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Journal of Experimental and Theoretical Physics

Implementation of Single-Qubit Quantum Gates Based on a Microwave Transition in a Single Rubidium Atom in an Optical Dipole Trap

Ilya I. Beterov, Elena A. Yakshina, Denis B. Tretyakov, Vasily M. Entin, N. V. Al’yanova, K. Yu. Mityanin, I. I. Ryabtsev

Published Mar 1, 2021• 5 citations
Publisher

Abstract

Abstract The results of experiments on the implementation of single-qubit quantum gates with a single 87Rb atom in an optical dipole trap with a wavelength of 850 nm are presented. The trap is formed by a long focal-length objective lens located outside the vacuum chamber of a magneto-optical trap. An atom is detected using a resonance fluorescence signal with an sCMOS video camera. The experiments involved the trapping and confinement of a single atom at times up to 50 s, optical pumping by polarized laser radiation, microwave transitions between two hyperfine sublevels of the ground state, and the measurement of the quantum state of the atom by pushing it from the trap. Rabi oscillations are observed during the “clock” microwave transition 5S1/2(F = 2, MF = 0) → 5S1/2(F = 1, MF = 0) between two operating qubit levels at a frequency of up to 4.2 kHz, a contrast of up to 95%, and a coherence time of up to 3 ms. These oscillations correspond to the implementation of two basic single-qubit quantum operations (Hadamard gate, NOT gate) from various initial qubit states with an average fidelity of 95.2 ± 3%.

DOI
10.1134/s1063776121030134

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Abstract The results of experiments on the implementation of single-qubit quantum gates with a single 87Rb atom in an optical dipole trap with a wavelength of 850 nm are presented. The trap is formed by a long focal-length objective lens located outside the vacuum chamber of a magneto-optical trap. An atom is detected using a resonance fluorescence signal with an sCMOS video camera. The experiments involved the trapping and confinement of a single atom at times up to 50 s, optical pumping by polarized laser radiation, microwave transitions between two hyperfine sublevels of the ground state, and the measurement of the quantum state of the atom by pushing it from the trap. Rabi oscillations are observed during the “clock” microwave transition 5S1/2(F = 2, MF = 0) → 5S1/2(F = 1, MF = 0) between two operating qubit levels at a frequency of up to 4.2 kHz, a contrast of up to 95%, and a coherence time of up to 3 ms. These oscillations correspond to the implementation of two basic single-qubit quantum operations (Hadamard gate, NOT gate) from various initial qubit states with an average fidelity of 95.2 ± 3%.
Abstract We report the results of experiments on implementing individually addressable one-qubit quantum gates on a microwave transition with two 87Rb atoms in two optical dipole traps. Addressing is carried out using additional focused laser light, which results in a differential light shift of the microwave transition frequency. In the absence of addressing in each of the atoms, Rabi oscillations are obtained on the microwave clock transition 5S1/2 (F = 2, mF = 0) → 5S1/2(F = 1, mF = 0) between two working levels of qubits with a frequency of up to 5.1 kHz, a contrast up to 98 %, and a coherence time up to 4 ms. When addressing is turned on, the probability of a microwave transition in the addressed atom is suppressed to an average value of less than 5 %. The Rabi oscillations remaining in the other atom have the same contrast and correspond to the implementation of individually addressable basic one-qubit quantum operations (Hadamard gate and NOT gate) from different initial states of a qubit with an average fidelity of 92% ± 3 %. After renormalising this fidelity to the error in the preparation and measurement of quantum states of qubits, an estimate of 97% ± 3% is obtained for the fidelity of individual qubit rotations.
Abstract Single alkali-metal atoms in arrays of optical dipole traps represent a quantum register that can be used for quantum computation and simulation based on short-term Rydberg excitations, which switch the interactions between qubits. To load single atoms into optical dipole traps and then detect them by resonance fluorescence, lenses with a large numerical aperture (NA > 0.5) inside a vacuum chamber and expensive EMCCD cameras are commonly used. We present our recent experimental results on demonstrating the trapping of single 87Rb atoms using a long-focus objective lens with a low numerical aperture (NA = 0.172) placed outside the vacuum chamber, and detecting single atoms with a low-cost sCMOS camera. We also present our current results on implementing a single-qubit gate based on optical pumping and subsequent microwave transition between two hyperfine sublevels of a single 87Rb atom with fidelity near 95%.
Qubits encoded in the electronic states of single atoms trapped in arrays of optical tweezers are a promising platform for a universal quantum computer. These qubits can be prepared in a well-defined quantum state, coherently manipulated using a nearresonant driving field, and their state detected with high fidelity. The most promising aspect of this platform is the large scalability, with arrays of up to 6100 qubits demonstrated[62].We present our progress in developing such a system with an array of single 85Rbatoms. We provide an overview of the experimental setup constructed for this purpose. Typically 50 atoms are loaded from a MOT into a 10×10 array of optical tweezers with sub-micrometer waists, with only a single atom present in a tweezer. The occupation of the tweezers is determined using a fluorescence image. We provide a characterisation of the trapping potentials experienced by the atoms. This characterisation is performed by measuring properties of the atoms in the tweezers, allowing for an in situ characterisation. In particular, the trap depth and trap frequencies were characterised. The temperature of the atoms after the initial fluorescence image was determined using the release and recapture technique [101] and the trapping lifetime of the atom was measured. With the ability to prepare, manipulate, and read out the electronic state of the atoms, an array of hyperfine qubits has been created. The qubits are encoded in the hyperfine clock states as |0⟩ := 52S1/2 |F = 2,mF = 0⟩ and |1⟩ := 52S1/2 |F = 3,mF = 0⟩. These long-lived first-order Zeeman shift insensitive states exhibit good coherence times, which we have characterized as T1=205 ± 3 ms , T2* = 2.01 ± 0.02 ms, andT2 echo = 67.1 ± 0.1 ms. State preparation is achieved by repetitions of optical and microwave pulses, to which the |0⟩ state is dark, allowing for population to accumulate in this state. The coherent evolution of the qubits have been performed using 3.035 GHz microwave radiation. The antenna used to produce this radiation is a home-built fullwave loop antenna. The antenna has allowed for addressing the qubits with Rabi frequencies up to Ω/2π ≈ 160 kHz. We have implemented the single-qubit Clifford gates using the global microwave drive. We determine using randomized benchmarking an166 Summary average gate fidelity of 0.99949(3), limited by Rabi frequency inhomogeneity over the array. To combat this fidelity limitation, we repeated the randomized benchmarking using the pulse length error robust SCROFULOUS pulses [135], which resulted in an increased gate fidelity of 0.999653(5). As a further extension of the capabilities of the system, we demonstrated a preliminary implementation of addressing a single atom int he array by applying a local Rz rotation to the selected qubit using a Stark shifting laser. The high level of control of the microwave radiation has allowed for an experimental verification of control noise-fidelity relations proposed by [115]. We have found good agreement between the experimentally measured fidelities and the proposed analytical relations developed using the stochastic Schrödinger equation. As a preliminary step towards implementing a two-qubit gate, we have performed coherent excitation of the |1⟩ state to the |r ⟩ :=602S1/2 |mJ = −1/2> Rydberg state using an off-resonant two-photon excitation. The low contrast of the Rabi oscillations on the |1⟩↔|r ⟩ transition was investigated using a simple Lindblad master equation based model. The largest contributors to the reduced contrast is SPAM error, intermediate state scattering and laser phase noise. Since Rydberg atoms interact via the van der Waals interaction, the spacing between atoms must be deterministically controlled. For this purpose, we have used an additional optical tweezer which can be dynamically moved using an acousto-optic deflector to rearrange the stochastically filled array into a desired configuration. By placing 2 atoms a distance ≈ 5 μm apart, we have demonstrated the p2 enhancement of the Rabi oscillation on the |1⟩↔|r ⟩ transition, a required first step towards implementing an entangling gate between the hyperfine qubits. To extend the temperature-limited T2* coherence time, we have implemented Λ-enhanced gray molasses cooling. We have opted to perform this cooling on the D2line as it is experimentally convenient to use this transition. Because using this transition for this purpose has not been reported in this isotope of Rb, we studied the efficacy of this cooling scheme under these circumstances. The reduced excited state hyperfine splitting of 85Rb compared to 87Rb has allowed for the study of the efficacy of this technique in the presence of additional transitions that may inhibit the cooling performance. Despite the challenges of the smaller hyperfine splitting, we have cooled the atoms to4.0±0.2 μK. This additional cooling is partially negated by the heating from the qubit state preparation procedure, but the additional cooling has allowed for the average T2*to be extended from ⟨T2*⟩ = 3.4 ± 0.1 ms to ⟨T2*⟩ = 5.3 ± 0.2 ms.
Abstract The trapping of single atoms in optical dipole traps is widely used in experiments on the implementation of quantum processors based on neutral atoms, and studying interatomic interactions. Typically, such experiments employ lenses with a large numerical aperture (NA > 0.5), highly sensitive EMCCD cameras, or photon counters. In this work, we demonstrate trapping and detection of single rubidium atoms using a long-focus objective lens with a numerical aperture NA = 0.172 and a FLir Tau CNV sCMOS camera.
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.
Based on single Cesium atoms trapped in a 1064 nm microscopic optical trap we have exhibited a single qubit encoded in the Cesium “clock states”. The single qubit initialization, detection and the fast state rotation with high efficiencies are demonstrated and this state manipulation is crucial for quantum information processing. The ground states Rabi flopping rate of 229.0 ± 0.6 kHz is realized by a two-photon Raman process. A clock states dephasing time of 3.0±0.7 ms is measured, while an irreversible homogeneous dephasing time of 124±17 ms is achieved by using the spin-echo technique. This well-controlled single atom provides an idea quantum qubit and quantum node for quantum information processing.