Hyperfine and optical barium ion qubits

A quantum computer, once implemented, is expected to have several applications with significant scientific and social utility due to its ability to execute specific algorithms with scaling laws quadratically or exponentially faster than any known classical algorithm that accomplishes the same task [1]. The fundamental unit of information in a quantum computer is the qubit, which is physically realized by any coherent quantum two-level system. At present, the best-developed qubit technology is provided by the hyperfine or optical levels of an elemental ion suspended in a radio frequency (rf) Paul trap [2]. That fact is in no small part thanks to decades of development of techniques in atomic physics to manipulate these profoundly quantum systems. Despite a long history in ion trapping [3–5], barium has never previously been demonstrated as an ionic qubit. Ba+ has several desirable characteristics for an ionic qubit. The odd isotope 137Ba+ is relatively abundant at 11%, which is sufficiently high that it can be trapped from a natural source without isotope-selective ionization [6,7]. Barium possesses a long-lived metastable state 5D5/2 (see Fig. 1), whose lifetime (35 s) is an order of magnitude greater than that of any other singly ionized alkali-earth-metal atom [8]. It is important for this state to be long lived since that decay rate restricts the qubit readout fidelity and sets a physical upper limit to optical qubit coherence times. Furthermore, the laser wavelengths for the 6S1/2 to 5D5/2 infrared “shelving” transition as well as barium’s visible-wavelength cooling transition are the longest of any ionic qubit candidate, which makes it favorable for remote photonic coupling through optical fiber. This property is essential for long distance entanglement between ionic qubits [9,10], since the postselection entanglement process is mediated by emitted photons. Current experiments are partly limited by attenuation of these photons in the optical fiber, an effect which is greatly reduced at longer wavelengths [11]. Here we report the trapping, state preparation, state rotation, and readout of two different 137Ba+ ionic qubits, one based on the narrow infrared optical transition at 1.76 μm and the other based on the ground-state hyperfine splitting. In the former case, sufficient coherence is observed in the quadrupole transition in a Doppler-cooled ion to drive about 10 Rabi rotations. Since the excited D5/2 state is disjoint from the laser cooling cycle, readout is effected by simply enabling the