Single-ion quantum lock-in amplifier

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Keselman, Anna; Ozeri, Roee

doi:10.1038/nature10010

Cited by 196 publications

(169 citation statements)

References 27 publications

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“…The width of this distribution can be intuitively interpreted as temperature, which we define as the time averaged energy divided by Boltzmann's constant for a single particle. This is a powerful notion, since many experiments require low residual kinetic energy, e.g., for precision metrology [8][9][10][11][12] or quantum computation and simulation [13,14]. In this article we study the spatial probability density of a Doppler cooled Mg + ion trapped in a linear radio frequency (rf) trap, confirm the expected Gaussian distribution, and demonstrate that our straightforward imaging approach enables precise thermometry, as required for a wide range of experiments.…”

Section: Introductionmentioning

confidence: 82%

Sub-millikelvin spatial thermometry of a single Doppler-cooled ion in a Paul trap

et al. 2012

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We report on observations of thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-milliKelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature.

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Section: Introductionmentioning

confidence: 82%

Sub-millikelvin spatial thermometry of a single Doppler-cooled ion in a Paul trap

et al. 2012

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“…Traditionally in these fields, the extreme sensitivity of coherent quantum dynamics to external perturbations has been viewed as a barrier to be surmounted. By contrast, quantum sensors have emerged that instead take advantage of this sensitivity; recent examples include electrometers and magnetometers based on superconducting qubits 3 , quantum dots 4 , spins in diamond [5][6][7][8] and trapped ions 9 .…”

mentioning

confidence: 99%

“…Previous works such as Refs. 5,6,9,25,26 carried out this phase adjustment, usually by carefully modulating the signal AC field, to 0(π/2) prior to measurement. Practical situations where the magnetic field arises from unknown samples may prevent this phase adjustment and result in inaccurate measurements which we address here.…”

mentioning

confidence: 99%

“…Highly sensitive quantum sensing techniques use multi-pulse dynamical decoupling (DD) sequences 3,6,9,[25][26][27] that are tuned to the frequency of a time-dependent field. The resulting fluctuating frequency shift is rectified and integrated by the pulse sequence to yield a detectable quantum phase, while effectively filtering out low frequency noise from the environment ( Fig.…”

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confidence: 99%

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Dual-channel lock-in magnetometer with a single spin in diamond

Nusran

Dutt

2013

Phys. Rev. B

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We present an experimental method to perform dual-channel lock-in magnetometry of timedependent magnetic fields using a single spin associated with a nitrogen-vacancy (NV) color center in diamond. We incorporate multi-pulse quantum sensing sequences with phase estimation algorithms to achieve linearized field readout and constant, nearly decoherence-limited sensitivity over a wide dynamic range. Furthermore, we demonstrate unambiguous reconstruction of the amplitude and phase of the magnetic field. We show that our technique can be applied to measure random phase jumps in the magnetic field, as well as phase-sensitive readout of the frequency.PACS numbers: 07.55. Ge,85.75.Ss,76.30.Mi The coherent evolution of a quantum state interacting with its environment is the basis for understanding fundamental issues of open quantum systems 1 , as well as for applications in quantum information science and technology 2 . Traditionally in these fields, the extreme sensitivity of coherent quantum dynamics to external perturbations has been viewed as a barrier to be surmounted. By contrast, quantum sensors have emerged that instead take advantage of this sensitivity; recent examples include electrometers and magnetometers based on superconducting qubits 3 , quantum dots 4 , spins in diamond [5][6][7][8] and trapped ions 9 .The nitrogen-vacancy (NV) defect center in diamond ( Fig. 1(a)) shows great promise as an ultra-sensitive solid-state magnetometer and magnetic imager because it features potentially atomic-scale resolution 6 , wide temperature range operation from 4 K -700 K 10 , and long coherence times that allow for high magnetic field sensitivity 11 . Recent demonstrations include nanoscale magnetic imaging 7,12,13 , coupling to nano-mechanical oscillators [14][15][16] , detection of single proximal nuclear spins [17][18][19][20] and nanoscale volumes of external electron and nuclear spins [21][22][23][24] .Magnetometry with diamond spin sensors detects the frequency shift of the NV spin resonance caused by the magnetic field via the Zeeman effect. Highly sensitive quantum sensing techniques use multi-pulse dynamical decoupling (DD) sequences 3,6,9,[25][26][27] that are tuned to the frequency of a time-dependent field. The resulting fluctuating frequency shift is rectified and integrated by the pulse sequence to yield a detectable quantum phase, while effectively filtering out low frequency noise from the environment ( Fig. 1(b)). Another advantage of these DD sequences is that they make the magnetometer insensitive to instabilities such as drifts in temperature or applied bias magnetic field.However, these state of the art quantum sensing methods also have significant drawbacks: the dynamic range is limited by the quantum phase ambiguity 28,29 , the sensitivity is a highly nonlinear function of field amplitude requiring prior knowledge of a working point for accurate deconvolution, and the classical phase of the field has to be carefully controlled to obtain accurate field ampli-Illustration of experimental setup f...

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“…To detect small amplitudes with the available F 0 in our set-up, we extend the spin-precession time to τ ≥ 20 ms. To avoid decoherence due to magnetic field fluctuations and coherently accumulate spin precession, we use a quantum lock-in [27] sequence where during the interaction time τ the spin precession is interrupted by a train of π-pulses that are synchronized with phase jumps enforced on the ODF beams [23]. In particular, we use a Carr-Purcell-Meiboom-Gill (CPMG) sequence with m = 8 ODF-π-ODF segments (τ = 2 m T , see Fig.…”

mentioning

confidence: 99%

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

et al. 2017

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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...

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Single-ion quantum lock-in amplifier

Cited by 196 publications

References 27 publications

Sub-millikelvin spatial thermometry of a single Doppler-cooled ion in a Paul trap

Sub-millikelvin spatial thermometry of a single Doppler-cooled ion in a Paul trap

Dual-channel lock-in magnetometer with a single spin in diamond

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

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