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

How can we systematically prepare multimode NOON states—entangled states of N photons distributed across multiple modes—in a way that is both controllable and scalable? High-fidelity preparation of these states is essential for quantum-enhanced metrology, yet it remains a significant experimental challenge.

The researchers develop a Floquet-engineered framework where a d-level quantum system (the controller) mediates the dynamics of d bosonic modes. By periodically modulating the coupling between the controller and the bosonic modes, they create an effective Hamiltonian that exhibits chiral excitation flow. The controller acts as a "quantum knob"; by preparing it in different eigenstates, researchers can coherently select the direction and velocity of the excitation transport. This allows for an exact qudit-controlled cyclic permutation of the bosonic modes, which is the key mechanism for generating multimode NOON states.

The study demonstrates that for any odd dimension d = 2s + 1, the system can be engineered to perform a cyclic shift of bosonic excitations. The authors explicitly detail the three-mode case (requiring one modulation harmonic) and the five-mode case (requiring two harmonics). They show that the controller-dependent chiral dynamics allow for the preparation of NOON states with programmable amplitudes and phases. Numerical simulations confirm that the protocol is robust against moderate frequency mismatches and coupling fluctuations, provided the driving frequency is chosen to balance the validity of the Floquet approximation against dissipation effects.

Multimode NOON states are powerful resources for multiphase estimation, offering Heisenberg-limited precision that outperforms classical strategies. This Floquet-based construction provides a scalable, systematic route to generating these complex entangled states in hybrid platforms, such as superconducting circuits coupled to magnons or 3D cavities. It offers a flexible architecture for quantum information processing and distributed quantum sensing.