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Register a new userDark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field
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We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43Ca+ ions at a magnetic field of 146 Gauss. This field gives access to a magnetic-field-independent atomic clock qubit transition within the ground level hyperfine structure of the ion, but also causes the complex internal structure of the 64 states relevant to Doppler cooling to be spread over many times the atomic transition line-width. Using a time-dependent optical Bloch equation simulation of the system we develop a simple scheme to Doppler-cool the ion on a two-photon dark resonance, which is robust to typical experimental variations in laser intensities, detunings and polarizations. We experimentally demonstrate cooling to a temperature of 0.3 mK, slightly below the Doppler limit for the corresponding two-level system, and then use Raman sideband laser cooling to cool further to the ground states of the ions radial motional modes. These methods will enable two-qubit entangling gates with this ion, which is one of the most promising qubits so far developed.
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We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the fluorescence rate during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of RF micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.
We study the speed/fidelity trade-off for a two-qubit phase gate implemented in $^{43}$Ca$^+$ hyperfine trapped-ion qubits. We characterize various error sources contributing to the measured fidelity, allowing us to account for errors due to single-qubit state preparation, rotation and measurement (each at the $sim0.1%$ level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between $97.1(2)%$ (for a gate time $t_g=3.8mu$s) and $99.9(1)%$ (for $t_g=100mu$s), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case.
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 ($960mu$m apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a quantum CCD architecture for a large-scale quantum information processor. 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, from which we calculate a spin-flip probability on the qubit transition of the non-addressed ion of $1.3times 10^{-6}$. Off-resonant excitation then becomes the dominant error process, at around $5 times 10^{-3}$. It can be prevented either by working at higher magnetic field, or by polarization control of the microwave field. We implement polarization control with error $2 times 10^{-5}$, which would suffice to suppress off-resonant excitation to the $sim 10^{-9}$ level if combined with spatial addressing. Such polarization control could also enable fast microwave operations.
Microwave near-field quantum control of spin and motional degrees of freedom of 25Mg+ ions can be used to generate two-ion entanglement, as recently demonstrated in Ospelkaus et al. [Nature 476, 181 (2011)]. Here, we describe additional details of the setup and calibration procedures for these experiments. We discuss the design and characteristics of the surface-electrode trap and the microwave system, and compare experimental measurements of the microwave near-fields with numerical simulations. Additionally, we present a method that utilizes oscillating magnetic-field gradients to detect micromotion induced by the ponderomotive radio-frequency potential in linear traps. Finally, we discuss the present limitations of microwave-driven two-ion entangling gates in our system.
Using trapped ions in an entangled state we propose detecting a magnetic dipole of a single atom at distance of a few $mu$m. This requires a measurement of the magnetic field gradient at a level of about 10$^{-13}$ Tesla/$mu$m. We discuss applications e.g. in determining a wide variation of ionic magnetic moments, for investigating the magnetic substructure of ions with a level structure not accessible for optical cooling and detection,and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measureing spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques well established in ion trap quantum information processing it is within reach of current technology.
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