D N Stacey

High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit.

We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine atomic clock states of ^{43}Ca^{+}. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T_{2}^{*}=50u2009u2009sec, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.

High-Fidelity Readout of Trapped-Ion Qubits

We demonstrate single-shot qubit readout with a fidelity sufficient for fault-tolerant quantum computation. For an optical qubit stored in 40Ca+ we achieve 99.991(1)% average readout fidelity in 10(6) trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145 micros average detection time. For 43Ca+, we propose and implement an optical pumping scheme to transfer a long-lived hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10 micros. We achieve 99.87(4)% transfer fidelity and 99.77(3)% net readout fidelity.

Implementation of a symmetric surface-electrode ion trap with field compensation using a modulated Raman effect

We describe a new electrode design for a surface-electrode Paul trap, which allows rotation of the normal modes out of the trap plane, and a technique for micromotion compensation in all directions using a two-photon process, which avoids the need for an ultraviolet laser directed to the trap plane. The fabrication and characterization of the trap are described, as well as its implementation for the trapping and cooling of single Ca+ ions. We also propose a repumping scheme that increases ion fluorescence and simplifies heating rate measurements obtained by time-resolved ion fluorescence during Doppler cooling.

The Faraday effect and magnetic circular dichroism in atomic bismuth

The authors give the theory of optical Faraday rotation and circular dichroism for a transition of mixed magnetic-dipole and electric-quadrupole character in the presence of hyperfine structure. The results are applied to two transitions of atomic bismuth, lambda 647.6 nm (Jj=3/2 to Jj=5/2) and lambda 875.5 nm (Jj=3/2 to Jj=3/2). They have studied the Faraday rotation profiles of these lines under high resolution; the results confirm the theoretical predictions and for each transition give a value for the ratio, chi , of the electric-quadrupole and magnetic-dipole reduced matrix elements, (Jj//( omega /4 square root 3)(-2er2C(2))//Ji) and (Jj// mu //Ji). They obtain chi =-0.60(2) for lambda 647.6 nm and chi =+0.13(7) for lambda 875.5 nm, to be compared with the theoretical values -0.65 and +0.11 respectively.

Laser spectroscopy of calcium isotopes

Improved measurements of isotope shifts in the 4s2 1S0-4s5s 1S0 transition of calcium are reported for the stable isotopes. A comparison with isotope shift measurements in other transitions by means of a King plot shows satisfactory agreement. Values of the changes in mean-square nuclear charge radius delta (r2) from a combined analysis of muonic isotope shifts and electron scattering data are used to separate the mass and field shifts in the optical lines. This procedure leads to values of delta (r2) for the calcium isotopes from 40Ca to 48Ca using all available high-precision data. The results for delta (r2)A,40 are 3.2(2.5), 215.3 (4.9), 125.4 (3.2), 283.2 (6.4), 118.8 (5.9), 124.2 (5.0), 5 (13) and -4.4(6.0)*10-3 fm2 for A=41 to 48 respectively. Values of the electronic factors relating the observed shifts of delta (r2) are deduced, and discussed in terms of configuration mixing in calcium.

A microfabricated ion trap with integrated microwave circuitry

We describe the design, fabrication, and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators, and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to give a large microwave field gradient to allow state-dependent manipulation of the ions motional degrees of freedom, the key to multi-qubit entanglement. The microwave field near the centre of the trap is characterised by driving hyperfine transitions in a single laser-cooled u200943Ca+ ion.

A reformulation of the theory of field isotope shift in atoms

The theory of the field isotope shift (FS) in atomic spectra is discussed critically and the results are presented in a form which is more straightforward than the expressions traditionally used to interpret experimental data. First-order perturbation theory is applied within the single-particle framework to the case of an s or p1/2 electron outside closed shells. Parameters to take account of many-body effects are subsequently included. The nuclear and electronic dependences of the FS are separately discussed. In a generalisation of the work of Seltzer (1986), it is shown that the former can be represented as a series of even charge moments: the coefficients of the first three terms for an s electron are given. The difference between the series for an s and a p1/2 electron is shown to be generally insignificant. The electronic dependence enters through the (relativistic) probability density N of the electron at the origin; for the case of an s electron. They relate N to the magnetic hyperfine splitting factor alpha s. A table which allows N to be found from a measurement of alpha s is given. Second-order field shifts are of the order of 10-3-10-4 of the first-order shifts for a two-neutron change.

Memory coherence of a sympathetically cooled trapped-ion qubit

We demonstrate sympathetic cooling of a 43Ca+ trapped-ion memory qubit by a 40Ca+ coolant ion sufficiently near the ground state of motion for fault-tolerant quantum logic, while maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during ten cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O (10^-4) infidelity per cooling cycle.

Measurement of parity non-conserving optical rotation in the 648 nm transition in atomic bismuth

Parity non-conserving (PNC) optical rotation has been measured by laser polarimetry in the 648 nm magnetic dipole transition (6p3 J=3/2 to 6p3 J=5/2) in atomic bismuth. The experiment involves finding the small differences in rotation between selected frequency points in the vicinity of the F=6 to F=7 hyperfine component. Faraday rotation, which can be distinguished from PNC rotation by its wavelength dependence, is used in locking the laser frequency and calibrating the PNC effect. Results obtained over a six-year period are summarised; a detailed discussion of error sources and associated tests is given. The final result for the PNC parameter of the 648 nm transition is R=(-9.3+or-1.4)*10-8. This is an agreement with the measurements of Birich et al (1984) but not with those of Barkov and Zolotorev (1980). It is also consistent with the standard model of the electroweak interaction, but the uncertainty in the atomic theory is now the limiting factor in the comparison.

Search for correlation effects in linear chains of trapped Ca+ ions

We report a precise search for correlation effects in linear chains of 2 and 3 trapped Ca+ ions. Unexplained correlations in photon emission times within a linear chain of trapped ions have been reported, which, if genuine, cast doubt on the potential of an ion trap to realize quantum information processing. We observe quantum jumps from the metastable 3d2D5/2 level for several hours, searching for correlations between the decay times of the different ions. We find no evidence for correlations: the number of quantum jumps with separations of less than 10 ms is consistent with statistics to within errors of 0.05%; the lifetime of the metastable level derived from the data is consistent with that derived from independent single-ion data at the level of the experimental errors (1%); and no rank correlations between the decay times were found with sensitivity to rank correlation coefficients at the level of |R| = 0.024.