Trapped-Ion Simulator Shows Sign-Flip of Bosonic Frequencies Converts Excitation Exchange to Correlated Pair Creation

The experiment relies on spin-dependent forces to independently tune effective frequencies and couplings of two bosonic modes. When frequencies share the same sign, the system exhibits standard beam-splitter-like exchange; opposite signs reorganize the resonance condition, activating parametric amplification instead. This produces stable oscillatory, critical, and exponentially growing regimes separated by a spin-dependent instability threshold, generating quadrature squeezing and bipartite motional entanglement.

In the dispersive regime the effective Hamiltonian realizes a two-mode parametric amplifier. Preparing the spin in superposition places different spin components in distinct stability regimes, creating tripartite spin-boson entanglement; post-selection then yields non-Gaussian bosonic states. The scheme uses parameters already accessible in current trapped-ion hardware, yet remains a numerical and analytical proposal rather than executed data.

Related trapped-ion work on the single-mode quantum Rabi model (e.g., 2017 Nature experiments) and parametric amplification in superconducting circuits provides the immediate context, but the sign-controlled multimode resonance structure is new. The main advance is programmable access to instability thresholds without additional nonlinearities.

Next steps require calibration of the two-mode instability threshold in a real device and verification of tripartite entanglement witnesses. A 20-ion chain with sub-kHz frequency control would suffice to test the predicted exponential growth rate within coherence times.