the QLLE context, the multi-mode extension introduces spatial localization, where the Wigner function’s negative regions correspond to soliton-like structures, as evidenced by photon population distributions [0.33, 0.90, 0.33]. This negativity is not merely a feature but a consequence of fundamental limits on classical simulability, relating to the Gottesman-Knill theorem’s extension to continuous variables, where non-Gaussian operations are necessary for universal quantum computation. Quantum hysteresis, observed in our hysteresis plots, is intimately linked to the Wigner representation through the bifurcation dynamics. Near the codimension-2 point, the system’s bistability manifests as distinct paths in phase space, with Wigner functions switching between Gaussian-like (low-photon) and cat-like (high-photon) forms, supported by spectral theory of Liouvillians that guarantees metastable states in dissipative phase transitions [30]. The forward and backward sweeps in our simulations demonstrate this path dependence, with the Wigner negativity peaking in the high-drive regime, underscoring the role of Kerr nonlinearity in engineering quantum resources. Overall, the Wigner function’s negativity serves as a diagnostic tool for the efficacy of our engineered ratios, directly tying to experimental verifiability in circuit QED setups, where homodyne measurements can reconstruct Wigner distributions to confirm cat-state fidelity. This work not only advances control protocols but also highlights the profound interplay between phase-space quasi-probabilities and dissipative quantum engineering, paving the way for fault-tolerant bosonic qubits.
We experimentally demonstrate the steady-state generation of propagating Wigner-negative states from a continuously driven superconducting qubit. We reconstruct the Wigner function of the radiation emitted into propagating modes defined by their temporal envelopes, using digital filtering. For an optimized temporal filter, we observe a large Wigner logarithmic negativity, in excess of 0.08, in agreement with theory. The fidelity between the theoretical predictions and the states generated experimentally is up to 99%, reaching state-of-the-art realizations in the microwave frequency domain. Our results provide a new way to generate and control nonclassical states, and may enable promising applications such as quantum networks and quantum computation based on waveguide quantum electrodynamics.
N\'eel ordered antiferromagnets exhibit two-mode squeezing such that their ground state is a nonclassical superposition of magnon Fock states. Here we theoretically demonstrate that antiferromagnets can couple to spin qubits via direct dispersive interaction stemming from, e.g., interfacial exchange. We demonstrate that this kind of coupling induces a magnon number-dependent level splitting of the excited state resulting in multiple system excitation energies. This series of level splittings manifests itself as nontrivial excitation peaks in qubit spectroscopy thereby revealing the underlying nonclassical magnon composition of the antiferromagnetic quantum state. By appropriately choosing the drive or excitation energy, the magnonic state can be controlled via the qubit, suggesting that Fock states of magnon pairs can be generated deterministically. This enables achieving states useful for quantum computing and quantum information science protocols.