Nonlinear reservoir engineering and control of a trapped-ion oscillator

Trapped-ions are one of the primary systems used for investigating the control of harmonic oscillators for quantum science. A central tool for trapped ion control has been Hamiltonians based on the "Lamb-Dicke approximation", which linearizes the laser-mediated spin-motion coupling by assuming that the ion's spatial wavefunction is much smaller than the laser wavelength. Here, we explicitly depart from this approximation to enter a new regime of quantum state control based on the non-linear nature of the atom-light interaction Hamiltonian. In this regime, the coupling strength between the light field and the atom is heavily modulated by the ion's motion. We exploit the nonlinearities of the interaction to engineer nonlinear reservoir engineering to stabilize cat-like manifolds of motional states of the trapped ion and demonstrate the use of non-linear Hamiltonians to control them. This method involves simultaneously driving red and blue detuned motional sidebands of various orders while simultaneously optically pumping the spin degree of freedom. 

I will outline the method theoretically, and then present experimental results from work performed using a microfabricated Penning ion trap. We investigate the dependence of the amplitude, symmetry and parity of the stabilized states on experimentally accessible parameters such as the sideband orders and the Lamb-Dicke parameter. By studying the dynamics of the system, we observe that the stabilization emerges from destructive interference between gain and loss processes of the dissipative operator. Lastly, we show that we can obtain locally dispersive Hamiltonians by engineering the appropriate nonlinear coupling, and employ these to measure the parity of motional states, which we use to initialize a pure cat state.