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arXiv:quant-ph/0609134 · Physical Review A

Fast quantum state control of a single trapped neutral atom

M. P. A. Jones, J. Beugnon, Alpha Gaétan, Jin Zhang, Gaétan Messin, Antoine Browaeys, Philippe Grangier

Published Apr 11, 2007• 103 citations
arXivHTMLPDF

Abstract

We demonstrate the initialization, readout, and high-speed manipulation of a qubit stored in a single $^{87}\mathrm{Rb}$ atom trapped in a submicrometer-sized optical tweezer. Single-qubit rotations are performed on a time scale below $100\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ using two-photon Raman transitions. Using the spin-echo technique, we measure an irreversible dephasing time of $34\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. The readout of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.

DOI
10.1103/physreva.75.040301

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We demonstrate the initialization, readout, and high-speed manipulation of a qubit stored in a single 87Rb^{87}\mathrm{Rb}87Rb atom trapped in a submicrometer-sized optical tweezer. Single-qubit rotations are performed on a time scale below 100ns100\phantom{\rule{0.3em}{0ex}}\mathrm{ns}100ns using two-photon Raman transitions. Using the spin-echo technique, we measure an irreversible dephasing time of 34ms34\phantom{\rule{0.3em}{0ex}}\mathrm{ms}34ms. The readout of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.
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.
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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.
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.
We report cooling of a single neutral atom to its three-dimensional vibrational ground state in an optical tweezer.After employing Raman sideband cooling for tens of milliseconds, we measure via sideband spectroscopy a three-dimensional ground-state occupation of about 90%.We further observe coherent control of the spin and motional state of the trapped atom.Our demonstration shows that an optical tweezer, formed simply by a tightly focused beam of light, creates sufficient confinement for efficient sideband cooling.This source of ground-state neutral atoms will be instrumental in numerous quantum simulation and logic applications that require a versatile platform for storing and manipulating ultracold single neutral atoms.For example, these results will improve current optical-tweezer experiments studying atom-photon coupling and Rydberg quantum logic gates, and could provide new opportunities such as rapid production of single dipolar molecules or quantum simulation in tweezer arrays.
Ultracold neutral atoms have emerged as a promising platform for scalable quantum computation. Universal single-qubit control requires high quality state preparation, spatially resolved manipulation, and projective readout of each qubit. For state preparation and readout, neutral atom platforms can apply techniques commonly used in quantum gas microscopes and single atom trapping machines. Furthermore, the ability to isolate the internal spin states of individual neutral atoms from both external fields and neighboring atoms allows for seconds-scale coherence times. Here, we will present progress on the coherent, site-resolved control of an array of atomic qubits comprised of neutral strontium atoms.