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arXiv:1004.0780

YoctoNewton force detection sensitivity using trapped ions

Michael J. Biercuk, Hermann Uys, J. Britton, Aaron P. VanDevender, J. J. Bollinger

Published Apr 6, 2010• 0 citations
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Abstract

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.

Related papers

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

Hermann Uys, Michael J. Biercuk, J.D. Britton +2 more

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.

•Sep 1, 2010•1 citation

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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.

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Experiments with Trapped Ions and Ultrafast Laser Pulses

K. G. Johnson

Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying qubit state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single qubit rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an oscillator), high speed operations (compared with conventional atom-laser interactions), and multi-qubit entanglement operations with speed that is not fundamentally limited by the trap oscillation frequency. We also present a method to provide higher stability in the radial mode ion oscillation frequencies of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent oscillations of an ion trapped in an oscillating rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher frequency motion. These ultrafast atomic qubit manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.

•Jan 1, 2016•0 citations
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/HzaN/\sqrt{Hz}aN/Hz​ (atto =10−18=10^{-18}=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 yNyNyN (yocto =10−24=10^{-24}=10−24), with a sensitivity 390±150\pm150±150 yN/HzyN/\sqrt{Hz}yN/Hz​ using crystals of n=60n=60n=60 9^{9}9Be+^{+}+ 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/HzyN/\sqrt{Hz}yN/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.
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.
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.
Abstract Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator, thus increasing its response by the mechanical quality factor. The measurement of low-frequency forces, that are below resonance, is a more difficult task as the resulting oscillation amplitudes are significantly lower. Here we use a single-trapped 88Sr+ ion as a force sensor. The ion is electrically driven at a frequency much lower than the trap resonance frequency. We measure small amplitude of motion by measuring the periodic Doppler shift of an atomic optical clock transition, enhanced using the quantum lock-in technique. We report frequency force detection sensitivity as low as 2.8 × 10−20 NHz−1/2.
The detection of weak forces is a central problem in physics and engineering, ranging in importance from fundamental pursuits such as precision tests of gravity, gravitational-wave detection, and searches for dark matter to applications such as force microscopy. These pursuits require a low-mass mechanical force transducer with a high quality factor, whose motion can be measured in a quantum-noise-limited manner. Here, we study the ultimate example of such a transducer: a single trapped electron. We propose and analyze in detail a scheme for high-sensitivity continuous force detection using a single trapped electron whose motion is coupled to a microwave cavity field via image currents induced in an antenna. We derive the fundamental and technical limits to the sensitivity of this scheme and show that despite the disparity in size between that of a single electron and the wavelength of the microwave field, it is possible to continuously monitor the charge's zero-point motion and use it as a force detector with a sensitivity as low as $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\phantom{\rule{0.2em}{0ex}}\mathrm{N}/\sqrt{\mathrm{Hz}}$ in the gigahertz regime. This sensitivity improves on the state of the art by 4 orders of magnitude and thus paves the way to experiments with previously unattainable precision.
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.
Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying qubit state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single qubit rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an oscillator), high speed operations (compared with conventional atom-laser interactions), and multi-qubit entanglement operations with speed that is not fundamentally limited by the trap oscillation frequency. We also present a method to provide higher stability in the radial mode ion oscillation frequencies of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent oscillations of an ion trapped in an oscillating rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher frequency motion. These ultrafast atomic qubit manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.