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arXiv:0811.3634 · Physical Review A

Accurate microwave control and real-time diagnostics of neutral-atom qubits

Worawarong Rakreungdet, Jae Hoon Lee, Kim Fook Lee, Brian Mischuck, Enrique Montaño, Poul Jessen

Published Feb 13, 2009• 44 citations
arXivHTMLPDF

Abstract

We demonstrate accurate single-qubit control in an ensemble of atomic qubits trapped in an optical lattice. The qubits are driven with microwave radiation, and their dynamics tracked by optical probe polarimetry. Real-time diagnostics is crucial to minimize systematic errors and optimize the performance of single-qubit gates, leading to fidelities of 0.99 for single-qubit $\ensuremath{\pi}$ rotations. We show that increased robustness to large, deliberately introduced errors can be achieved through the use of composite rotations. However, during normal operation the combination of very small intrinsic errors and additional decoherence during the longer pulse sequences precludes any significant performance gain in our current experiment.

DOI
10.1103/physreva.79.022316

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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.

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We demonstrate accurate single-qubit control in an ensemble of atomic qubits trapped in an optical lattice. The qubits are driven with microwave radiation, and their dynamics tracked by optical probe polarimetry. Real-time diagnostics is crucial to minimize systematic errors and optimize the performance of single-qubit gates, leading to fidelities of 0.99 for single-qubit \ensuremathπ\ensuremath{\pi}\ensuremathπ rotations. We show that increased robustness to large, deliberately introduced errors can be achieved through the use of composite rotations. However, during normal operation the combination of very small intrinsic errors and additional decoherence during the longer pulse sequences precludes any significant performance gain in our current experiment.
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 use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for 43Ca+^{43}{\mathrm{Ca}}^{+}43Ca+ hyperfine ``atomic clock'' qubits in a cryogenic (100 K) surface trap. For a single qubit, we benchmark an error of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ per Clifford gate (implemented using 600 ns $\ensuremath{\pi}/2$ pulses). For 2 qubits in the same trap zone (ion separation $5\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ per addressed $\ensuremath{\pi}/2$ gate. The scheme scales theoretically to larger numbers of qubits in a single register.
Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below 10−410^{-4}10−4, heat the atom by less than~Δn=0.01Δn = 0.01Δn=0.01, while being robust to alignment errors of the potential up to 505050~nm and thermal excitation up to nˉ=3\bar{n} = 3nˉ=3. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only ∼10\sim 10∼10~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.
The design of many proposed quantum computational platforms is driven by competing needs: isolating the quantum system from the environment to prevent decoherence, and easily and accurately controlling the system with external fields. Neutral-atom optical-lattice architectures provide environmental isolation through the use of states that are robust against fluctuating external fields, yet external fields are nevertheless essential for qubit addressing. Here we demonstrate the selection of individual qubits with external fields, despite the fact that the qubits are in field-insensitive superpositions. We use a spatially inhomogeneous external field to map selected qubits to a different field-insensitive superposition, minimally perturbing unselected qubits, despite the fact that the addressing field is not spatially localized. We show robust single-qubit rotations on neutral-atom qubits located at sites within a double-well configuration with minimal dephasing of neighboring qubits. This precise coherent control is an important step forward for lattice-based neutral-atom quantum computation, and is quite generally applicable to state transfer and qubit isolation in other architectures using field-insensitive qubits. Additionally this double-well proof-of-principle work should be quite applicable in the single-site addressability regime currently being explored by several groups. Additionally we present work demonstrating the near-elimination of the differential light shift for various qubit transitions, using a novel scheme balancing differential shifts with residual vector light shifts of nominally field-insensitive transitions. For details see references [1–6]
The rapid growth in size of quantum devices demands efficient ways to control them, which is challenging for systems with thousands of qubits or more. Here, we present a simple yet powerful solution: robust, site-dependent control of an arbitrary number of qubits in parallel with only minimal local tunability of the driving field. Inspired by recent experimental advances, we consider access to only one of three constrained local control capabilities: local control of either the phase or amplitude of the beam at each qubit, or individual Z rotations. In each case, we devise parallelizable composite pulse sequences to realize arbitrary single-qubit unitaries robust against quasistatic amplitude and frequency fluctuations. Numerical demonstration shows that our approach outperforms existing sequences such as BB1 and CORPSE in almost all regimes considered, achieving average fidelity > 0.999 under a decoherence rate of ∼ 10 − 5 , even with a few percent amplitude and frequency error. Our results indicate that even for very large qubit ensembles, accurate, individual manipulation can be achieved despite substantial control inhomogeneity.
Ensemble nitrogen-vacancy (NV) centers are widely used for quantum sensing and magnetometry, where performance depends on the accurate implementation of microwave pulse sequences. In these systems, inhomogeneous broadening and short coherence times limit reliable multi-pulse control, while hardware imperfections and off-resonant excitation distort implemented rotations, making direct calibration of arbitrary gates tedious. To address this, we implement a control framework with a ZXZXZ gate decomposition which uses fixed-angle, phase-parameterized pulses, enabling universal single-qubit control from a single calibrated $ π/2$ primitive (Xπ/2X_{π/2}Xπ/2​) along with virtual Z operations. We compare a standard pulse with a composite pulse designed for high-power operation in a regime where the Rabi frequency is comparable to the hyperfine splitting, leading to non-uniform evolution across hyperfine levels. Using pre-determined combinations of π/2π/2π/2 pulse sequences, we observe that standard pulses rapidly deviate from ideal behavior under repeated application, while the composite pulse suppresses this error accumulation by more than 70%\%% for longer sequences despite its longer duration. In contrast, randomized benchmarking yields similar decay factors for both implementations, highlighting its limited sensitivity to coherent control errors. These results establish a practical route to robust control in short-coherence ensemble systems and emphasize the importance of pulse-level characterization.