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arXiv:1110.4593 · Physical Review A

Possibility of magic trapping of a three-level system for Rydberg blockade implementation

Muir J. Morrison, Andrei Derevianko

Published Mar 12, 2012• 5 citations
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Abstract

The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of magic optical traps. We analyze magic trapping of a prototype three-level system: a Rydberg state along with two qubit states: hyperfine states attached to a $J=1/2$ ground state. Our numerical results show that, while such a magic trap for alkali metals would require prohibitively large magnetic fields, the group IIIB metals such as Al are suitable candidates.

DOI
10.1103/physreva.85.033414

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The Rydberg blockade mechanism has shown noteworthy promise for scalable quantum computation with neutral atoms. Both qubit states and gate-mediating Rydberg state belong to the same optically trapped atom. The trapping fields, while being essential, induce detrimental decoherence. Here we theoretically demonstrate that this Stark-induced decoherence may be completely removed using powerful concepts of magic optical traps. We analyze magic trapping of a prototype three-level system: a Rydberg state along with two qubit states: hyperfine states attached to a J=1/2J=1/2J=1/2 ground state. Our numerical results show that, while such a magic trap for alkali metals would require prohibitively large magnetic fields, the group IIIB metals such as Al are suitable candidates.
Rydberg interactions of trapped alkali-metal atoms are used widely to facilitate quantum gate operations in quantum processors and repeaters. In most laboratory realizations using this protocol, the Rydberg states are repelled by the trapping laser fields, requiring that the fields be turned off during gate operations. Here we create a quasi-two-level system in a regime of Rydberg excitation blockade for a mesoscopic Rb ensemble of several hundred atoms confined in a magic-wavelength optical lattice. We observe many-body Rabi oscillations between the ground and collective Rydberg state. In addition we use Ramsey interference techniques to obtain the light shifts of both the lower and upper states of the collective qubit. Whereas the coupling producing the Rabi oscillations is enhanced by a factor of sqrt[N], there is no corresponding enhancement for the light shifts. We derive an effective two-level model which is in good agreement with our observations. Trapped Rydberg qubits and an effective two-level description are expected to have broad applicability for studies of quantum simulation and networking using collective encoding in ensembles of neutral atoms.
Abstract We predict the possibility of ‘triply magic’ optical lattice trapping of neutral divalent atoms. In such a lattice, the 1 ⁢ S 0 and 3 P 0 clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation out of the motional ground state as a result of the excitations between the clock and the Rydberg states. We also calculate trapping laser-induced photoionization rates of divalent Rydberg atoms at magic frequencies. We find that such rates are below the radiative spontaneous-emission rates, due to the presence of Cooper minima in photoionization cross-sections.
Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias BBB field along a circularly polarized trapping laser field. We map out these BBB fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.
Abstract Long ground-Rydberg coherence lifetime is interesting for implementing high-fidelity quantum logic gates, many-body physics, and other quantum information protocols. However, the potential formed by a conventional far-off-resonance red-detuned optical-dipole trap (ODT) is usually repulsive for Rydberg atoms, which will result in fast atom loss and low repetition rate of the experimental sequence. These issues can be addressed by a magic ODT. We performed the calculation of ODT’s magic detuning for confinement of ground-state and Rydberg-state cesium atoms with the same potential well. We used a sum-over-states method to calculate the dynamic polarizabilities of 6S 1/2 ground state and highly-excited ( n S 1/2 and n P 3/2 ) Rydberg state of cesium atoms, and identify corresponding magic detuning for optical wavelengths in the range of 850–1950 nm. We estimated the trapping lifetime of cesium Rydberg atoms confined in the magic ODT by including different dissipative mechanisms. Furthermore, we have experimentally realized an 1879.43 nm single-frequency laser system with a watt-level output power for setting up the magic ODT for 6S 1/2 ground-state and 84P 3/2 Rydberg-state cesium cold atoms.
We propose blue-detuned optical traps that are suitable for trapping of both ground-state and Rydberg excited atoms. The addition of a background compensation field or a suitable choice of the trap geometry provides a magic trapping condition for ground-state and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200-kHz differential trap shift between Cs ground states and 125s125s125s Rydberg states for 10 $\ensuremath{\mu}\mathrm{K}$ Cs atoms are presented. Consideration of the trapping potential and photoionization rates suggests that these traps will be useful for quantum-information experiments with atomic qubits.