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arXiv:2103.16308 · Physical Review A

Generation of a single-ion large oscillator

Ryoichi Saito, Takashi Mukaiyama

Published Nov 19, 2021• 9 citations
arXivHTMLPDF

Abstract

We demonstrate the generation of a trapped ion oscillator with a scale of $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ via fast trap center displacement. Applying an offset voltage to the ion trap electrode helps achieve a displacement of the trap center within the timescale of 5 ns. The fluorescence dynamics of the ion is analyzed after the displacement to estimate the oscillation amplitude. The realized trap displacement is seven times larger than that achieved in previous work. Thus, this result is an important step toward the realization of a gyroscope using a single trapped ion.

DOI
10.1103/physreva.104.053114

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We demonstrate the generation of a trapped ion oscillator with a scale of 10\ensuremathμm10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}10\ensuremathμm via fast trap center displacement. Applying an offset voltage to the ion trap electrode helps achieve a displacement of the trap center within the timescale of 5 ns. The fluorescence dynamics of the ion is analyzed after the displacement to estimate the oscillation amplitude. The realized trap displacement is seven times larger than that achieved in previous work. Thus, this result is an important step toward the realization of a gyroscope using a single trapped ion.
In this paper, we propose and demonstrate a new method for measuring the trap frequency from the fluorescence dynamics of an ion, initiated using fast trap-center displacement. Here, we observe the coherently excited motion of an ion in a harmonic trap using time-resolved fluorescence detection. Furthermore, Fourier analysis of the ion fluorescence signal was used to determine the trap frequency of an ion with high precision and reproducibility. The results show that our proposed method can be an alternative way to determine trap frequencies in an ion trap experiment.
Fast control of quantum systems is essential to make use of quantum properties before they degrade by decoherence. This is important for quantum-enhanced information processing, as well as for pushing quantum systems towards the boundary between quantum and classical physics. 'Bang-bang' control attains the ultimate speed limit by making large changes to control fields much faster than the system can respond, but is often challenging to implement experimentally. Here we demonstrate bang-bang control of a trapped-ion oscillator using nanosecond switching of the trapping potentials. We perform controlled displacements with which we realize coherent states with up to 10,000 quanta of energy. We use these displaced states to verify the form of the ion-light interaction at high excitations far outside the usual regime of operation. These methods provide new possibilities for quantum-state manipulation and generation, alongside the potential for a significant increase in operational clock speed for trapped-ion quantum information processing.
A single trapped ion driven away from the equilibrium position behaves like a Duffing oscillator. We demonstrate in a homebuilt surface-electrode trap (SET) the motion transduction of a trapped-ion oscillator from one dimension to another along with amplification of motional amplitudes and energies under the full control of the radio-frequency drive voltage. The phenomena, originated from different layouts and fabrication asymmetry of the SET, can be understood by complicated Duffing nonlinear equations. Our scheme provides an effective mechanism to investigate very complicated nonlinear behavior in trapped-ion setups and is expected to have extensive applications.
Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is particularly well suited for trapping ions with unstable nuclei, due to its large range of stability parameters that facilitates external injection online to an accelerator. The motion of an ion in such a linear combined trap is investigated theoretically and experimentally. In the trap ions oscillate harmonically in the radial direction and move nearly harmonically between fixed boundaries along the longitudinal axis. The presence of a homogeneous magnetic field and the applied dc and rf electric fields, lead to a set of coupled Mathieu equations. Their approximate solutions exhibit motional frequencies, which are combinations of shifted macromotion frequencies and the cyclotron frequency. The dependence of these motional frequencies on the applied trapping fields was studied in detail. For the measurements we used small clouds of laser cooled B9e+ ions and crystallized B9e+ ions. The observed oscillation frequencies are compared to both the results of zeroth order analytical solutions and to numerical simulations in which the frequency spectrum was obtained from the ion orbits by using the fast fourier transform formalism. The various motional resonances were experimentally recorded by applying a weak dipole excitation field to one of the trap electrodes, and by simultaneously observing at resonance the changes in the fluorescence intensity. Depending on the detuning of the cooling laser the ions gain energy during the motional excitation process in such a way that they are shifted further in or out of optical resonance by the Doppler effect. This leads to either positive or negative ion motion signals at the various ion oscillation frequencies.
Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the ion crystal motion to the internal spin degree of freedom of the ions using an oscillating spin-dependent optical dipole force. The resulting induced spin precession is proportional to the displacement amplitude of the crystal, and is measured with near-projection-noise-limited resolution. A 49pm49\phantom{\rule{4pt}{0ex}}\mathrm{pm}49pm displacement is detected with a signal-to-noise ratio of 1 in a single experimental determination, which is an order-of-magnitude improvement over prior phase-incoherent experiments. This displacement amplitude is 40 times smaller than the zero-point fluctuations. With our repetition rate, an 8.4pm/Hz8.4\phantom{\rule{4pt}{0ex}}\mathrm{pm}/\sqrt{\mathrm{Hz}}8.4pm/Hz​ displacement sensitivity is achieved, which implies 12(yN/ion)/Hz12\phantom{\rule{0.16em}{0ex}}(\mathrm{yN}/\mathrm{ion})/\sqrt{\mathrm{Hz}}12(yN/ion)/Hz​ and $77\phantom{\rule{0.16em}{0ex}}(\ensuremath{\mu}\mathrm{V}/\mathrm{m})/\sqrt{\mathrm{Hz}}$ sensitivities to forces and electric fields, respectively. This displacement sensitivity, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below ${10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}\mathrm{yN}$/ion and 1nV1\phantom{\rule{4pt}{0ex}}\mathrm{nV}1nV/m, respectively.
Nonlinear mechanical resonators display rich and complex dynamics and are important in many areas of fundamental and applied sciences. Here, we present a general strategy to generate mechanical nonlinearities for trapped particles by transverse driving in a funnel-shaped potential. Employing a trapped ion platform, we study the nonlinear oscillation, bifurcation, and hysteresis of a single calcium ion and demonstrate a 20-fold enhancement of the signal from a zeptonewton-magnitude harmonic force through the effect of vibrational resonance. Our results represent a first step in combining the rich nonlinear dynamics with the precision control over mechanical motions offered by atomic physics and open up possibilities for exploiting nonlinear mechanical phenomena in the quantum regime.