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Localized Excitation of Single Atom to a Rydberg State with Structured Laser Beam for Quantum Information

Leila Mashhadi, Gholamreza Shayeganrad

Published Apr 10, 2019• 1 citation
Publisher

Abstract

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.

DOI
10.5772/intechopen.82319

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Three-photon Gaussian–Gaussian–Laguerre–Gaussian excitation of a localized atom to a highly excited Rydberg state

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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.

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Ultrafast Quantum Random Access Memory Utilizing Single Rydberg Atoms in a Bose-Einstein Condensate

Kelly R. Patton, Uwe R. Fischer

We propose a long-lived and rapidly accessible quantum memory unit, for which the operational Hilbert space is spanned by states involving the two macroscopically occupied hyperfine levels of a miscible binary atomic Bose-Einstein condensate and the Rydberg state of a single atom. It is shown that an arbitrary qubit state, initially prepared using a flux qubit, can be rapidly transferred to and from the trapped atomic ensemble in approximately 10 ns and with a large fidelity of 97%, via an effective two-photon process using an external laser for the transition to the Rydberg level. The achievable ultrafast transfer of quantum information therefore enables a large number of storage and retrieval cycles from the highly controllable quantum optics setup of a dilute ultracold gas, even within the typically very short flux qubit lifetimes of the order of microseconds.

arXiv:1307.0963•Physical Review Letters•Dec 12, 2013•34 citations
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.
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.
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.
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.
In an experiment on three-photon laser excitation 5S 1/2 → 5P 3/2 → 6S 1/2 → 37P 3/2 of a single 87 Rb, Rydberg atom in an optical dipole trap, we have observed for the first time three-photon Rabi oscillations between the ground and the Rydberg states. A single atom was detected optically by resonance fluorescence signal using a low-noise sCMOS video camera. The relative probability for the atom to remain in the trap after the action of three synchronized exciting laser pulses with durations varying from 100 ns to 2 µs was measured. A distinctive feature of the experiment was the use of intense laser radiation with a wavelength of 1367 nm at the second excitation step, providing a single-photon Rabi frequency up to 2 GHz to control the effective detunings of intermediate levels of the three- photon transition due to the dynamic Stark effect. Rabi oscillations with frequencies from 1 to 5 MHz were registered depending on the intensity of laser pulses of the first and second excitation steps with coherence time 0.7–0.8 µs. Ways to increase the coherence time and contrast of three-photon Rabi oscillations for applications in quantum information with Rydberg atoms are discussed.
With the advent of laser cooling and trapping, neutral atoms have become a foundational source of accuracy for applications in metrology and are showing great potential for their use as qubits in quantum information. In metrology, neutral atoms provide the most accurate references for the measurement of time and acceleration. The unsurpassed stability provided by these systems make neutral atoms an attractive avenue to explore applications in quantum information and computing. However, to fully investigate the field of quantum information, we require a method to generate entangling interactions between neutral-atom qubits. Recent progress in the use of highly-excited Rydberg states for strong dipolar interactions has shown great promise for controlled entanglement using the Rydberg blockade phenomenon. I report the use of singly-trapped cesium atoms as qubits for applications in metrology and quantum information. Each atom provides a physical basis for a single qubit by encoding the required information into the ground-state hyperfine structure of cesium. Through the manipulation of these qubits with microwave and optical frequency sources, we demonstrate the capacity for arbitrary single-qubit control by driving qubit rotations in three orthogonal directions on the Bloch sphere. With this control, we develop an atom interferometer that far surpasses the force sensitivity of other approaches by applying the well-established technique of light-pulsed atom-matterwave interferometry to single atoms. Following this, we focus on two-qubit interactions using highly-excited Rydberg states. Through the development of a unique single-photon approach to Rydberg excitation using an ultraviolet laser at 319 nm, we observe the Rydberg blockade interaction between atoms separated by 6.6(3) microns. Motivated by the observation of Rydberg blockade, we study the application of Rydberg-dressed states for a quantum controlled-phase gate. Using a realistic simulation of the dressed-state dynamics, we calculate a controlled-phase gate fidelity of 94% that is primarily limited by Doppler frequency shifts. Finally, we employ our single-photon excitation laser to measure the Rydberg-dressed interaction, thus demonstrating the viability of this approach.
We propose a long-lived and rapidly accessible quantum memory unit, for which the operational Hilbert space is spanned by states involving the two macroscopically occupied hyperfine levels of a miscible binary atomic Bose-Einstein condensate and the Rydberg state of a single atom. It is shown that an arbitrary qubit state, initially prepared using a flux qubit, can be rapidly transferred to and from the trapped atomic ensemble in approximately 10 ns and with a large fidelity of 97%, via an effective two-photon process using an external laser for the transition to the Rydberg level. The achievable ultrafast transfer of quantum information therefore enables a large number of storage and retrieval cycles from the highly controllable quantum optics setup of a dilute ultracold gas, even within the typically very short flux qubit lifetimes of the order of microseconds.