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arXiv:1903.05763 · Physical Review Letters

Coherent Control of the Rotational Degree of Freedom of a Two-Ion Coulomb Crystal

Erik Urban, Neil Glikin, Sara Mouradian, Kai Krimmel, Boerge Hemmerling, Hartmut Häffner

Published Sep 24, 2019• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.123.133202

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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.
In this thesis, I present the design, implementation, and characterization of a novel, rotationally symmetric ion trap. Our compact design creates a toroidal trapping potential for charged atoms that has a radius that is much smaller than the height at which the ions are positioned above the surface of the trap. We trap ions at a height of 385~mu\\mumum and a radius of 45~mu\\mumum as expected from simulation. We demonstrate that this ring is rotationally symmetric with imperfections in the potential of much less than 3~mK. With two ions contained in a point Paul trap, we demonstrate the creation of a 100~kHz rotating ring using a rotating quadrupole. By releasing the quadrupole potential, we demonstrate the ability to create superpositions of rotational states using the modulation of the laser light produced by the classical rotation of the crystal in a symmetric potential. Superpositions of rotational states differing by up to four quanta are observed. With these rotational superpositions, we describe an experiment capable of observing the identical nature of two ions in a Coulomb crystal. By creating a rotational interferometer, one can coherently exchange two particles and observe their interference upon recombination. We describe what this interference signature would be and how particle indistinguishability would affect it. We present experimental efforts towards realizing this exchange and reflect on our unexpectedly short rotational superposition coherence times.
The quantum rotor is one of the simplest model systems in quantum mechanics, but only in recent years has theoretical work revealed general fundamental scaling laws for its decoherence. For example, a superposition of orientations decoheres at a rate proportional to the sine squared of the angle between them. Here, we observe scaling laws for rotational decoherence dynamics for the first time, using a 4 μm diameter planar rotor composed of two Paul-trapped ions. We prepare the rotational motion of the ion crystal into superpositions of angular momentum with well-defined differences ranging from 1-3ℏ, and measure the rate of decoherence. We also tune the system-environment interaction strength by introducing resonant electric field noise. The observed scaling relationships for decoherence are in excellent agreement with recent theoretical work, and are directly relevant to the growing development of rotor-based quantum applications.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
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.
Leading quantum platforms are largely limited to one or two dimensions, whereas three-dimensional Coulomb crystals of trapped ions self-assemble into dense qubit arrays with no rearrangement overhead. Coherent optical control of such crystals has nonetheless been out of reach, because the optical transition couples to nearly all 3N3N3N collective modes, i.e., a thermally occupied quasi-continuum bath. Here we cool about 3,600 modes of a crystal of over 1,200 ions below single-phonon occupation, using a continuous cooling band that spans more than five octaves in vibrational spectrum, from about 50 kHz to 2.1 MHz. The crystal then serves as a register of optical qubits, allowing global initialization, coherent manipulation and collective detection. We demonstrate ensemble optical coherence of 21.6 milliseconds and reduce the optical-transition frequency uncertainty from 389 Hz for a single ion to 12 Hz for over a thousand ions, approaching the expected projection-noise scaling. Our approach could be extended to even larger crystals with phonon-mediated many-body couplings, opening a route towards entanglement-enhanced precision metrology and three-dimensional quantum simulation, particularly with spatial-shaped illumination for region-resolved collective control.
Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729 nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).