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Ground state cooling of the radial motion of a single ion in a penning trap and coherent manipulation of small numbers of ions

Pavel Hrmo

Published May 1, 2018• 2 citations
Publisher

Abstract

This thesis extends the recently reported ground state sideband cooling of the axial motion of a single ion to a broader frequency range of the axial motion, the radial motion and ion crystals. Once cold, coherent control of these different configurations is demonstrated. The experimental work in this thesis uses 40Ca+ ions that can be coherently addressed on a narrow linewidth optical transition at 729 nm. The technique of axialization that resonantly couples the two radial modes of motion is used to enhance laser Doppler cooling leading to mean phonon occupation numbers in the low hundreds for both modes. The sideband cooling technique is then used to simultaneously cool both the motional modes to within one phonon of the ground state for the first time evers. Sideband cooling is then also employed to cool the axial modes of many ion Coulomb crystals in two different configurations. For two ions in a 1D chain, motional occupation numbers of nbar_COM=0.30(4) and nbar_B=0.07(3) are achieved. For two ions in a planar 2D configuration the result for the two modes are nbar_T=nbar_COM<0.1. This technique is scaled up to demonstrate ground state occupation of up to 10 ions in the planar configuration. The axial mode of motion of a single motion is used to characterise the coherent addressing capabilities in our system through optical and motional Ramsey spectroscopy. We observe optical coherence times of 1.78(4) ms and motional coherence times of 590(12) ms. Dynamical decoupling techniques are shown to extend these coherence times. Furthermore, basic decoherence models are validated in high-lying non-thermal motional states that are prepared by a sideband heating technique. Progress towards entangling gates is demonstrated using a bichromatic laser beam to prepare non-classical states of motion.

DOI
10.25560/61471

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For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.

•Nov 1, 2014•1 citation
This thesis extends the recently reported ground state sideband cooling of the axial motion of a single ion to a broader frequency range of the axial motion, the radial motion and ion crystals. Once cold, coherent control of these different configurations is demonstrated. The experimental work in this thesis uses 40Ca+ ions that can be coherently addressed on a narrow linewidth optical transition at 729 nm. The technique of axialization that resonantly couples the two radial modes of motion is used to enhance laser Doppler cooling leading to mean phonon occupation numbers in the low hundreds for both modes. The sideband cooling technique is then used to simultaneously cool both the motional modes to within one phonon of the ground state for the first time evers. Sideband cooling is then also employed to cool the axial modes of many ion Coulomb crystals in two different configurations. For two ions in a 1D chain, motional occupation numbers of nbar_COM=0.30(4) and nbar_B=0.07(3) are achieved. For two ions in a planar 2D configuration the result for the two modes are nbar_T=nbar_COM<0.1. This technique is scaled up to demonstrate ground state occupation of up to 10 ions in the planar configuration. The axial mode of motion of a single motion is used to characterise the coherent addressing capabilities in our system through optical and motional Ramsey spectroscopy. We observe optical coherence times of 1.78(4) ms and motional coherence times of 590(12) ms. Dynamical decoupling techniques are shown to extend these coherence times. Furthermore, basic decoherence models are validated in high-lying non-thermal motional states that are prepared by a sideband heating technique. Progress towards entangling gates is demonstrated using a bichromatic laser beam to prepare non-classical states of motion.
From subatomic particles to macromolecules, quantum mechanics has a deep impact in understanding the interactions and nature of such constituents of matter. The paradoxical observations of entanglement in quantum systems is used in quantum computations. Ion traps are among the leading platforms which provide clean and highly controllable quantum systems. This thesis presents the study of quantum coherence aiming to devise and test coherent control with trapped ions in a Penning trap. Our apparatus contains one or more calcium ions that are confined in space using DC electric and magnetic fields. Doppler cooling and resolved sideband cooling of trapped ions are carried out to perform high fidelity quantum control. The ions are prepared in their motional ground state via a multi-stage resolved sideband cooling technique. The cooling methods are first verified through simulations. The axial mean phonon numbers for a single ion are measured to be 0.03 ± 0.01 and 0.012 ± 0.009 at 187 kHz and 420 kHz axial frequencies, respectively. The heating rate is measured to be 2.5 ± 0.5 phonons/s, which is consistent with the previous measurements in our system. Similarly, the radial motional modes of a single ion are cooled to 〈n_+ 〉<0.4 and 〈n_- 〉<0.6 from mean phonon numbers corresponding to each mode of around 100. Preliminary studies are carried out of the axial motional modes of a 1D chain and 2D planar crystals, extending sideband cooling to small ICC's in a Penning trap. Coherent control is examined in our system and the optical coherence time and motional coherence time are estimated to be approximately 1 ms and 0.5 s, respectively. Furthermore, a single ion is prepared outside the Lamb-Dicke regime via a sideband heating technique and coherent studies are performed in such a regime via a laser beam.
We have recently demonstrated the laser cooling of a single 40Ca+ ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S12↔ D52. Here we report on the extension of this technique to small ion Coulomb crystals made of two or three 40Ca+ ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of n¯COM=0.30(4) for the centre of mass (COM) mode and n¯B=0.07(3) for the breathing mode of the two-ion string with corresponding heating rates of 11(2) s-1 and 1(1)s-1 at a trap frequency of 162 kHz. The occupation of the ground state of the axial modes (ntilt=nCOM=0) is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) s-1 at a trap frequency of 355 kHz.
Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of 97%97\%97%, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.
Low-entropy motional states of ion Coulomb crystals are an essential prerequisite for a plethora of applications and are typically prepared by laser cooling. As larger crystals are operated in the quantum regime, it remains unclear, and has recently become debated, whether increasing the ion number can be beneficial for cooling. Here, we investigate theoretically and experimentally many-ion sideband cooling and the role of collective effects in different spin-motion coupling regimes. For weak coupling, the many-body effects are insignificant. In the strong-coupling regime, however, the spin and motional subsystems undergo a coherent state swap, enabling cooling by a suitably timed laser pulse. Using planar Coulomb crystals with up to 91 ions, we demonstrate that the residual mean phonon occupation after one such pulse scales as 1/N21/N^21/N2 with the number of ions. By iterating the pulses, we measure mean phonon occupations <2⋅10−4<2\cdot10^{-4}<2⋅10−4. For large crystals in the coherent regime, we further show that the spin-motion dynamics becomes largely independent of the initial phonon statistics. Through spin measurements, the state-swap mechanism can be utilized to probe the phonon distribution in the mode.
Doppler and sideband cooling are long-standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion Doppler cooled to $\ensuremath{\sim}100$ phonons in both radial modes at a magnetron frequency of 52 kHz and a modified cyclotron frequency of 677 kHz. For these frequencies, we then show that mean phonon numbers of 0.35(5) for the modified cyclotron and 1.7(2) for the magnetron motions are achieved after 68 ms of sideband cooling.
For 35 years, laser-cooled trapped ions have been at the frontier of progress in quantum computing, quantum simulation and precision measurement, and remain one of the most valuable tools in these fields to this day. Most of these experiments are predicated upon or benefit from the ability to place ions in the motional quantum ground state, a technique that was first demonstrated in radiofrequency ion traps 25 years ago. For a range of crucial experiments that are impossible to conduct in radiofrequency traps or are not well suited to this architecture, Penning traps provide an important alternative. However, the performance of Penning traps had been limited by the fact that ground-state cooling was yet to be achieved in such a system. This thesis reports the first demonstration of resolved-sideband cooling in a Penning trap, for 40Ca+ions cooled with light at 729-nm, achieving a ground state occupation of 99% in one dimension. Demonstrations of the coherent manipulations possible at this level of confinement are presented. The ion heating rate is measured and although higher than might be expected given the unusually large ion-electrode distance remains amongst the lowest reported in any trap to date. Achieving this result required the development of a number of new experimental systems and major upgrades to the stability and reliability of the experiment, the details of which are also given. The thesis also presents theoretical work into the use of two-dimensional Coulomb crystals in a Penning trap as a resource for quantum information. Using the symmetries of the crystal, we find that it is possible to engineer complex entangled states, specifically two small quantum error correcting codes, using a very small number of global entangling pulses. Efficient entanglement protocols such as these are vital for the implementation of useful quantum error correction.