A High Motional Frequency Ion Trapping Regime for Quantum Information Science

Abstract

We investigate high frequency motional states of trapped atomic ions. Trapped ions in rf traps are confined by an approximate harmonic potential and exhibit quantum motional states that mediate essential techniques in quantum computing, simulation, networking, and precision measurement. However, motional state decoherence mechanisms, heating and dephasing, are broadly limiting: reduced two-qubit gate fidelities; lower fidelity and lifetime of highly nonclassical bosonic states; long laser cooling times; and large recoil heating rates. These also challenge the scalability of increasingly sophisticated protocols. We propose high motional frequency ion trapping as an operating regime that addresses these challenges and reshapes the design landscape for quantum information experiments and quantum control techniques. We report an experimentally motivated investigation of realizing this high-frequency regime and discuss the consequences for laser cooling, motional state coherence, fidelity and lifetime of nonclassical bosonic states, and scalability of experimental runtimes. We report clear design trajectories for ion traps to reach high motional frequency, a new limiting mechanism for laser cooling at these high frequencies, and more than an order-of-magnitude speedup in experimental duty cycles with larger speed ups possible for quantum error correction protocols. Taken together, high motional frequency ion trapping has broad implications for the future of quantum information experiments.

Figures (7)

• Figure 1: The effect of trap design parameters on confinement frequency $\nu$. The top row of panels are schematic cross-sections of a 4-rod rf trap with labeled experimental variables on each panel representing possible design variations. (a) Reduced ion mass to increase $Q/m$. (b) Reduced ion-electrode distance $r_0$. (c) Increased $V_0$ or $\Omega_{\text{rf}}$. (d) Estimates of the radial confinement frequency $\nu$ for different mass ions, across a range of ion-electrode distances $r_0$ and rf voltage amplitudes $V_0$. Micromotion amplitude is fixed to $q = 0.4$ and contours label the secular frequency $\nu$ at specific values. We assume an in-phase rf drive on one diagonal electrode pair (shown) and an out-of-phase rf drive on the other pair (not shown).
• Figure 2: Summary schematic of the design flow for experimentally realizing a high motional frequency ion trap. Starting with the selection of the target micromotion amplitude $q$ and motional frequency $\nu$, $\Omega_{\text{rf}}$ is then fixed by Eq. \ref{['eq:sec-freq-omega-rf']}. The remaining experimental design choices, in orange, $V_0$, $r_0$, and $Q/m$ are balanced against each other to meet hardware constraints and practical considerations. Leading experimental design considerations are listed by each variable.
• Figure 3: Comparison of Doppler cooling rates and limits between the resolved and unresolved sideband regimes. Considered ratios are $\nu/\Gamma = 0.1$ (a) and $\nu/\Gamma=2.5$ (b) with the same Lamb-Dicke parameter $\eta=0.1$ and initial thermal state $\bar{n}_0=10$. (a) Unresolved regime with atomic linewidth on left and cooling dynamics on the right. (b) Resolved regime with, on the left, the atomic linewidth showing the now spectrally resolved sidebands and, on the right, the cooling dynamics. The resolved regime cools $\sim$10 times faster and to $\sim$100 times lower steady state $\bar{n}$. (c) Contributions to the mean occupation steady state $\bar{n}_s$ in the resolved Doppler regime by spontaneous emission and anomalous heating [see Eq. \ref{['eq:steady-state-nbar']}].
• Figure 4: Cooling and heating processes effecting $\bar{n}$ under laser cooling and anomalous heating. Operator $A_+$ increases motional occupation while $A_-$ decreases it under the absorption and emission of photons. Anomalous heating, in red, increases motional occupation at a rate $\dot{\bar{n}}_{\text{an}}$. The combined picture of atom-photon processes and ambient noise affecting the motional state changes the commonly derived steady-state mean occupation $\bar{n}_s$ [Eq. \ref{['eq:steady-state-nbar']}] to become a more encompassing model.
• Figure 5: Reduction of primary decoherence mechanisms of trapped-ion quantum motional states for increasing $\nu$. (a) Schematic of decoherence mechanisms for trapped-ion motional states: anomalous heating and dephasing from noisy electric fields and photon recoil heating. (b) Wigner function of the nonclassical "cat" state $|i\alpha\rangle + |-i\alpha\rangle$ for $\alpha = 3$ where $|\alpha\rangle = e^{-|\alpha|^2/2}\sum_{n=0}^{\infty}(\alpha^n/\sqrt{n!})|n\rangle$. (c) Preparation fidelity of the $\alpha=3$ cat state assuming a 10 s$^{-1}$ dephasing rate, 100 $s^{-1}$ heating rate, and thermal spread of the initial motional state $\bar{n} = 0.1$ for a $\nu = 2\pi\times 1$ MHz trap. Each error term reduces for increased $\nu$ as described in the text. (d) The probability of exciting the motional ground state $|n=0\rangle$ due to recoil heating. For $\nu = 2\pi\times 2$ MHz, the probability is 85% and reduces to 25% for $\nu = 2\pi\times 30$ MHz.