Ultrasensitive detection of force and displacement using trapped ions

Abstract

The ability to detect extremely small forces and nanoscale displacements is vital for disciplines such as precision spin-resonance imaging [1], microscopy [2], and tests of fundamental physical phenomena [3][4][5]. Current force-detection sensitivity limits have surpassed 1 aN/ √ Hz [6,7] (atto = 10 −18 ) through coupling of nanomechanical resonators to a variety of physical readout systems [1,[7][8][9][10]]. Here we demonstrate that crystals of trapped atomic ions [11,12] behave as nanoscale mechanical oscillators and may form the core of exquisitely sensitive force and displacement detectors. We report the detection of forces with a sensitivity 390±150 yN/ √ Hz (more than three orders of magnitude better than existing reports using nanofabricated devices [7]), and discriminate ion displacements ∼18 nm. Our technique is based on the excitation of tunable normal motional modes in an ion trap [13] and detection via phase-coherent Doppler velocimetry [14,15], and should ultimately permit force detection with sensitivity better than 1 yN/ √ Hz [16]. Trappedion-based sensors could permit scientists to explore new regimes in materials science where augmented force, field, and displacement sensitivity may be traded against reduced spatial resolution. Trapped atomic ions exhibit well characterized and broadly tunable (kHz to MHz) normal motional modes in their confining potential [16,17]. The presence of these modes, the light mass of atomic ions, and the strong coupling of charged particles to external fields makes trapped ions excellent detectors of small forces with tunable spectral response [13]. Another advantage is that readout is achieved through resonant-fluorescence detection using only a single laser. Previous studies have suggested that by using ions it is possible to measure forces approaching the yoctonewton scale, for instance, through experiments on motional heating in Paul traps due to fluctuating electric fields [18][19][20], or resonant excitation techniques [17,21].In particular, small forces applied to ions in weak trapping potentials (trapping frequencies ∼0.1 MHz or lower) can excite micron-scale motional excursions resolvable using real-space imaging [21,22].While the intrinsic sensitivity of trapped ions to external forces and fields is well supported, it remains an experimental challenge to determine the maximum achievable sensitivity to a given external excitation as set by systematic limitations including the efficiency of a measurement procedure. Establishing ions as components in ultrasensitive detectors requires two primary issues to be addressed: a known excitation must be applied to allow precise calibration of the system's response; and it must be possible to compare the results of these experiments with the existing literature on detectors based on integrated nanostructures. Our aims are to unify the seemingly disparate fields of nanotechnology and atomic devices, through use of comparable experimental conditions and a demonstration of the potential utility of ion-based sensors...

Single-crystal diamond nanomechanical resonators with quality factors exceeding one million

“…Several other routes have been explored, including, for example, surface cleaning under ultra high-vacuum conditions 14 or the use of doubly clamped beams at high spring tension 15 . Exciting recent progress has further been made with bottom-up devices such as suspended carbon nanotube 16 , silicon nanowire 17 or trapped ion 18 oscillators. All of these approaches have their drawbacks, however.…”

Ion-trajectory analysis for micromotion minimization and the measurement of small forces

“…Another application of precise position measurements is the determination of small forces, where trapped ions have been proven to be excellent probes [53,54]. We demonstrate this with the example of the light pressure force [55] acting on a laser-cooled ion in a Paul trap.…”

Quantum force estimation in arbitrary non-Markovian Gaussian baths

“…is satisfied and that the form of the QFI for the best state is also (6). Substituting the variance of the quadrature…”

“…As a matter of comparison, we give the asymptotical behaviour of the optimal time interval and of the corresponding QFI when a term of 1st order in τ appears at the denominator of (6). This happens when the time interval τ between each measurement is bigger than the evolution time scales of the bath correlation function (see Appendix D 2) or when the dynamics is Markovian (which implies obviously that τ is bigger than the evolution time scales of the bath correlation function).…”