Quantum harmonic oscillator state control in a squeezed Fock basis

Understand

We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms.

• We demonstrate that for squeezed Fock states with low $n$ the engineered Hamiltonians reproduce the $\sqrt{n}$ scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields.
• Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of $n = 6$ with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states.
• These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.