Demonstration of Hamiltonian amplification in a trapped ion system

In quantum physics, it is often desirable to be able to increase the strength of an interaction Hamiltonian beyond what is natively available in the system. Squeezing can be used to amplify certain types of quantum interactions, but typically some knowledge of the interaction is required for effective amplification. This poses a challenge for quantum sensing applications where the interaction Hamiltonian may not be fully known. We implement a proposal [Arenz et al., Quantum 4, 271 (2020)] for phase-insensitive amplification of arbitrary interaction Hamiltonians coupling to a quantum harmonic oscillator with the form H = βa^† + β^†a. We realize the quantum harmonic oscillator in the motion of a single trapped ²⁵Mg⁺ ion, and perform amplification via a series of rapid squeezing pulses along alternating quadratures. We demonstrate the phase-insensitive amplification of a coherent displacement Hamiltonian by ∼3.4, and of a Jaynes-Cummings Hamiltonian by ∼1.5. Phase-insensitive amplification of small displacements could be useful for quantum sensing applications such as dark matter detection.