Entanglement of trapped-ion clock states (5 pages)

Xiaolong Deng

Rowan Brad Quni-Gudzinas

We propose a trapped-ion experiment to test the Sufficient Condition Theorem: that diagonal clock-rest coupling in the clock eigenbasis produces exact ultrametric conditional state overlaps (UVR = 0%), while nondiagonal coupling produces a universal ~32% violation rate. The experiment uses a single trapped ion with internal electronic states as the clock and motional Fock states as the rest system. Laser-driven carrier and sideband transitions provide tunable diagonal/nondiagonal coupling. Conditional state tomography at multiple clock readings yields the overlap matrix, whose Parisi ultrametricity violation rate is the observable. All required capabilities are established with current trapped-ion technology. Estimated timeline: 8 weeks on an existing apparatus. If confirmed, this experiment verifies the physical foundations of the Bridge Theorem connecting Page-Wootters conditional states to Bruhat-Tits buildings, with implications for CMB phenomenology and p-adic holography.

P. C. Haljan, P. J. Lee, Kathy-Anne Brickman +3 more

A M\o{}lmer-S\o{}rensen entangling gate is realized for pairs of trapped $^{111}\mathrm{Cd}^{+}$ ions using magnetic-field insensitive ``clock'' states and an implementation offering reduced sensitivity to optical phase drifts. The gate is used to generate the complete set of four entangled states, which are reconstructed and evaluated with quantum-state tomography. An average target-state fidelity of 0.79 is achieved, limited by available laser power and technical noise. The tomographic reconstruction of entangled states demonstrates universal quantum control of two ion qubits, which through multiplexing can provide a route to scalable architectures for trapped-ion quantum computing.

Dietrich G. Leibfried

Christoph Becher, Jan Benhelm, D. Chek-al-kar +16 more

David J. Wineland, Jonas Bergquist, Till Rosenband +5 more

Techniques developed for quantum-information processing using trapped ions may be useful in future atomic clocks. Here, we summarize experiments at NIST that (1) use quantum gates to entangle ions and thereby improve the measurement signal-to-noise ratio in spectroscopy and (2) implement sympathetic cooling and quantum state transfer techniques, which might be used to increase the number of choices of ions used for clocks.