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Journal of Modern Optics

Tightly trapped highly excited Rydberg atom in dipole–quadrupole potential landscape

Leila Mashhadi

Published Sep 5, 2019• 3 citations
Publisher

Abstract

In this paper, coherent Rydberg excitation of a single four-level atom in tightly confining trap so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT) by considering Laguerre Gaussian (LG) beams spatial features is demonstrated. The self-trapping potential results from the position dependent differential AC Stark shift of the ground state and Rydberg state in the effective quadrupole Rydberg excitation. By introducing the effective stiffness of the FORDQT potential in terms of the key parameters of the first and Rydberg excitation laser beams, a technique to obtain sub-micron localization of Rydberg excitation is explored. The complete matched trapping potential of the ground state and Rydberg state near the center of the trap maintains the coherence of the Rydberg excitation. Transfer of optical orbital angular momentum from the LG-beam to the Rydberg-state via localized effective quadrupole excitation process paves the way for implementation of high fidelity qudit gates in high dimensional quantum information process.

DOI
10.1080/09500340.2019.1660814

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In this paper, coherent Rydberg excitation of a single four-level atom in tightly confining trap so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT) by considering Laguerre Gaussian (LG) beams spatial features is demonstrated. The self-trapping potential results from the position dependent differential AC Stark shift of the ground state and Rydberg state in the effective quadrupole Rydberg excitation. By introducing the effective stiffness of the FORDQT potential in terms of the key parameters of the first and Rydberg excitation laser beams, a technique to obtain sub-micron localization of Rydberg excitation is explored. The complete matched trapping potential of the ground state and Rydberg state near the center of the trap maintains the coherence of the Rydberg excitation. Transfer of optical orbital angular momentum from the LG-beam to the Rydberg-state via localized effective quadrupole excitation process paves the way for implementation of high fidelity qudit gates in high dimensional quantum information process.
Sufficient control over the excitation of the Rydberg atom as a quantum memory is crucial for the fast and deterministic preparation and manipulation of the quantum information. Considering the Laguerre-Gaussian (LG) beam spatial features, localized excitation of a four-level atom to a highly excited Rydberg state is presented. The position-dependent AC-Stark shift of the first and Rydberg state in the effective quadrupole two-level description of a far-detuned three-photon Rydberg excitation results in a steep trapping potential for Rydberg state. The transfer of optical orbital angular momentum from LG beam to the Rydberg state via quadrupole transition in the last Rydberg excitation process offers a long-lived and controllable qudit quantum memory. The effective quadrupole Rabi frequency is presented as a function of ratio of the first to Rydberg excitation laser beam waist and the center of mass position inside the trap. It depicts high accuracy of detecting Rydberg atom at the center of the trap, which can pave the way for implementation of high-fidelity qudit gate.
Abstract Optical vortices are currently one of the most intensively studied topics in light–matter interaction. In this work, a three-step axial Doppler- and recoil-free Gaussian–Gaussian-Laguerre–Gaussian (GGLG) excitation of a localized atom to the highly excited Rydberg state is presented. By assuming a large detuning for intermediate states, an effective quadrupole excitation related to the Laguerre–Gaussian (LG) excitation to the highly excited Rydberg state is obtained. This special excitation system radially confines the single highly excited Rydberg atom independently of the trapping system into a sharp potential landscape into the so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT). The key parameters of the Rydberg excitation to the highly excited state, namely the effective Rabi frequency and the effective detuning including a position-dependent AC Stark shift, are calculated in terms of the basic parameters of the LG beam and of the polarization of the excitation lasers. It is shown that the obtained parameters can be tuned to have a precise excitation of a single atom to the desired Rydberg state as well. The features of transferring the optical orbital and spin angular momentum of the polarized LG beam to the atom via quadrupole Rydberg excitation offer a long-lived and controllable qudit quantum memory. In addition, in contrast to the Gaussian laser beam, the doughnut-shaped LG beam makes it possible to use a high intensity laser beam to increase the signal-to-noise ratio in quadrupole excitation with minimized perturbations coming from stray light broadening in the last Rydberg excitation process.
This article investigates the quadrupole excitation of a trapped atom exposed to the tightly focused Laguerre-Gaussian (LG) beams with parallel and antiparallel spin angular momentum (SAM) and orbital angular momentum (OAM) under nonparaxial conditions. The Rabi frequency profile of allowed quadrupole transition channels, modified by SAM and OAM interaction, in the focal plane is provided. In the case of antiparallel SAM and OAM, the excitation probability undergoes substantial modification due to the considerable contribution of longitudinal intensity variations in tightly focused condition. The findings offer insights into controlling localized atom transition, including OAM transfer, with potential applications in qudit-based technologies.
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.
Precise individual addressing of single atoms in quantum registers formed by optical trap arrays is essential to achieve high-fidelity quantum gates in neutral-atom quantum computers and simulators. Two-qubit quantum gates are typically implemented using coherent two-photon laser excitation of atoms to strongly interacting Rydberg states. However, two-photon excitation encounters challenges in individual addressing with tightly focused laser beams due to atom position uncertainty and the spatial inhomogeneity in both Rabi frequencies and light shifts. In this work, we theoretically demonstrate that the fidelity of individual addressing is significantly enhanced by employing coherent three-photon laser excitation of Rydberg states. For a specific example of $5{s}_{1/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{1}}{\ensuremath{\rightarrow}}5{p}_{3/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{2}}{\ensuremath{\rightarrow}}7{s}_{1/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{3}}{\ensuremath{\rightarrow}}np$ excitation in 87Rb^{87}\mathrm{Rb}87Rb atoms, we find that upon strong laser coupling in the second step (Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{2}$) and moderate coupling in the first and third steps (Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{3}$), the three-photon Rabi frequency is given by $\mathrm{\ensuremath{\Omega}}={\mathrm{\ensuremath{\Omega}}}_{1}{\mathrm{\ensuremath{\Omega}}}_{3}/{\mathrm{\ensuremath{\Omega}}}_{2}$. If the spatial distributions of $({\mathrm{\ensuremath{\Omega}}}_{1}{\mathrm{\ensuremath{\Omega}}}_{3})$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$ are arranged to be identical, $\mathrm{\ensuremath{\Omega}}$ becomes independent of atom position, even within very tightly focused laser beams. This approach dramatically improves individual addressing of Rydberg excitation for neighboring atoms in trap arrays compared to conventional two-photon excitation schemes. Our findings are crucial for large-scale quantum registers of neutral atoms, where distances between adjacent atoms should be minimized to ensure stronger Rydberg interactions and compact arrangement of atom arrays.
Abstract Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.