Quantum harmonic oscillator state control in a squeezed Fock basis

TL;DR

This paper demonstrates precise control of a trapped-ion quantum harmonic oscillator in a squeezed Fock basis, enabling the creation of highly squeezed states and superpositions with potential applications in quantum metrology and information.

Contribution

It introduces engineered Hamiltonians for controlling squeezed Fock states, reproducing Jaynes-Cummings physics and enabling ladder climbing to high excitations with significant squeezing.

Findings

Reproduces $\sqrt{n}$ scaling for low $n$ in engineered Hamiltonians

Creates squeezed Fock states up to $n=6$ with 8.7 dB squeezing

Demonstrates superpositions of squeezed Fock states

Abstract

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.