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arXiv:2208.02976 · Physical Review A

Floquet generation of a magnonic NOON state

Shi-fan Qi, Jun Jing

Published Jan 4, 2023• 16 citations
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Abstract

We propose a concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then, an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counterrotating interactions. We can obtain a high-fidelity NOON state in the presence of quantum dissipation on all components.

DOI
10.1103/physreva.107.013702

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We propose a concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then, an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counterrotating interactions. We can obtain a high-fidelity NOON state in the presence of quantum dissipation on all components.
The NOON states are valuable quantum resources, which have a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Here we propose a fast, concise, and reliable protocol for deterministically generating the NOON states of two resonators coupled to a single ▵▵▵-type superconducting qutrit. In particular, we derive the effective Hamiltonians at the points of the multiphoton resonances by virtue of the strong counter-rotating interaction between the resonator modes and the qutrit. Based on these crucial effective Hamiltonians, our protocol simplifies the previous ones using the single-photon resonance and consequently reduces the number of operations for state preparation. To test the robustness of this protocol, we analyze the effects from both the decoherence including dissipation and dephasing and the crosstalk of resonator modes on the state fidelity through a Lindblad master equation in the eigenbases of the full Hamiltonian.
We propose an efficient two-stage protocol for generating distant entanglement in a magnon-mediated hybrid quantum system, where magnons serve dual roles as both interaction mediators and qubits. This integrated design reduces the physical component count while leveraging the inherent advantages of magnons, such as their strong coupling via magnetic dipole interactions, low dissipation, and high integrability. In our setup, a superconducting resonator interfaces between a local superconducting qubit (SQ) and a local magnonic system (QM1), which is waveguide-coupled to a remote magnonic system (QM2). The protocol comprises two stages: (i) deterministic Bell-state generation between the SQ and QM1 using shortcuts to adiabaticity, and (ii) coherent state transfer to QM2 via engineered Hamiltonian dynamics. This adiabatic characteristic enhances robustness against environmental dissipation. Numerical simulations under realistic noise conditions confirm strong resilience to decoherence, achieving fidelity F>0.90F > 0.90F>0.90 and negativity N2>0.40\mathcal{N}_2 > 0.40N2​>0.40. These results establish the protocol as a scalable and practical building block for distributed quantum networks.
We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.
We propose a protocol for generating magnonic squeezed states (MSS) and their superpositions (SMSS) in a hybrid system comprising a superconducting flux qubit magnetically coupled to the Kittel mode of a yttrium iron garnet (YIG) sphere. The flux qubit provides an intrinsic longitudinal interaction with the magnon mode, which, under resonant microwave driving, gives rise to an effective qubit-state-dependent squeezing Hamiltonian. Numerical simulations incorporating realistic dissipation demonstrate that magnon quadrature noise reduction exceeding 8 dB8~\mathrm{dB}8 dB is achievable with experimentally accessible parameters.~By preparing the qubit in a superposition state followed by projective measurement, we further obtain symmetric and antisymmetric superpositions of orthogonally squeezed magnon states exhibiting clear phase-space interference fringes.~We discuss how the fourfold rotational symmetry of these states supports a bosonic logical encoding with potential for protecting against dominant error channels in magnonic platforms.
The NOON states possess Heisenberg-limited phase sensitivity and are crucial for quantum-enhanced metrology. In our work, we develop a Floquet-engineered conditional-routing framework in which a ddd-level quantum controller mediates the dynamics of ddd bosonic modes. For an arbitrary odd dimension d=2s+1d=2s+1d=2s+1, the ddd-level system can act as a ``quantum knob" by tuning its initial states to coherently control the direction of chiral excitation flow, such that different controller eigenstates generate distinct cyclic-routing branches of the bosonic excitations. By choosing sss harmonics, we construct an exact qudit-controlled cyclic permutation and use it to formulate a general protocol for preparing odd-ddd-mode NOON states. The same framework also enables programmable complex amplitudes through appropriate preparation of the controller state. As concrete realizations, we show that the three-mode case requires only a single harmonic and exhibits two oppositely directed chiral branches together with a stationary branch, whereas the five-mode case requires two harmonics and both nearest- and next-nearest-neighbor chiral hoppings. Meanwhile, taking the three-mode realization as a representative example, we assess the influence of systematic imperfections and dissipation on the conditional-routing dynamics and identify parameter regimes in which the routing operation remains accurate. Our results establish a systematic Floquet construction for controllable chiral routing and multimode NOON-state generation in arbitrary odd-dimensional networks, with potential applications in quantum information processing and quantum metrology.
Abstract Generating and manipulating magnon quantum states for quantum information processing is a central topic in quantum magnonics. The conventional strategy amplifies the nonlinear interaction among magnons to manifest their quantum correlations at cryogenic temperatures, which is challenging for magnets with vanishingly small nonlinearities. Here we propose an unconventional approach to prepare entangled states of two distant magnon modes by applying a two-tone Floquet field to each magnet inside a microwave cavity. The Floquet driving can effectively generate parametric interaction between magnons and photons, and thus opens an indirect entanglement channel between the two magnon modes mediated by cavity photons. By optimizing the relative ratio of the magnon–photon coupling and the detuning between the magnon modes, the two magnon modes can reach a stationary and robust entanglement, of which the strength is enhanced compared with entanglement generated via magnetic nonlinearities. Furthermore, one-way steering between the two magnets is realized by engineering unequal damping rates of the two magnets while the steering asymmetry can be efficiently modulated by tuning the coupling strength of magnons and cavity photons. The essential physics of our findings universally applies to a wide class of magnets with small nonlinearities and may find promising applications in engineering robust magnon quantum states for quantum information science.