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.
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.
Laser cooling and trapping of neutral atoms is of great significance for studying the physical and chemical properties of atoms. To further realize the spatial localization of atoms, optical dipole trap (ODT) was proposed to manipulate individual atoms, ions or molecules and has become an increasingly important technique in the field of cold atomic physics and quantum optics. To eliminate the differential light shift of transitions between atomic states, ODT can be turned off during excitation/radiation. However, it will shorten the trap lifetime of the atom and reduce the repetition rate of the single photon. The AC stark shift can be eliminated experimentally by constructing blue-detuned dark ODT, but the micron-level dark ODT usually requires more complex experimental equipment and is not easy to operate. Therefore, magic-wavelength ODT was constructed to realize that the transition frequency of photons between atomic states is the same as in free space. When the trapping laser makes the differential light shift of the transition between the two atomic states zero, the laser wavelength is called the magic wavelength. The magic-wavelength ODT can eliminate the differential light shift of the transition between atoms, improve the repetition rate of the experimental sequence and weaken the atomic decoherence. In recent years, it has become a powerful tool for manipulating cold atoms, especially for coherently manipulating the atomic inner states. In the present work, with the theory of multi-level model, we calculate the dynamic electric polarizability of the 6S1/2 ground state and the 6P3/2 excited state connecting the D2 line of cesium atom in a range of 800–1000 nm, and obtain the magic wavelength of the optical trapping laser to trap the ground state and the excited state. Since the polarizability of atomic states with angular momentum greater than 0.5 is very sensitive to the polarization angle, the polarization-angle-dependent magic wavelength and the corresponding magic polarizability are analyzed by taking the linearly-polarized trapping laser for example. The magic polarization angle is 54.7° and the magic wavelength at this angle are 886.4315 and 934.0641 nm, respectively. The robustness of the magic conditions and the feasibility of the experimental operation are further analyzed.
The existence of an anisotropic tensor part of atomic states with an angular momentum greater than 1/2 causes their dynamic polarizabilities to be very sensitive to the polarization direction of the laser field. Therefore, the magic wavelength of the transition between two atomic states also depends on the polarization angle between the quantized axis and the polarization vector. We perform a calculation of the magic conditions of the 6S1/2↔nP3/2 (n = 50–90) Rydberg transition of cesium atoms by introducing an auxiliary electric diople transition connected to the target Rydberg state and a low-excited state. The magic condition is determined by the intersection of dynamic polarizabilities of the 6S1/2 ground state and the nP3/2 Rydberg state. The dynamic polarizability is calculated by using the sum-over-states method. Furthermore, we analyze the dependence of magic detuning on the polarization angle for a linearly polarized trapping laser and establish the relationship between magic detuning and a principal quantum number of the Rydberg state at the magic angle. The magic optical dipole trap can confine the ground-state and Rydberg-state atoms simultaneously, and the differential light shift in the 6S1/2↔nP3/2 transition can be canceled under the magic condition. It is of great significance for the application of long-lifetime high-repetition-rate accurate manipulation of Rydberg atoms on high-fidelity entanglement and quantum logic gate operation.
For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.
Optical dipole traps (ODT) with far-off-resonance laser are important tools in more and more present cold-atom experiments, which allow confinement of laser-cooled atoms with a long storage time. Particularly, the magic wavelength ODT can cancel the position-dependent spatially inhomogeneous light shift of desired atomic transition, which is introduced by the ODT laser beam. Now it plays an important role in the state-insensitive quantum engineering and the atomic optical clock. To verify the magic wavelength or the magic wavelength combination for D2 line transition of cesium (Cs) and rubidium (Rb) atoms, we calculated and analyzed the light shift of the 133Cs 6S1/2 - 6P3/2 transition for a monochromatic ODT, and also the 87Rb 5S1/2 - 5P3/2 transition for a dichromatic ODT with a laser frequency ratio of 2:1. Also a dichromatic magic-wavelength ODT laser system for 87Rb atoms is proposed and experimentally realized by employing the quasi-phase-matched frequency doubling technique with telecom laser and fiber amplifier.
Dynamic polarizabilities of cesium Rydberg states, explicitly
nS1/2,nP1/2,nP3/2,nD3/2, and
nD5/2, where the principal quantum number
n is 40--70, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-state approach. We identify double magic wavelengths in the range of
1000−−2000 nm for simultaneous trapping of the ground state and a Rydberg state, which are red detuned and blue detuned, respectively, with respect to a low-lying excited auxiliary state. Based on calculations of the radiative lifetime, blackbody-radiation-induced transitions, and population transfer out of the Rydberg and auxiliary states (estimated within two-state and master-equation models), we conclude that magic wavelength trapping is particularly promising experimentally for the
nDJ,∣MJ∣ Rydberg series with angular momentum
J=3/2 and projection quantum numbers ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2$ (auxiliary state
8P1/2) and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}3/2$ (auxiliary state
8P3/2), using trap depths as large as $10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{K}$. Moreover, by tuning the angle between the quantization axis and the polarization vector of the light, we identify triple and quadruple magic wavelengths, for which the polarizabilities of the ground state, a Rydberg state, and, respectively, one and two low-lying excited states are equal. Our comprehensive theoretical study provides much needed guidance for ongoing experimental efforts on cesium Rydberg-state-based quantum simulations that operate on timescales up to several microseconds.