Amplitude Sensing below the Zero-Point Fluctuations with a Two-Dimensional Trapped-Ion Mechanical Oscillator

Abstract

We present a technique to measure the amplitude of a center-of-mass (COM) motion of a twodimensional ion crystal of ∼100 ions. By sensing motion at frequencies far from the COM resonance frequency, we experimentally determine the technique's measurement imprecision. We resolve amplitudes as small as 50 pm, 40 times smaller than the COM mode zero-point fluctuations. The technique employs a spin-dependent, optical-dipole force to couple the mechanical oscillation to the electron spins of the trapped ions, enabling a measurement of one quadrature of the COM motion through a readout of the spin state. We demonstrate sensitivity limits set by spin projection noise and spin decoherence due to off-resonant light scattering. When performed on resonance with the COM mode frequency, the technique demonstrated here can enable the detection of extremely weak forces (< 1 yN) and electric fields (< 1 nV/m), providing an opportunity to probe quantum sensing limits and search for physics beyond the standard model.Measuring the amplitude of mechanical oscillators has engaged physicists for more than 50 years [1, 2] and, as the limits of amplitude sensing have dramatically improved, produced exciting advances both in fundamental physics and in applied work. Examples include the detection of gravitational waves [3], the coherent quantum control of mesoscopic objects [4], improved force microscopy [5], and the transduction of quantum signals [6]. During the past decade, optomechanical systems have facilitated increasingly sensitive techniques for reading out the amplitude of a mechanical oscillator [7][8][9][10][11], with a recent demonstration obtaining a measurement imprecision more than two orders of magnitude below z ZP T , the amplitude of the ground-state zero-point fluctuations [12]. Optomechanical systems have assumed a wide range of physical systems, including toroidal resonators, nanobeams, and membranes, but the basic principle involves coupling the amplitude of a mechanical oscillator to the resonant frequency of an optical cavity mode [4].Crystals of laser-cooled, trapped ions behave as atomic-scale mechanical oscillators [13][14][15] with tunable oscillator modes and high quality factors (∼10 6 ). Furthermore, laser cooling enables ground-state cooling and non-thermal state generation of these oscillators. Trapped-ion crystals therefore provide an ideal experimental platform for investigating the fundamental limits of amplitude sensing. Prior work has demonstrated the detection of coherently driven amplitudes larger than the zero-point fluctuations of the trapped ion oscillator [14][15][16], and reported impressive force sensing by injection locking an optically amplified oscillation of a single trapped ion [17].In this Letter we experimentally and theoretically analyze a technique to measure the center-of-mass (COM) motion of a two-dimensional, trapped-ion crystal of ∼100 ions with a sensitivity below z ZP T . We employ a timevarying spin-dependent force F 0 cos (µt) that couples the amplitude of the COM motion with...

Trapped-ion quantum computing: Progress and challenges

“…Stroboscopic methods of address can be used to control ions in such a system, but most work to date has effected uniform excitation. Recent work using these systems has resulted in the creation of manybody entanglement in large 2D ion crystals of hundreds of ions [64] with application to quantum simulation of critical systems and non-equilibrium dynamics in general [65,66], as well as enhanced quantum sensing [67]. However, since it is generally more straightforward to individually manipulate ions that are part of stationary arrays, Paul traps, with oscillating electric fields in the RF range, are the main focus for researchers in QC.…”

The TRAPSENSOR facility: an open-ring 7 tesla Penning trap for laser-based precision experiments

“…Among six Penning-trap experiments in the world performing laser cooling on positive ion species, only one at the Imperial College in London is using 40 Ca + ions (B=1.86 tesla) [50]. One experiment uses 25 Mg + at GSI-Darmstadt (B=4.1 tesla) [62], and four experiments use 9 Be + ions; at NIST-Boulder (B=4.45 tesla) [63], and at the Universities of Hannover (B= 5 tesla) [26], Mainz (B=1.95 tesla) [64] and Sydney (B∼2 tesla) [65]. In this publication, we have shown the first fluorescence measurement (photons with λ = 397 nm), proving the interaction of the ions with the lasercooling beams.…”

Efficient approach for quantum sensing field gradients with trapped ions

“…(2) is replaced by the effective frequency δ in (6). We note that recently a similar spin-boson interaction was used to measure experimentally a center-of-mass motion of two-dimensional ion crystal in a Penning trap [7].…”

“…Recently, the detection of force that is off resonance with the trapping frequency of the singe trapped ion was experimentally demonstrated with force sensitivity in the range of aN (10 −18 N) per √ Hz using Doppler velocimetry technique [6]. Sensing of amplitude of motion in an ensemble of ions in Penning trap below the zero-point fluctuations was demonstrated [7]. On the other hand the internal states of the trapped ions can be used as a high sensitive magnetometer for detecting very weak magnetic fields [8,9].…”