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.
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×\else\texttimes\fi10\ensuremath−27N/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.
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/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±150yN/Hz using crystals of n=609Be+ 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/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.
Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As illustrations, we suggest some applications in particle physics. We outline a nondestructive time-of-flight measurement capable of sub-eV energy resolution for slowly moving, collimated particles. We also show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges ≪e. Our calculations may also be useful in the characterization of noise in quantum computers coming from backgrounds of charged particles.
Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.
Detecting an itinerant microwave photon with high efficiency is an outstanding problem in quantum optics at microwave frequencies and in the fundamental quantum mechanics experimental toolbox. This subject has attracted a lot of attention and there are growing number of excellent experimental demonstrations and theoretical proposals towards this aim. However, due to the extremely low energy of microwave quanta, efficiently detecting a propagating microwave photon in a non-absorbing manner is still an unresolved challenge and it is the focus of the major part of this thesis. Motivated by a recent experiment that shows a superconducting artificial atom (a transmon) in a one-dimensional microwave transmission line exhibits gigantic cross-Kerr nonlinearities, 1000 times larger than in comparable optical systems, I investigate the possibility of detection single microwave photons using a transmon induced cross-Kerr-like interaction between two microwave fields. The photon number in one field is inferred through the measurement of the displacement of the other field. The first project on this subject is to investigate the feasibility of detecting a single microwave photon with signal-to-noise ratio (SNR) greater than unity using a three-level approximation for the transmon in an open transmission line, due to the saturation of transmon response to the probe intensity. After that, an improved scheme was proposed to overcome the limitations in the preceding work. By using a cavity probe field the signal photon induced probe displacement is strongly enhanced. Further additional transmon-cavity units can be cascaded to further improve the detection efficiency. It is shown that with only two transmons the distinguishability to resolve a single-photon state from the vacuum is up to 90%. One advantage of this photon detection scheme is that it does not rely on the absorption of single microwave photons, which enables repeated measurements and further applications. Moreover, I also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: the higher the measurement efficiency, the greater is the decoherence. Apart from the investigation on the single microwave photon detection, this thesis also studies nonlinear dynamics of a hybrid coupled-resonator and opto-mechanical system. It is shown that the saddle-node bifurcation and the Hopf bifurcation appear in the system, which leads to bistability and limit cycle dynamics of the mechanical position and the output light intensity. More importantly, the opto-mechanical nonlinearity dramatically changes the transparency window of the coupled resonator induced transparency (CRIT) and based on the narrow and bistable CRIT transparency window, the proposed system is shown to be a good platform for the weak impulsive force detection with a good sensitivity.