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Detecting yocto (10-24) newton forces with trapped ions

Hermann Uys, Michael J. Biercuk, J.D. Britton, Aaron P. van Devender, J. J. Bollinger

Published Sep 1, 2010• 1 citation

Abstract

We report a calibrated measurement of 174 yoctonewton (1× 10−24 N = 1 yN), using a cloud of 60 Be ion confined in a Penning ion trap. These measurements suggest that ion traps may form the basis of a new class of ultra-sensitive deployable force sensors. 1. Summary Measurement of extremely small forces is of interest in a variety of fields ranging from atomic-force-microscopy, to electron spin resonance, to tests of fundamental principles. State-of-the-art small force detection relies on using thin cantilevers of which the resonant vibrational response is probed in reaction to an external force. Such systems have achieved force sensitivities on the order of attonewtons [1]. It has been suggested that single trapped ions could achieve force sensitivities on the order of ∼ 1 yn and consequently be used as a new class of force sensor [2]. Here we demonstrate a calibrated, yoctonewton scale force measurement using 60 Be ions confined in a Penning ion trap. The ions are subjected to a small oscillating electric field and their resonant response is probed using phase sensitive detection of modulations in the fluorescence intensity of a probe beam near-resonant with the S1/2 −→ P3/2 transition. We detect forces as small as 174 yn corresponding to a force sensitivity of 390±150 yn/ √ Hz. Extrapolated sensitivities are consistent with ∼ 1.7 yn/√Hz in the single ion limit [3]. Figure 1: Resonant response of Be ions under the influence of weak, oscillating electric fields. Left-most column Experiment, modulations in fluorescence intensity as a function of driving force simulation for different drive times (indicated in right-most column). Central column Theoretical simulation corresponding to left column. Right-most column cross sections through data in left-most column with theoretical fits.

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YoctoNewton force detection sensitivity using trapped ions

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The ability to detect extremely small forces is vital for a variety of disciplines including precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1 $aN/\sqrt{Hz}$ (atto $=10^{-18}$) through coupling of micro or nanofabricated mechanical resonators to a variety of physical systems including single-electron transistors, superconducting microwave cavities, and individual spins. These experiments have allowed for probing studies of a variety of phenomena, but sensitivity requirements are ever-increasing as new regimes of physical interactions are considered. Here we show that trapped atomic ions are exquisitely sensitive force detectors, with a measured sensitivity more than three orders of magnitude better than existing reports. We demonstrate detection of forces as small as 174 $yN$ (yocto $=10^{-24}$), with a sensitivity 390$\pm150$ $yN/\sqrt{Hz}$ using crystals of $n=60$ $^{9}$Be$^{+}$ ions in a Penning trap. Our technique is based on the excitation of normal motional modes in an ion trap by externally applied electric fields, detection via and phase-coherent Doppler velocimetry, which allows for the discrimination of ion motion with amplitudes on the scale of nanometers. These experimental results and extracted force-detection sensitivities in the single-ion limit validate proposals suggesting that trapped atomic ions are capable of detecting of forces with sensitivity approaching 1 $yN/\sqrt{Hz}$. We anticipate that this demonstration will be strongly motivational for the development of a new class of deployable trapped-ion-based sensors, and will permit scientists to access new regimes in materials science.

arXiv:1004.0780•Apr 6, 2010•0 citations

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Developing nanomechanical oscillators for ultrasensitive force detection is very useful in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radiofrequency electric field by a nanosensor made of a single trapped ${}^{40}{\mathrm{Ca}}^{+}$ ion under injection locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 $\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.2em}{0ex}}\mathrm{yN}/\sqrt{\mathrm{Hz}}$. Further with 3-dB squeezing applied on the oscillation phase variance, we achieve a successful detection of the smallest force to be $86.5\ifmmode\pm\else\textpm\fi{}70.1$ yN.

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Abstract A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled40Ca+ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperatureTaxial ≲ 10 mK in the forced-frequency rangeωz = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/μm, for a measured quality factorQ = 3875(45), and a decay time constantγz = 88(2) s−1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 μeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.

arXiv:1612.08577•Scientific Reports•Aug 10, 2017•16 citations

We report a calibrated measurement of 174 yoctonewton (1× 10−24 N = 1 yN), using a cloud of 60 Be ion confined in a Penning ion trap. These measurements suggest that ion traps may form the basis of a new class of ultra-sensitive deployable force sensors. 1. Summary Measurement of extremely small forces is of interest in a variety of fields ranging from atomic-force-microscopy, to electron spin resonance, to tests of fundamental principles. State-of-the-art small force detection relies on using thin cantilevers of which the resonant vibrational response is probed in reaction to an external force. Such systems have achieved force sensitivities on the order of attonewtons [1]. It has been suggested that single trapped ions could achieve force sensitivities on the order of ∼ 1 yn and consequently be used as a new class of force sensor [2]. Here we demonstrate a calibrated, yoctonewton scale force measurement using 60 Be ions confined in a Penning ion trap. The ions are subjected to a small oscillating electric field and their resonant response is probed using phase sensitive detection of modulations in the fluorescence intensity of a probe beam near-resonant with the S1/2 −→ P3/2 transition. We detect forces as small as 174 yn corresponding to a force sensitivity of 390±150 yn/ √ Hz. Extrapolated sensitivities are consistent with ∼ 1.7 yn/√Hz in the single ion limit [3]. Figure 1: Resonant response of Be ions under the influence of weak, oscillating electric fields. Left-most column Experiment, modulations in fluorescence intensity as a function of driving force simulation for different drive times (indicated in right-most column). Central column Theoretical simulation corresponding to left column. Right-most column cross sections through data in left-most column with theoretical fits.

The ability to detect extremely small forces is vital for a variety of disciplines including precision spin-resonance imaging, microscopy, and tests of fundamental physical phenomena. Current force-detection sensitivity limits have surpassed 1

aN/\sqrt{Hz}

(atto

=10^{-18}

) through coupling of micro or nanofabricated mechanical resonators to a variety of physical systems including single-electron transistors, superconducting microwave cavities, and individual spins. These experiments have allowed for probing studies of a variety of phenomena, but sensitivity requirements are ever-increasing as new regimes of physical interactions are considered. Here we show that trapped atomic ions are exquisitely sensitive force detectors, with a measured sensitivity more than three orders of magnitude better than existing reports. We demonstrate detection of forces as small as 174

yN

(yocto

=10^{-24}

), with a sensitivity 390

\pm150

yN/\sqrt{Hz}

using crystals of

n=60

^{9}

Be

^{+}

ions in a Penning trap. Our technique is based on the excitation of normal motional modes in an ion trap by externally applied electric fields, detection via and phase-coherent Doppler velocimetry, which allows for the discrimination of ion motion with amplitudes on the scale of nanometers. These experimental results and extracted force-detection sensitivities in the single-ion limit validate proposals suggesting that trapped atomic ions are capable of detecting of forces with sensitivity approaching 1

yN/\sqrt{Hz}

. We anticipate that this demonstration will be strongly motivational for the development of a new class of deployable trapped-ion-based sensors, and will permit scientists to access new regimes in materials science.

Developing nanomechanical oscillators for ultrasensitive force detection is very useful in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radiofrequency electric field by a nanosensor made of a single trapped

{}^{40}{\mathrm{Ca}}^{+}

ion under injection locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 $\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.2em}{0ex}}\mathrm{yN}/\sqrt{\mathrm{Hz}}$. Further with 3-dB squeezing applied on the oscillation phase variance, we achieve a successful detection of the smallest force to be $86.5\ifmmode\pm\else\textpm\fi{}70.1$ yN.

Forces drive all physical interactions. High-sensitivity measurement of the effect of forces enables the quantitative investigation of physical phenomena. Laser-cooled trapped atomic ions are a well-controlled quantum system whose low mass, strong Coulomb interaction, and readily detectable fluorescence signal make them a favorable platform for precision metrology. We demonstrate a three-dimensional sub-attonewton sensitivity force sensor based on a super-resolution imaging of a single trapped ion. The force is detected by measuring the ion's displacement in three dimensions with nanometer precision. Observed sensitivities were 372 ± 9, 347 ± 18, and 808 ± 51 zN/[Formula: see text], corresponding to 24×, 87×, and 21× above the quantum limit. We verified this technique by measuring a 95-zN light pressure force, an important systematic effect in optically based sensors.

The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing a near-resonant radio frequency field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the spatial location of the ion is determined with an unprecedented wavelength-relative resolution of 5

\times

10

^{-9}

, corresponding to an absolute precision of 0.12 nm. Measurements of an electrostatic force on a single ion demonstrate a sensitivity of 2.2

\times

10

^{-23} ~\text{N}/\sqrt{\text{Hz}}

. The real-time measurement of an atom's position complements the well-established technique of scanning near-field radio frequency transmission microscopy and opens up a novel route to using this method with path breaking spatial and force resolution.

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.

Abstract A single-ion reservoir has been tested, and characterized in order to be used as a highly sensitive optical detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled40Ca+ion stored in a Paul trap with rotational symmetry. The performance is observed through the axial motion of the ion, which is equivalent to an underdamped and forced oscillator. Thus, the results can be projected also to Penning traps. We have found that, for an ion oscillator temperatureTaxial ≲ 10 mK in the forced-frequency rangeωz = 2π × (80,200 kHz), the reservoir is sensitive to a time-varying electric field equivalent to an electric force of 5.3(2) neV/μm, for a measured quality factorQ = 3875(45), and a decay time constantγz = 88(2) s−1. This method can be applied to measure optically the strength of an oscillating field or induced (driven) charge in this frequency range within times of tens of milliseconds. Furthermore the ion reservoir has been proven to be sensitive to electrostatic forces by measuring the ion displacement. Since the heating rate is below 0.3 μeV/s, this reservoir might be used as optical detector for any ion or bunch of charged particles stored in an adjacent trap.