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arXiv:1510.08958 · New Journal of Physics

Dark-resonance Doppler cooling and high fluorescence in trapped Ca-43 ions at intermediate magnetic field

D. T. C. Allcock, T. P. Harty, M. A. Sepiol, H. A. Janacek, Christopher J. Ballance, Andrew M. Steane, D M Lucas, Derek N. Stacey

Published Feb 12, 2016• 12 citations
arXivHTMLPDF

Abstract

We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43 Ca + 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 ion's 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.

DOI
10.1088/1367-2630/18/2/023043

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Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap – an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in 43Ca+ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T*2 ≈ 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in 43Ca+, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.

•Jan 1, 2016•1 citation
We demonstrate simple and robust methods for Doppler cooling and obtaining high fluorescence from trapped 43 Ca + 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 ion's 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.
This thesis describes work on numerical modelling of the 43Ca+ ion in a Paul trap using the optical Bloch equations. This is a challenging system to study, with many states involved in the internal dynamics. A major outcome is the development of a cooling scheme for the 146.09 gauss atomic clock transitions which makes use of a dark resonance. It is much more effective than methods that avoid coherent effects. The scheme is realised in experiment. Complicated fluorescence data is modelled very well, and predictions for the ion's motional temperature show good agreement with measured values. Data and fits for an ion that has been Doppler cooled below the Doppler limit are presented. I describe GLOBES, a set of routines that simulates an arbitrary ion in the presence of an arbitrary system of laser beams using the optical Bloch equations. Techniques used to efficiently calculate the steady state, analyse fluorescence scans and solve time-dependent problems for small and large times are discussed. A new routine SILVER IMPER that leapfrogs over the initial dynamics to model the approach to the steady state is introduced. Doppler cooling in 40Ca+ is analysed and two extensions made to the basic theory. The ‘excursion method’ of calculation takes account of the non-linear variation with velocity of the scattering rate. The ‘dynamic method’ allows for the fact that the ion may not be in equilibrium with the incident radiation during its oscillations, a necessity as the timescale of the external motion is of order the characteristic timescale of the internal motion for standard secular frequencies. This 'dynamic effect' is a general property of trapped ion systems and is also observed in a two-state system. A two-variable fluorescence scan taken from a four-laser, five-level system in 40Ca+ is analysed. Techniques to fit large data sets and automatically resolve resonant features are demonstrated. A general treatment of resonant behaviour in three, four and five level pump/probe systems is used to describe the data. This is verified by a second, tailor-made set of scans.
Efficient Three-Dimensional Sub-Doppler Cooling of 40^{40}40Ca+^++ in a Penning Trap
We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a 40^{40}40Ca+^++ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) μμμs, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 μμμs as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.
This thesis is concerned with the development of an intermediate magnetic field "clock-qubit" in 43Ca+ at 146G and techniques to manipulate this qubit using microwaves and lasers. While 43Ca+ has previously been used as a qubit, its relatively complicated level structure - with a nuclear spin of 7/2 and low-lying D-states -- makes cooling it in the intermediate field an intimidating prospect. As a result, previous experiments have used small magnetic fields of a few gauss where coherence times are limited and off-resonant excitation is a significant source of experimental error. We demonstrate a simple scheme that allows 43Ca+ to be cooled in the intermediate field without any additional experimental complexity compared with low fields. Using the clock-qubit, we achieve a coherence time of T*2 = 50 (10)s - the longest demonstrated in any single qubit. We also demonstrate a combined state preparation and measurement error of 6.8(6)x 10-4 - the lowest achieved for a hyperfine trapped ion qubit [NVG+13] - and single-qubit logic gates with average errors of 1.0(3) x 10-6 - more than an order of magnitude better than the previous record [BWC+11]. These results represent the state-of-the-art in the field of single-qubit control. Moreover, we achieve them all in a single scalable room-temperature ion trap using experimentally robust techniques and without relying on the use of narrow-linewidth lasers, magnetic field screening or dynamical decoupling techniques. We also present work on a recent scheme [OWC+11] to drive two-qubit gates using microwaves. We have constructed an ion trap with integrated microwave circuitry to perform these gates. Using this trap, we have driven motional sideband transitions, demonstrating the spin-motion coupling that underlies the two-qubit gate. We present an analysis of likely sources of experimental error during a future two-qubit gate and the design and preliminary characterisation of apparatus to minimise the main error contributions. Using this apparatus, we hope to perform a two-qubit gate in the near future.
We study the formation and destabilization of dark states in a single trapped 88Sr+{}^{88}{\mathrm{Sr}}^{+}88Sr+ ion caused by the cooling and repumping laser fields required for Doppler cooling and fluorescence detection of the ion. By numerically solving the time-dependent density matrix equations for the eight-level system consisting of the sublevels of the 5s2S1/25s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}5s2S1/2​, 5p2P1/25p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}5p2P1/2​, and 4d2D3/24d{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{D}_{3/2}4d2D3/2​ states, we analyze the different types of dark states and how to prevent them in order to maximize the scattering rate, which is crucial for both the cooling and the detection of the ion. The influence of the laser linewidths and ion motion on the scattering rate and the dark resonances is studied. The calculations are then compared with experimental results obtained with an endcap ion trap system located at the National Research Council of Canada and found to be in good agreement. The results are applicable also to other alkaline-earth-metal ions and isotopes without hyperfine structure.
Trapped ions, as one of the pillars of progress in frequency metrology and quantum optics, require a complex experimental environment with well-defined conditions. We present that a feature called dark resonance, provided by the trapped ion itself, can be used as a versatile sensor for enhanced in-situ analysis of interacting fields. The dark resonance is formed in the lambda-type energy level scheme of a laser cooled 40Ca+ ion and corresponds to a fluorescence quenching. The method uses an analysis of the detection times of photons emitted from the upper energy level, which is excited via two optical dipole transitions. The two excitation lasers are phase locked to an optical frequency comb to reduce their linewidths and for precise control of their optical frequencies within the dark resonance. The amplitudes of interacting fields are obtained using the Fourier transform of the ion fluorescence or photon correlation measurements. This paper shows that the method can be applied for sensing of electric, magnetic and electromagnetic fields. Firstly, we present the potential for frequency analysis of the secular motion of a few-ion Coulomb crystal, which corresponds to the axial static electric field of a linear ion trap. Secondly, we demonstrate the optical frequency analysis of the employed lasers driving the two transitions. In the last case we show the analysis of an alternating magnetic field at the position of single ion.
Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap – an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in 43Ca+ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T*2 ≈ 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in 43Ca+, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.