Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

Ion trap frequency measurement from fluorescence dynamics

Kota Saito, Ryoichi Saito, Takashi Mukaiyama

Published Sep 1, 2022• 4 citations
Publisher

Abstract

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.

DOI
10.1063/5.0100007

Related papers

Ion dynamics and oscillation frequencies in a linear combined trap

T. Nakamura, S. Ohtani, M. Wada +3 more

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.

Journal of Applied Physics•Mar 1, 2001•11 citations

Monitoring a single ion's motion by second-order photon correlations

D. Rotter, Manas Mukherjee, François Dubin +1 more

For a single trapped ion, second-order time correlations of fluorescence photons are measured in a self-homodyne configuration by beating the fluorescence with itself. At the nanosecond timescale, the correlations are governed by electronic excitation and decay of the ion and anti-bunching in the resonance fluorescence is observed and quantitatively reproduced. On the other hand, at the microsecond timescale the motion of the ion determines the correlations: secular motional modes, their amplitude and relative coherence are measured. Besides precisely monitoring the trap frequencies, our observations also quantify the temporal stability of the trapping potential.

New Journal of Physics•Apr 10, 2008•19 citations

Weighing of trapped ion crystals and its applications

Kevin Sheridan, Matthias Keller

We have developed a novel scheme to measure the secular motion of trapped ions. Employing pulsed excitation and analysis of the fluorescence of laser-cooled ions, we have measured the centre-of-mass mode frequency of single as well as entire ion crystals with a frequency precision better than 5 × 10 −4 within an interrogation time on the order of seconds, limited only by the fluorescence collection efficiency and the background noise. We have used this method to measure the mass of ions and observed charge exchange collisions between trapped calcium isotopes.

arXiv:1106.2771•New Journal of Physics•Dec 1, 2011•18 citations

Coherently displaced oscillator quantum states of a single trapped atom

Katherine C McCormick, Jonas Keller, David J Wineland +2 more

Coherently displaced number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a projective measurement via state-dependent fluorescence, with near-unit fidelity. This leads to a rich set of line shapes when recording the internal-state excitation probability after a sideband excitation, as a function of the frequency detuning of the displacement drive with respect to the ion's motional frequency. We precisely characterize the coherent displacement based on the resulting line shapes, which exhibit sharp features that are useful for oscillator frequency determination from the single quantum regime up to very large coherent states with average occupation numbers of several hundred. We also introduce a technique based on multiple coherent displacements and free precession for characterizing noise on the trapping potential in the frequency range of 500 Hz–400 kHz. Signals from the ion are directly used to find and eliminate sources of technical noise in this typically unaccessed part of the spectrum.

arXiv:1811.00668•Quantum Science and Technology•Feb 7, 2019•16 citations

Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals

M. Affolter, Kevin Gilmore, J. E. Jordan +1 more

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 $49\phantom{\rule{4pt}{0ex}}\mathrm{pm}$ 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 $8.4\phantom{\rule{4pt}{0ex}}\mathrm{pm}/\sqrt{\mathrm{Hz}}$ displacement sensitivity is achieved, which implies $12\phantom{\rule{0.16em}{0ex}}(\mathrm{yN}/\mathrm{ion})/\sqrt{\mathrm{Hz}}$ 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 $1\phantom{\rule{4pt}{0ex}}\mathrm{nV}$/m, respectively.

arXiv:2008.00035•Physical Review A•Nov 9, 2020•25 citations

Heterodyne measurement of the resonance fluorescence of a single ion

J. T. Höffges, H. W. Baldauf, W. Lange +1 more

The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.

Journal of Modern Optics•Oct 1, 1997•60 citations
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.
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.
For a single trapped ion, second-order time correlations of fluorescence photons are measured in a self-homodyne configuration by beating the fluorescence with itself. At the nanosecond timescale, the correlations are governed by electronic excitation and decay of the ion and anti-bunching in the resonance fluorescence is observed and quantitatively reproduced. On the other hand, at the microsecond timescale the motion of the ion determines the correlations: secular motional modes, their amplitude and relative coherence are measured. Besides precisely monitoring the trap frequencies, our observations also quantify the temporal stability of the trapping potential.
We have developed a novel scheme to measure the secular motion of trapped ions. Employing pulsed excitation and analysis of the fluorescence of laser-cooled ions, we have measured the centre-of-mass mode frequency of single as well as entire ion crystals with a frequency precision better than 5 × 10 −4 within an interrogation time on the order of seconds, limited only by the fluorescence collection efficiency and the background noise. We have used this method to measure the mass of ions and observed charge exchange collisions between trapped calcium isotopes.
Coherently displaced number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a projective measurement via state-dependent fluorescence, with near-unit fidelity. This leads to a rich set of line shapes when recording the internal-state excitation probability after a sideband excitation, as a function of the frequency detuning of the displacement drive with respect to the ion's motional frequency. We precisely characterize the coherent displacement based on the resulting line shapes, which exhibit sharp features that are useful for oscillator frequency determination from the single quantum regime up to very large coherent states with average occupation numbers of several hundred. We also introduce a technique based on multiple coherent displacements and free precession for characterizing noise on the trapping potential in the frequency range of 500 Hz–400 kHz. Signals from the ion are directly used to find and eliminate sources of technical noise in this typically unaccessed part of the spectrum.
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.
The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.