Phonon-number-resolving detection of multiple local phonon modes in trapped ions

We propose and demonstrate phonon-number-resolving detection of the multiple local phonon modes in a trapped-ion chain. To mitigate the effect of phonon hopping during the detection process, the probability amplitude of each local phonon mode is mapped to the auxiliary long-lived motional ground states. Sequential state-dependent fluorescence detection is then performed. In the experiment, we have successfully observed the time evolution of two local phonon modes in two ions, including the phonon-number correlation between the two modes.

Figure 1

(a) Phonon-number-resolving detection of multiple local phonon modes. The sequence for the $\mathit{j}\mathrm{th}$ ion in an $\mathit{N}$-ion chain is shown schematically. (b) Simplified mapping process used in the experiment. The composite pulse technique has been used instead of adiabatic passage. The probability amplitude of $|n_y=0\rangle$ is transferred to $|D_{5/2},m_j=-5/2\rangle \equiv |e_0\rangle$ (shelving-up pulse). A blue-sideband (BSB) $\pi$ pulse is then applied. (c) Schematic illustration of the experimental setup.

Figure 2

Phonon-number-resolving detection of a single ion. Results for initial states of (a) $|n_y=0\rangle$, (b) $|n_y=1\rangle$, and (c) $|n_y=2\rangle$. Labels A and B represent data obtained from fitting of the blue-sideband Rabi oscillation (black bar) and phonon-number-resolving detection (red bar), respectively.

Figure 3

Results of phonon-number-resolving detection for two ions with two phonons. Red, orange, and black circles represent the measured probability amplitude of $|1,1\rangle$, $|2,0\rangle$, and $|0,2\rangle$, where the first and second numbers represent the phonon numbers for the first and second ions, respectively. Each time step corresponds to the collection of 500 experiments. The error bars represent the statistical uncertainties of $1\sigma$. The dashed curves represent the numerical calculation of each local phonon mode. The simulation was performed based on the Hamiltonian given in Eq. (3).