Xiaoshui Lin

Quantum-enhanced multiparameter sensing is often associated with distributed architectures or 2-anticoherent states, whereas squeezing in a single collective ensemble is typically limited to single-parameter metrology. Here, we show that a single ensemble can support simultaneous multiparameter squeezing when each sensor is promoted from a qubit to a qudit (i.e., spin with $d$ energy levels). We develop a general framework in which the optimal product probe state, the corresponding global readout observables, and the associated squeezing parameters are all determined from the single-site quantum Fisher information matrix. We then present a minimal qudit construction for two-parameter vector magnetic field sensing with local dimension $d=3$. We further identify a collective twisting-like interacting Hamiltonian that generates such multiparameter-squeezed states and numerically demonstrate scalable metrological gain. In particular, for a trapped-ion qutrit chain with power-law interactions, we obtain up to 12 dB enhancement in two-parameter sensing for $N=256$ sensors. Our results establish qudit-enabled multiparameter squeezing in a single ensemble as a distinct route to multiparameter quantum metrology with global readout, and highlight its potential advantage over distributed multi-ensemble strategies in the fixed-sensor-budget regime.

Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance. In this model, the Mathieu equation plays the most fundamental role for us to understand the stability and instability of a single ion. In this work, we investigate the dynamics of trapped ions with the Coulomb interaction based on the Hamiltonian equation. We show that the many-body interaction will not influence the phase diagram for instability. Then, the dynamics of this model in the large damping limit will also be analytically calculated using few trapped ions. Furthermore, we find that in the presence of modulation, synchronization dynamics can be observed, showing an exchange of velocities between distant ions on the left side and on the right side of the trap. These dynamics resemble to that of the exchange of velocities in Newton's cradle for the collision of balls at the same time. These dynamics are independent of their initial conditions and the number of ions. As a unique feature of the interacting Mathieu equation, we hope this behavior, which leads to a quasi-periodic solution, can be measured in current experimental systems. Finally, we have also discussed the effect of anharmonic trapping potential, showing the desynchronization during the collision process. It is hopped that the dynamics in this many-body Mathieu equation with damping may find applications in quantum simulations. This model may also find interesting applications in dynamics systems as a pure mathematical problem, which may be beyond the results in the Floquet theorem.