Month: October 2025

I will discuss the integrability property of a stochastic and quantum deformation of the Rule 54 cellular automaton: the simplest microscopic (deterministic) reversible model in 1+1 discrete space and time dimensions with strong local interactions. First, I will introduce the Rule 54 model and its two deformations: In the stochastic case, I couple the system to stochastic boundary reservoirs and show that the resulting non-equilibrium steady states can be constructed explicitly in matrix product form. In the quantum case, I explain how the model can be embedded into the Yang-Baxter integrability framework. It turns out that Yang- Baxter integrability is more common than previously thought! Based on ongoing work with T. Prosen.

Continuous-variable quantum systems enable encoding complex states in fewer modes through large-scale non-Gaussian states. Motion, as a continuous degree of freedom, underlies phenomena from Cooper pair dynamics to levitated macroscopic objects. Hence, realizing high-energy, spatially extended motional states remains key for advancing quantum sensing, simulation, and foundational tests.

In the talk, I will present the following control tasks for various nonlinear mechanical systems, including trapped atoms, levitated particles, and clamped oscillators with spin-motion coupling.
(i) Nonharmonic potential modulation: Optimal control of a particle in a nonharmonic potential enables generation of non-Gaussian states and arbitrary unitaries within a chosen two-level subspace [1].
(ii) Macroscopic quantum states of levitated particles: Rapid preparation of a particle’s center of mass in a macroscopic superposition is achieved by releasing it from a harmonic trap into a static double-well potential after ground-state cooling [2].
(iii) Phase-insensitive force sensing: For randomized phase-space displacements, quantum optimal control identifies number-squeezed cat states as optimal for force sensitivity under lossy dynamics [3].

These approaches exploit either intrinsic nonharmonicity or coherent nonlinear coupling, providing a unified framework for motion control in continuous-variable quantum systems—from levitated nanoparticles to optical and microwave resonators—paving the way toward universal quantum control of mechanical motion.

[1] PTG, H. Pichler, C. A. Regal, O. Romero-Isart, Quantum control of continuous systems via nonharmonic potential modulation, Quantum 9, 1824 (2025)
[2] M. Roda-Llordes, A. Riera-Campeny, D. Candoli, PTG, O. Romero-Isart, Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys. Rev. Lett. 132, 023601 (2024)
[3] PTG, R. Filip, Optimal phase-insensitive force sensing with non-Gaussian states, arXiv: 2505.20832 (2025)