Blockade of phonon hopping in trapped ions in the presence of multiple local phonons

Driving an ion at a motional sideband transition induces the Jaynes-Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we realize phonon blockade in the presence of multiple local phonons in a trapped-ion chain. This work constitutes a concrete study on the evolution of multiple local phonons with or without phonon blockade.

Figure 1

(a) Harmonic ladder of eigenstates of local phonons. (b) Anharmonic ladder of JC eigenstates.

Figure 2

Experiments on blocking the excitation of the first local phonon. Temporal dynamics of local phonons (a) without blockade and (b) with blockade. The time step between data points is 20 $\mu \mathrm{s}$. Each data point is an average of 500 measurements. The dashed lines are numerically simulated results. The phonon hopping occurs during the state preparation and the mapping process; therefore, the results start with a derivative.

Figure 3

Experiments on blocking the excitation of the second local phonon using mapping with blue-sideband (BSB) $\pi$ pulses for state analysis. Experimental sequences (a) without blockade and (c) with blockade. We varied hopping (blockade) duration $\tau$ to observe the multiphonon dynamics. Here, SBC represents the sideband cooling. Experimental results (b) without blockade and (d) with blockade. The red and blue (open) circles in the graphs represent the probabilities for Ion 1 and Ion 2, respectively. The solid lines [black line in Fig. 3, red and blue lines in Fig. 3] represent numerical calculations. Each point is the average of 50 experiments. The error bars represent the statistical uncertainties of $1\sigma$.

Figure 4

Experiments on blocking the excitation of the second local phonon using blue-sideband (BSB) Rabi oscillations for state analysis. Experimental sequences (a) without blockade and (c) with blockade. Here, SBC and CAR represent the sideband cooling and the carrier pulse, respectively. To deduce the phonon number distribution, we observe the blue-sideband Rabi oscillation of Ion 1. Experimental results (b) without blockade and (d) with blockade are shown. The probabilities for $|0\rangle$, $|1\rangle$, and $|2\rangle$ obtained from the analysis of the blue-sideband Rabi oscillation are plotted. The dashed lines are numerically calculated results for each Fock state.