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arXiv:2609.14524

Preparation of Multimode NOON States via Floquet-Engineered Conditional Chiral Excitation

Mengxue Li, Bo Tian, H. Z. Shen, Haodi Liu, Gangcheng Wang

quant-phSubmitted Sep 13, 2026• Announced Sep 15, 2026• 0 citations
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Abstract

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 $d$-level quantum controller mediates the dynamics of $d$ bosonic modes. For an arbitrary odd dimension $d=2s+1$, the $d$-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 $s$ harmonics, we construct an exact qudit-controlled cyclic permutation and use it to formulate a general protocol for preparing odd-$d$-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.

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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.
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.
This thesis investigates the fast and controlled generation of highly entangled many-body quantum states in systems of ultracold bosonic atoms. We focus in particular on the preparation of NOON states and their multimode generalizations, which constitute central resources for quantum metrology due to their enhanced sensitivity to parameter estimation. Working within Bose-Hubbard models in the self-trapping regime, where interaction effects dominate the dynamics, we exploit collective tunneling phenomena to isolate effective subspaces suitable for state engineering. To overcome the intrinsic slowness of adiabatic protocols, we introduce a control strategy based on the combined use of geodesic control and counterdiabatic driving, referred to as \textit{geodesic counterdiabatic driving}. This approach enables accelerated state preparation using time-independent and experimentally accessible control parameters, while reaching the quantum speed limit. We demonstrate the efficiency and robustness of the method for generating high-fidelity NOON states in optical lattices. Finally, we extend the framework to the creation of NOON states with vortices in two-dimensional harmonic traps and discuss applications to quantum-enhanced metrology, highlighting the feasibility of rotation sensing beyond classical limits.
Superpositions of macroscopically distinct coherent states, or cat states, are a key resource for quantum technologies. In particular, two-mode binomial cat states can give rise to exact quantum error correction in continuous-variable quantum computing. However, their preparation typically requires non-Gaussian initial states, such as Fock or NOON states, which are challenging to realize experimentally. Here, we propose a protocol to generate two-mode binomial cat states where the only requirements are Gaussian initial states in combination with heralded heterodyne measurements. Our approach utilizes cross-Kerr interactions between bosonic modes commonly realizable in superconducting circuit architectures. We show that by adjusting the input state parameters, our protocol remains robust to dissipation under realistic experimental conditions. Our work provides a practical route to realizing multinomial cat states in current experimental platforms without requiring non-Gaussian initial resources, overcoming a key limitation of existing preparation schemes.
The ability to route quantum states between arbitrary nodes in a multinode network is one of the many facets required to build future large-scale quantum computing devices. Quantum routing can be implemented based on chiral dynamics, while their related research stays in three-node networks. In this paper, we give the target Hamiltonian for realizing chiral dynamics in arbitrary NNN-node networks. Based on the derived Hamiltonian, we present key features of chiral state transfer in multinode spin and bosonic networks. For the realistic implementation of the required Hamiltonian, we propose a modulation scheme to generate the matched effective Floquet Hamiltonian. Furthermore, we numerically simulate the multinode chiral dynamics with realistic parameters in superconducting circuits, and the results clearly show multinode chiral state transfer. Our work provides a universal and fundamental framework for understanding chiral dynamics in multinode networks. These findings will stimulate quantum state transfer, quantum routing, and nonreciprocal circulators in multinode networks.
In condensed matter, Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Quantum Hall states (in the continuum) or Fractional Chern Insulators (on the lattice). As the latter, CSL are remarkable states of matter, exhibiting topological order and chiral edge modes. Preparing CSL on quantum simulators like cold atom platforms is still an open challenge. Here we propose a simple setup on a finite cluster of spin-1/2 located at the sites of a square lattice. Using a Resonating Valence Bond (RVB) non-chiral spin liquid as initial state on which fast time-modulations of strong nearest-neighbor Heisenberg couplings are applied, following different protocols (out-of-equilibrium quench or semi-adiabatic ramping of the drive), we show the slow emergence of such a CSL phase. An effective Floquet dynamics, obtained from a high-frequency Magnus expansion of the drive Hamiltonian, provides a very accurate and simple framework fully capturing the out-of-equilibrium dynamics. An analysis of the resulting prepared states in term of Projected Entangled Pair states gives further insights on the topological nature of the chiral phase. Finally, we discuss possible applications to quantum computing.
Large Fock states are important resources for bosonic quantum information and quantum-enhanced metrology, but preparing them with high probability at large excitation numbers remains challenging, as deterministic methods become increasingly control-intensive, while measurement-based approaches typically suffer from low heralding probabilities. Here we propose a protocol that combines quantum nondemolition photon-number encoding with quantum amplitude amplification to enable high-probability heralded generation of large Fock states. Starting from a cavity mode prepared in a coherent state, Quantum Phase Estimation encodes photon-number information into a multi-qubit register, while Quantum Amplitude Amplification boosts the probability of a desired target outcome before measurement. The scheme has an immediate implementation in dispersive circuit-QED, but can be analogously adapted to other bosonic platforms with QND photon-number readout, such as cavity-QED. With a register of up to eight qubits, near-deterministic preparation of Fock states with hundreds of excitations is possible. We also show that the protocol can serve as the first stage of an extension toward generating a two-mode NOON state via a conditional beam-splitter operation.