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Quantum dynamics of small numbers of ions in a penning trap

G. Stutter

Published Nov 1, 2015• 1 citation
Publisher

Abstract

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 $97\%$, 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.

DOI
10.25560/31473

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•Feb 1, 2013•1 citation
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±0.011\nzbar = 0.029\pm 0.011\nzbar=0.029±0.011 from an initial \nzbar≈24\nzbar \approx 24\nzbar≈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 nˉ˙z=\SI0.56±0.52\per\second\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}nˉ˙z​=\SI0.56±0.52\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≈150\ncbar\approx150\ncbar≈150 after Doppler cooling to \ncbar=0.6\ncbar=0.6\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.
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.
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.
Resolved-sideband cooling of a single 9^99Be+^++ ion in a Penning trap
Manipulating individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling applications from quantum information processing to precision metrology. The key ingredient is ground-state cooling of the particle's motion through resolved-sideband laser cooling. Ultra-high-presicion experiments using Penning ion traps will greatly benefit from the reduction of systematic errors offered by full motional control, with applications to atomic masses and ggg-factor measurements, determinations of fundamental constants or related tests of fundamental physics. In addition, it will allow to implement quantum logic spectroscopy, a technique that has enabled a new class of precision measurements in radio-frequency ion traps. Here we demonstrate resolved-sideband laser cooling of the axial motion of a single 9^99Be+^++ ion in a cryogenic 5 Tesla Penning trap system using a two-photon stimulated-Raman process, reaching a mean phonon number of nˉz=0.10(4)\bar{n}_z = 0.10(4)nˉz​=0.10(4). This is a fundamental step in the implementation of quantum logic spectroscopy for matter-antimatter comparison tests in the baryonic sector of the Standard Model and a key step towards improved precision experiments in Penning traps operating at the quantum limit.
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.
This thesis presents work aimed towards achieving sideband cooling of 40Ca+ ions in a Penning trap. The observation of an increase in the number of quantum jumps as a function of the trapping magnetic field is first presented. This observation is explained by the ion falling into a long-lived D5/2 state, out of which the ion is not being re-pumped. The ion can fall into this state due to mixing of the fine structure components with the same mJ quantum number induced by the applied magnetic field. A calculation of the mixing and shelving rate as a function of magnetic field strength is presented. This theory matches well with the experimental results observed. This work has been presented in a publication in which a perturbative analysis was used. An alternative analysis is presented here in which the full Hamiltonian is diagonalised. The essential conclusions however remain unchanged. This ‘J-state mixing’ effect means re-pumping from each of the six D5/2 state sub-levels of our ion is required for efficient laser cooling. This is achieved by the addition of a system comprising an 854 nm laser and a fibre EOM to provide the radiation required to re-pump these levels. The same EOM is then used to re-pump out of the four sub-levels of the D3/2 state using a single 866 nm laser. This is a great simplification of the experimental setup required to cool a 40Ca+ ion in a Penning trap which would otherwise require ten separate lasers to independently address each of the D sub-states. Achieving efficient repumping leads to the ability to perform pulsed spectroscopy on the quadrupole S1/2 → D5/2 transition in 40Ca+ . Preliminary results of this spectroscopy in a radio-frequency trap are presented.
Laser cooled ions in a Penning trap can be isolated from the environment by placing them in vacuum and only interacting with them through optical and RF fields. The number of trapped particles can be varied from a single ion up to thousands. Confinement is provided by a static homogeneous magnetic field and a quadrupole electric potential. In the natural frame of the ions, this appears as a 3D simple harmonic potential. Therefore three dimensional structures can be formed in the absence of any additional RF field which may lead to heating as is the case with RF traps. There are 3N different motional modes for N particles. I present an analysis of the motion of a single particle showing that the energy levels for all three modes are equally spaced. I also describe the interaction between a trapped two level atom and an optical field. During my time in the lab the laser and computer control of the experiment has been significantly improved. In addition, an existing trap was modified to provide greater optical access and fluorescence collection. This allowed the vibrational levels superimposed on the internal states of a single 40Ca+ ion to be resolved via a narrow linewidth, electric quadrupole transition. This is the first observation of magnetron and modified cyclotron sidebands on an optical transition. When more than one calcium ion is laser cooled, and their temperature reduced below 5mK, they form a Coulomb crystal. The locations of the ions minimise the total potential energy which is comprised of the Coulomb repulsion and trap potential. The fluorescence collection optics have been arranged to resolve individual ions in these crystals. Information about the motion of the ions is deduced by comparing photos from the experiment to numerical simulations. Previously, only two ions have ever been aligned along the magnetic field in a Penning trap. I present strings of up to 29 particles and suggest the only limitation, apart from the electrode structure, is the overlap of the laser beams with the ions.