Study of decoherence in radial local phonon hopping within trapped-ion string

Abstract

We systematically investigate local phonon hopping in the radial direction of a linear trapped-ion string. We measure the decay of hopping as a function of key trap parameters and analyze the results in terms of the decay time and the number of oscillations. We attribute the loss of coherence to nonlinear coupling between different modes. Despite quantitative differences, the overall trends in our numerical simulations are similar to those of the experimental results. This work establishes a method for evaluating phonon hopping coherence and provides insight into the underlying decoherence mechanisms.

Figures (5)

• Figure 1: Experimental time sequence for observing phonon hopping. SBC: sideband cooling; RSB/BSB: red/blue sideband; EMCCD: electron-multiplying charge-coupled device. The circled numbers correspond to the steps in the sequence outlined in the main text.
• Figure 2: Phonon-hopping results corresponding to case of the experimentally obtained maximum number of oscillations ($268.3 \pm 25.8$) in our experiment. The corresponding radial trap frequency $\omega_y/2\pi$ is 2.85 MHz and the inter-ion distance $d_0$ is 12.2 $\mu$m. The blue dots are the experimental measurements and the green curve is the result obtained from fitting the function $ae^{-bx}\sin (cx+d) +fx$. Each point in the experimental results is the average of 20 measurements, and the error bars represent the statistical uncertainty of the measured population arising from the finite number of experimental repetitions. (a) Full experimental data and numerical calculations for phonon hopping. (b-d) Magnified views of different time periods for phonon-hopping process.
• Figure 3: Phonon-hopping results corresponding to case of longest decay time in our experiment ($42.5 \pm 3.3~\mathrm{ms}$). The corresponding radial trap frequency $\omega_y/2\pi$ is 2.85 MHz and the inter-ion distance $d_0$ is 31.7 $\mu$m. The blue dots are the experimental measurements and the green curve is the result obtained from fitting the function $ae^{-bx}\sin (cx+d) +fx$. Each point in the experimental results is the average of 20 measurements, and the error bars represent the statistical uncertainty of the measured population arising from the finite number of experimental repetitions. (a) Full experimental data and numerical calculations for phonon hopping. (b-d) Magnified views of different time periods for phonon-hopping process.
• Figure 4: Experimental results for decay time (red circles with error bars) compared with numerical simulations based on the Kerr-only model (green triangles) and a combined Kerr and electric-potential noise model (black crosses). Numerically simulated results in the case of only electric-potential noise are also indicated by blue dashed curves (central value) and blue dotted curves (lower and upper bounds of the confidence interval). (a) Decay time against inter-ion distance $d_0 = \{12.2,\,15.9,\,19.4,\,31.7\}\,\mu\mathrm{m}$ with the radial trap frequency fixed at $\omega_y/2\pi = 2.85\,\mathrm{MHz}$. (b) Decay time against radial trap frequency $\omega_y/2\pi = \{2.43,\,2.64,\,2.85,\,3.11\}\,\mathrm{MHz}$ with the inter-ion distance fixed at $d_0 = 19.1\,\mu\mathrm{m}$.
• Figure 5: Experimental results for number of oscillations (red circles with error bars) compared with numerical simulations based on the Kerr-only model (green triangles) and a combined Kerr and electric-potential noise model (black crosses). Numerically simulated results in the case of only electric-potential noise are also indicated by blue dashed curves (central value) and blue dotted curves (lower and upper bounds of the confidence interval). (a) Number of oscillations against inter-ion distance $d_0 = \{12.2,\,15.9,\,19.4,\,31.7\}\,\mu\mathrm{m}$ with the radial trap frequency fixed at $\omega_y/2\pi = 2.85\,\mathrm{MHz}$. (b) Number of oscillations against radial trap frequency $\omega_y/2\pi = \{2.43,\,2.64,\,2.85,\,3.11\}\,\mathrm{MHz}$ with the inter-ion distance fixed at $d_0 = 19.1\,\mu\mathrm{m}$.