A dissipative quantum simulator of lasing dynamics at the few quanta level

We demonstrate a trapped-ion system with engineered competing dissipation channels, implemented independently on two ion species co-trapped in a Paul trap. We use control of the spin-oscillator couplings via motional sideband drives and engineered decay rates via optical pumping to explore the phase diagram of this system, which is analogous to that of a (phonon) laser. Reconstruction of the phonon distribution via the readout of the motional sideband oscillation allows us to show the phase transition from a dark to the bright and coherent lasing phase. In contrast to earlier work [1] our laser works close to the quantum ground state with average phonon numbers below ten. In the lasing phase, we demonstrate phase locking of the oscillator to an additional resonant drive. We use readout of the characteristic function [2] to show symmetry breaking of the Wigner function when locked. We also observe the intrinsic phase diffusion of the lasing process starting from a displaced coherent state. The readout of the characteristic function once again shows washing out of the initial asymmetry. The toolbox of techniques is extensible to squeezed laser systems through the use of additional laser drives, is predicted to offer advantages in sensing [3], and provides methods for the general use of the mixed-ion-species platform in the simulation of dissipative spin-boson systems.