Nonlinear Quantum Optics with Trapped Ions

Dzmitry Matsukevich

Centre for Quantum Technologies and Department of Physics

National University of Singapore

Due to large accessible Hilbert space, mechanical motional states of the trapped ions are attractive for quantum simulations and quantum computing. However, such applications require strong and well controlled interactions between the normal modes of motion. In this talk I will discuss how the nonlinear couplings between the motional modes similar to degenerate and non-degenerate parametric oscillator models in quantum optics arise due to anharmonicity of the Coulomb interaction between the ions. I will show how such nonlinear coupling helps to implement a small thermal machine: an absorption refrigerator. I will also discuss how coupling of spin and motion of the ions enables experimental implementation of a SWAP test for measuring overlap between two infinitely-dimensional quantum states of harmonic oscillators and describe its application for quantum machine learning tasks.