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Physical Review A

Long-lived coherence between ground and Rydberg levels in a magic-wavelength lattice

Jacob Lampen, Huy Minh Nguyen, Lin Li, P. R. Berman, A. Kuzmich

Published Sep 17, 2018• 43 citations
Publisher

Abstract

By confining atoms in a state-insensitive optical lattice, the lifetime of the ground-state--Rydberg coherence is increased to $\ensuremath{\ge}20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$, an order of magnitude improvement over previous experiments using freely diffusing atoms. Using these enhanced lifetimes, we measure the so-called magic lattice wavelengths for Rb and use them to extract the $6{p}_{3/2}\text{\ensuremath{-}}n{s}_{1/2}$ reduced electric dipole matrix elements. Good agreement is found with values obtained using an effective one-electron potential for principal quantum numbers $n$ between $n=30$ and $n=70$. We develop a theoretical model based on quantized motion to map out the ground-state--Rydberg coherence as a function of time that is in good agreement with the experimental results. The availability of long coherence times may present new opportunities for high-resolution spectroscopy and quantum information science.

DOI
10.1103/physreva.98.033411

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By confining atoms in a state-insensitive optical lattice, the lifetime of the ground-state--Rydberg coherence is increased to \ensuremath≥20\ensuremathμs\ensuremath{\ge}20\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}\ensuremath≥20\ensuremathμs, an order of magnitude improvement over previous experiments using freely diffusing atoms. Using these enhanced lifetimes, we measure the so-called magic lattice wavelengths for Rb and use them to extract the 6p3/2\ensuremath-ns1/26{p}_{3/2}\text{\ensuremath{-}}n{s}_{1/2}6p3/2​\ensuremath-ns1/2​ reduced electric dipole matrix elements. Good agreement is found with values obtained using an effective one-electron potential for principal quantum numbers nnn between n=30n=30n=30 and n=70n=70n=70. We develop a theoretical model based on quantized motion to map out the ground-state--Rydberg coherence as a function of time that is in good agreement with the experimental results. The availability of long coherence times may present new opportunities for high-resolution spectroscopy and quantum information science.
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.
Rydberg ensembles have many diverse and important applications for quantum information and quantum optics. For example, Rydberg ensembles can generate non-classical states of light which would be useful in a quantum network, and they could be used as qubits in a future quantum computer. For this reason, this thesis will present investigations of light-matter interactions in Rydberg ensembles. Non-classical states of light, such as single-photon states, are important for many quantum communication protocols. We have performed an experiment that demonstrates the generation of single-photon states from a Rydberg ensemble. We then studied the second-order correlations between this single-photon state of light and an incident coherent field. Under these conditions, we observed Hanbury Brown Twiss interference between the emission from a driven super-atom and a coherent field in the absence of stimulated emission. For a universal quantum computing architecture, coherence times must be much longer than gate operations. We observe ground-Rydberg coherence times in excess of 20 microseconds by using a "magic-wavelength" optical lattice to confine the atoms. Using this coherence time, we measured the differential nuclear-spin-dependent light shifts for principal quantum numbers, n, between n = 30 and n = 65, which is relevant for future high-fidelity Rydberg qubits in optical potentials. Also, we measured the hyperfine constant for atomic Rb to be 35.71 GHz with an uncertainty of 0.18 GHz.
A magic optical dipole trap (ODT) can confine atoms in the ground state and a highly excited state with the same light shifts, resulting in a long-range coherent lifetime between them, which plays an important role in high-fidelity quantum logic gates, multi-body physics and other quantum information. Here, we use a sum-over-states model to calculate the dynamic polarizabilities of the 6S1/2 ground state and 46S1/2 Rydberg state of Cs atoms and identify corresponding magic wavelengths and magic detunings for trapping the two states in the range of 900–1950 nm. Then, we analyze the robustness of the magic condition and the feasibility of the experimental operation. Furthermore, we estimate the trapping lifetime of Cs Rydberg atoms by considering different dissipation mechanisms, such as photon scattering and photoionization in the magic ODT. The photoexcitation and photoionization of Cs atoms under the action of three-step laser pulses are calculated by the rate equation. The presented results for magic-wavelength ODTs are of great significance for quantum information and quantum computing based on Rydberg atoms.
The short Doppler-limited coherence time of the laser-excited Rydberg state, usually orders of magnitude shorter than the lifetime of the Rydberg state, hinders the Rydberg-mediated quantum technologies. Here, we show that a 649~nm~−-−~658~nm two-photon excitation of the 6sng 1G46sng~^1G_46sng 1G4​ Rydberg state from a long-lived d-orbital clock state of barium can be achieved with a two-photon wavevector that is tiny, which effectively removes the Doppler-limited decoherence. Moreover, the 6sng 1G46sng~^1G_46sng 1G4​ Rydberg state has strong dipole-dipole interaction due to small Förster defect with nearby Rydberg states and possesses long radiative lifetime. These can benefit quantum computing based on individually trapped neutral atoms, and can enable long-lived Rydberg polaritons in atomic media, which brings fresh opportunities in all-optical quantum information.
We demonstrate magic wavelengths for the 6s 2S1/2−6p 2P3/2,1/26s ~ {^2}S_{1/2}-6p ~ {^2}P_{3/2,1/2}6s 2S1/2​−6p 2P3/2,1/2​ transitions in the Cs atom due to the circularly polarized light. In addition, we also obtain magic wavelengths using the linearly polarized light in order to verify the previously reported values and make a comparative study with the values obtained for the circularly polarized light. Most of these wavelengths are found to be in the optical region and could be of immense interest to the experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, 6p 2P1/26p ~{^2}P_{1/2}6p 2P1/2​ and 6p 2P3/26p ~{^2}P_{3/2}6p 2P3/2​ states. We use the available precise values of the electric dipole (E1) matrix elements for the most dominantly contributing transitions from the lifetime measurements of the above excited states and obtain other relevant important E1 matrix elements by employing a relativistic coupled-cluster method approximating at the singles and doubles level. Accuracies in these quantities are substantiated by comparing our evaluated scalar polarizability values with the corresponding experimental results.
We calculate the ionization lifetime of rubidium atoms trapped in an intense light field as a function of wavelength and principal quantum number n . The ionization lifetimes of ground state atoms range from essentially infinite to less than one second, for example in a 532 nm laser field with intensity 10 6 W cm −2 . The ionization lifetime of Rydberg states can be extremely short, e.g. the lifetime of the 35d state in a CO 2 laser field with intensity 10 5 W cm −2 and wavelength 10.6 μm is of order 100 ns. These results have important implications for achieving long coherence times, and for entanglement schemes based on Rydberg excitation in far-detuned optical lattices. In particular, fast photo-ionization could seriously compromise the possible realization of quantum gates based on Rydberg excitation of alkali atoms in a CO 2 laser lattice.