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 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 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%.
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 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.
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.
As a conventional approach, optical dipole trap (ODT) arrays with linear polarization have been widely used to assemble neutral-atom qubits for building a quantum computer. However, due to the inherent scalar differential light shifts (DLS) of qubit states induced by trapping fields, the microwave-driven gates acting on single qubits suffer from errors on the order of 10^{-3}. Here, we construct a DLS compensated ODT array based upon a recently developed magic-intensity trapping technique. In such a magic-intensity optical dipole trap (MI-ODT) array, the detrimental effects of DLS are efficiently mitigated so that the performance of global microwave-driven Clifford gates is significantly improved. Experimentally, we achieve an average error of (4.7±1.1)×10^{-5} per global gate, which is characterized by randomized benchmarking in a 4×4 MI-ODT array. Moreover, we experimentally study the correlation between the coherence time and gate errors in a single MI-ODT with an optimum error per gate of (3.0±0.7)×10^{-5}. Our demonstration shows that MI-ODT array is a versatile platform for building scalable quantum computers with neutral atoms.
We study a system of neutral atoms trapped in a three-dimensional optical lattice suitable for the encoding, initialization and manipulation of atomic qubits. The qubits are manipulated by applied electromagnetic fields interacting with dipole moments of the atoms via light shifts, Raman transitions, Zeeman shifts, and microwave transitions. Our lattice is formed by three orthogonal one-dimensional lattices, which have different frequencies so that interference terms average to zero. This geometry allows considerable freedom in designing the component one-dimensional lattices, so that they provide not only confinement but also independent control in each dimension. Our atomic qubits are initialized from a laser-cooled atomic sample by Raman sideband cooling in individual lattice potential wells. We have demonstrated accurate and robust one-qubit manipulation using resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneities in the microwave Rabi frequency and the light shifted qubit transition frequency. Observation of qubit dynamics in near real time allows us to minimize these inhomogeneities, and therefore optimize qubit logic gates. For qubits in the lattice, we infer a fidelity of 0.990(3) for a single pi-pulse. We have also explored the use of NMR-type pulse techniques in order to further reduce the effect of errors and thus improve gate robustness in the atom/lattice system. Our schemes for two-qubit quantum logic operations are based on controlled collisional interactions. We have experimented with two schemes in order to probe these collisions. The first involves manipulation of the center-of-mass wavepackets of two qubits in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately, this scheme has proven extremely sensitive to phase errors, as the wavepackets are moved by the optical lattice. The other scheme starts with two qubits in spatially separated traps, and utilizes microwaves to drive one or both qubits into a third trap in-between the two qubits. Once the wavepackets overlap, the collisions create a large energy shift which can be probed spectroscopically.
We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution, and qubit rotations on individual atoms are performed with 99% contrast. In a final readout operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.