Abstract
We propose an ideal scheme for preparing vibrational SU(1, 1) ⊗ SU(1, 1) states in a two-dimensional ion trap using red and blue second sideband resolved driving of two orthogonal vibrational modes. Symmetric and asymmetric driving provide two regimes to realize quantum state engineering of the vibrational modes. In one regime, we show that time evolution synthesizes so-called SU(1, 1) Perelomov coherent states, that is separable squeezed states and their superposition too. The other regime allows engineering of lossless 50/50 SU(2) beam splitter states that are entangled states. These ideal dynamics are reversible, thus, the non-classical and entangled states produced by our schemes might be used as resources for interferometry.
Highlights
Quantum state engineering studies the preparation, manipulation, and characterization of arbitrary quantum states
We are interested in the quantum state engineering of orthogonal vibrational modes that show squeezing and entanglement with an underlying SU(1, 1) ⊗ SU(1, 1) symmetry
We will show that red driving with symmetric coupling is able to produce lossless 50/50 SU(2) beam splitter vibrational states that are factorized from the internal state of the ion
Summary
Quantum state engineering studies the preparation, manipulation, and characterization of arbitrary quantum states. We will show that red driving with symmetric coupling is able to produce lossless 50/50 SU(2) beam splitter vibrational states that are factorized from the internal state of the ion. We suggest driving two normal phonon modes of the center of mass motion of a trapped ion[20,21], such that the effective Hamiltonian,
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