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arXiv:2007.04149 · Journal of Physics B Atomic Molecular and Optical Physics

Coherence properties of highly-excited motional states of a trapped ion

Vincent Jarlaud, Pavel Hrmo, Manoj K. Joshi, Richard Claude Thompson

Published Oct 19, 2020• 13 citations
arXivHTMLPDF

Abstract

Abstract We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of 1 s, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allows measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long coherence times despite the incoherent preparation of the states. Such states can be useful for sensitive motional dephasing measurements.

DOI
10.1088/1361-6455/abc271

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Abstract We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of 1 s, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allows measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long coherence times despite the incoherent preparation of the states. Such states can be useful for sensitive motional dephasing measurements.
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.
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.
We demonstrate the preparation and coherent control of the angular momentum state of a two-ion crystal. The ions are prepared with an average angular momentum of 7850ℏ freely rotating at 100 kHz in a circularly symmetric potential, allowing us to address rotational sidebands. By coherently exciting these motional sidebands, we create superpositions of states separated by up to four angular momentum quanta. Ramsey experiments show the expected dephasing of the superposition which is dependent on the number of quanta separating the states. These results demonstrate coherent control of a collective motional state described as a quantum rotor in trapped ions. Moreover, our Letter offers an expansion of the utility of trapped ions for quantum simulation, interferometry, and sensing.
We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish clock states in 27Al+, which avoids ground-state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the (1)S0 ground state of 27Al+.
We investigate high frequency motional states of trapped atomic ions. Trapped ions in rf traps are confined by an approximate harmonic potential and exhibit quantum motional states that mediate essential techniques in quantum computing, simulation, networking, and precision measurement. However, motional state decoherence mechanisms, heating and dephasing, are broadly limiting: reduced two-qubit gate fidelities; lower fidelity and lifetime of highly nonclassical bosonic states; long laser cooling times; and large recoil heating rates. These also challenge the scalability of increasingly sophisticated protocols. We propose high motional frequency ion trapping as an operating regime that addresses these challenges and reshapes the design landscape for quantum information experiments and quantum control techniques. We report an experimentally motivated investigation of realizing this high-frequency regime and discuss the consequences for laser cooling, motional state coherence, fidelity and lifetime of nonclassical bosonic states, and scalability of experimental runtimes. We report clear design trajectories for ion traps to reach high motional frequency, a new limiting mechanism for laser cooling at these high frequencies, and more than an order-of-magnitude speedup in experimental duty cycles with larger speed ups possible for quantum error correction protocols. Taken together, high motional frequency ion trapping has broad implications for the future of quantum information experiments.