Engineering of microfabricated ion traps and integration of advanced on-chip features

Atomic ions trapped in electromagnetic potentials have long been used for fundamental studies in quantum physics. Over the past two decades, trapped ions have been successfully used to implement technologies such as quantum computing, quantum simulation, atomic clocks, mass spectrometers and quantum sensors. Advanced fabrication techniques, taken from other established or emerging disciplines, are used to create new, reliable ion-trap devices aimed at large-scale integration and compatibility with commercial fabrication. This Technical Review covers the fundamentals of ion trapping before discussing the design of ion traps for the aforementioned applications. We overview the current microfabrication techniques and the various considerations behind the choice of materials and processes. Finally, we discuss current efforts to include advanced, on-chip features in next-generation ion traps

Optical Bloch equations with multiply connected states

The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a two-state system driven by two lasers with different intensities and frequencies and to a three-state Λ-system with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold 40Ca+ ion when subject to a single laser frequency driving the 4S1/2-4P 1/2 transition and a laser with two strong sidebands driving 3D 3/2-4P1/2. © 2008 IOP Publishing Ltd

Precision measurement of the 43Ca+ nuclear magnetic moment

We report precision measurements of the nuclear magnetic moment of 43Ca+, made by microwave spectroscopy of the 4s2S1/2∣∣F=4,M=0⟩→∣∣F=3,M=1⟩ ground level hyperfine clock transition at a magnetic field of ≈146G, using a single laser-cooled ion in a Paul trap. We measure a clock-transition frequency of f=3199941076.920(46)Hz from which we determine μI/μN=−1.315350(9)(1) where the uncertainty (9) arises from uncertainty in the hyperfine A constant, and the (1) arises from the uncertainty in our measurement. This measurement is not corrected for diamagnetic shielding due to the bound electrons. We make a second measurement which is less precise but agrees with the first. We use our μI value in combination with previous NMR results to extract the change in shielding constant of calcium ions due to solvation in D2O:Δσ=−0.00022(1)

High-fidelity spatial addressing of Ca-43 qubits using near-field microwave control

Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, whilst enabling arbitrary parallel operations. We demonstrate addressing of long-lived $^{43}\text{Ca}^+$ "atomic clock" qubits held in separate zones of a microfabricated surface trap with integrated microwave electrodes. By coherently cancelling the microwave field in one zone we measure a ratio of Rabi frequencies between addressed and non-addressed qubits of up to 1400, implying an addressing error of $1.3\times 10^{-6}$. Off-resonant excitation prevents this error level being directly demonstrated, but we also show polarization control of the microwave field with error $2\times 10^{-5}$, sufficient to suppress off-resonant excitation out of the qubit states to the $\sim 10^{-9}$ level. Such polarization control could enable fast microwave operations

Integration von Visualisierung und Simulation fuer Stroemungsberechnungen mit automatischer Gittererzeugung

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Fast quantum logic gates with trapped-ion qubits

Quantum bits (qubits) based on individual trapped atomic ions are a promising technology for building a quantum computer. The elementary operations necessary to do so have been achieved with the required precision for some error-correction schemes. However, the essential two-qubit logic gate that is used to generate quantum entanglement has hitherto always been performed in an adiabatic regime (in which the gate is slow compared with the characteristic motional frequencies of the ions in the trap), resulting in logic speeds of the order of 10 kilohertz. There have been numerous proposals of methods for performing gates faster than this natural 'speed limit' of the trap. Here we implement one such method, which uses amplitude-shaped laser pulses to drive the motion of the ions along trajectories designed so that the gate operation is insensitive to the optical phase of the pulses. This enables fast (megahertz-rate) quantum logic that is robust to fluctuations in the optical phase, which would otherwise be an important source of experimental error. We demonstrate entanglement generation for gate times as short as 480 nanoseconds-less than a single oscillation period of an ion in the trap and eight orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The power of the method is most evident at intermediate timescales, at which it yields a gate error more than ten times lower than can be attained using conventional techniques; for example, we achieve a 1.6-microsecond-duration gate with a fidelity of 99.8 per cent. Faster and higher-fidelity gates are possible at the cost of greater laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser. It offers the prospect of combining the unrivalled coherence properties, operation fidelities and optical connectivity of trapped-ion qubits with the submicrosecond logic speeds that are usually associated with solid-state devices