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Spectroscopy of a Trapped Ion in a Standing Wave

Jan‐Karl Burkhardt

Published May 2, 2014• 0 citations
OpenAlex

Abstract

With the recent surge for an experimentally viable quantum computer, trapped ions have come to the forefront as one of the most practical systems from which to construct a quantum computing architecture. This work has continued to explore the feasibility of using trapped ions as quantum bits, addressing the issue of quantum decoherence due to non-resonant excitation by studying the spectroscopy of a trapped ion through a standing wave. \n \nThe standing wave studied in this thesis was formed on the face of a surface-electrode ion trap held at cryogenic temperatures. Although the trap was not built with a reflective surface in mind, a lower bound on the fringe visibility was measured to be 0.717. By moving the ion through the nodes and anti-nodes of the wave, the carrier and sidebands of the S_1/2 to D_5/2 transition, commonly used for information storage, were selectively stimulated and suppressed.

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With the recent surge for an experimentally viable quantum computer, trapped ions have come to the forefront as one of the most practical systems from which to construct a quantum computing architecture. This work has continued to explore the feasibility of using trapped ions as quantum bits, addressing the issue of quantum decoherence due to non-resonant excitation by studying the spectroscopy of a trapped ion through a standing wave. \n \nThe standing wave studied in this thesis was formed on the face of a surface-electrode ion trap held at cryogenic temperatures. Although the trap was not built with a reflective surface in mind, a lower bound on the fringe visibility was measured to be 0.717. By moving the ion through the nodes and anti-nodes of the wave, the carrier and sidebands of the S_1/2 to D_5/2 transition, commonly used for information storage, were selectively stimulated and suppressed.
The purpose of this work is to investigate methods by which the quantum states of trapped ions may be better controlled and measured for the applications of quantum computing, quantum simulation, and the generation of atomic frequency standards. We report on two primary projects: first, we control the relative coupling strengths of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding the technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions, with the cycles for the two cases 180◦ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum computation and quantum simulation. Second, we investigate methods proposed in Ref. [36] which may improve the performance of trapped ion (or atom) frequency standards when the interrogating local oscillator is of limited quality. These methods could be applied to future generations of small-scale frequency standards, which are in demand for applications such as local GPS networks and distributed sensors. We propose a scheme for implementing these methods in a 40Ca+ based frequency standard, and outline the technical requirements for doing so. Finally, we present preliminary results characterizing single-ion coherence times and ion “state destruction” events in our system, and discuss how they will affect the realization of the proposed scheme.
We control the relative coupling strength of carrier and first-order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases ${180}^{\ensuremath{\circ}}$ out of phase with each other. This technique allows for the suppression of off-resonant carrier excitations when addressing the motional sidebands, and has applications in quantum simulation and quantum control. Using the standing-wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.
We present a surface-electrode Paul trap featuring integrated photonics elements, where ions are illuminated with two interfering beams at 729 nm forming a standing wave along the trap axis. In this field configuration, it is possible to excite the motional sidebands of a trapped ion while suppressing the off- resonant coupling to the corresponding carrier transition. This is of particular interest for quantum information processing, as it would allow implementing faster and lower error Mølmer-Sørensen entangling gates.We characterize the optical properties of the chip by scanning with sub-wavelength resolution the position of a single ion through the standing wave and observing Rabi oscillations for carrier and first motional sideband of different quadrupole transitions. We characterize both the strength of resonant couplings and the AC Stark shift induced by off-resonant couplings. We measure noise and drifts in the ion position and observe high stability in the standing wave profile without the need for active phase stabilization.Integrated optics allow to reliably reproduce the same field configuration in different regions of the chip, opening the way for implementing distributed, parallel quantum operations. We show the ability to control ions in different regions of the trap at the same time. We implemented real-time control of the DC voltages controlling the axial configuration of the trapping potential which enables us to load multiple ion crystals, merge, split, and shuttle them across the device.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.