Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state.

Quantum absorption refrigerator with trapped ions.

In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge.

Quantum Simulation with a Trilinear Hamiltonian.

Interaction among harmonic oscillators described by a trilinear Hamiltonian ℏξ(a^{†}bc+ab^{†}c^{†}) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coulomb potential in a linear trapped three-ion crystal, we experimentally implement it among three normal modes of motion in the strong-coupling regime, where the coupling strength is much larger than the decoherence rate of the ion motion. We use it to simulate the interaction of an atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down-conversion in the regime of a depleted pump.

Cross-Kerr Nonlinearity for Phonon Counting.

State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions.

Quantum Parametric Oscillator with Trapped Ions.

A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states.