Developing the isolation and control of ultracold atomic systems to the level of single quanta has led to significant advances in quantum sensing, yet demonstrating a quantum advantage in real world applications by harnessing entanglement remains a core task. Here, we realize a many-body quantum-enhanced sensor to detect weak displacements and electric fields using a large crystal of $\sim 150$ trapped ions. The center of mass vibrational mode of the crystal serves as high-Q mechanical oscillator and the collective electronic spin as the measurement device. By entangling the oscillator and the collective spin before the displacement is applied and by controlling the coherent dynamics via a many-body echo we are able to utilize the delicate spin-motion entanglement to map the displacement into a spin rotation such that we avoid quantum back-action and cancel detrimental thermal noise. We report quantum enhanced sensitivity to displacements of $8.8 \pm 0.4~$dB below the standard quantum limit and a sensitivity for measuring electric fields of $240\pm10~\mathrm{nV}\mathrm{m}^{-1}$ in $1$ second ($240~\mathrm{nV}\mathrm{m}^{-1}/\sqrt{\mathrm{Hz}}$).
Single-shot conditional displacement gate between a trapped atom and traveling light
Faculty of Science and Engineering, Waseda University（早稻田大学理工学部）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；Corporate Laboratory, Toshiba Corporation（东芝公司企业实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we present the first experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in the phase space. The resulting dynamics is equivalent to a "fast-motion video" of the adiabatic trajectory. The robustness of this protocol is…
We introduce a quantum sensing protocol for detecting the parameters characterizing the phase space displacement by using a single trapped ion as a quantum probe. We show that thanks to the laser-induced coupling between the ion's internal states and the motion mode the estimation of the two conjugated parameters describing the displacement can be efficiently performed by a set of measurements of the atomic state populations. Furthermore, we introduce a three-parameter protocol capable to detect the magnitude, the transverse direction and the phase of the displacement. We characterize the unce…
We present a protocol for using trapped ions to measure rotations via matter-wave Sagnac interferometry. The trap allows the interferometer to enclose a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without losing contrast. Since this technique does not require the ions to be confined in the Lamb-Dicke regime, thermal states with many phonons should be sufficient for operation.
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the Coulomb interaction to be estimated. We show that its effects are always small enough to allow high fidelity. In particular, the method can be applied to two ions in the same trap. We also show that gates between non-neighbour ions, and hence a Toffoli (three-qubit controlled-NOT) gate, can be achieved. We discuss how the gate can be applied to logical qubits en…
We present a technique to measure the amplitude of a center-of-mass (COM) motion of a two-dimensional ion crystal of $\sim$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 s…
We demonstrate the generation of a trapped ion oscillator having large oscillation amplitude of $16.9~{\rm μm}$. Applying an offset voltage to the ion trap electrode helped achieve a displacement of the trap center within the time scale of 5 ns. The fluorescence dynamics of the ion were analyzed after the displacement to estimate the oscillation amplitude. The realized trap displacement is one order magnitude larger than that achieved in the previous work. Thus, this result is an important step toward the realization of a gyroscope using a single trapped ion.
Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a projective measurement via state-dependent fluorescence, with near-unit fidelity. This leads to a rich set of line shapes when recording the internal-state excitation probability after a sideband excitation, as a function of the frequency detuning of the displacement drive with respect to the ion's motional frequency. We precisely characterize the coherent displ…
We have studied the dynamics of one and two laser-cooled trapped $^{40}$Ca$^+$ ions by applying electric fields of different nature along the axial direction of the trap, namely, driving the motion with a harmonic dipolar field, or with white noise. These two types of driving induce distinct motional states of the axial modes; a coherent oscillation with the dipolar field, or an enhanced Brownian motion due to an additional contribution to the heating rate from the electric noise. In both scenarios, the sensitivity of an isolated ion and a laser-cooled two-ion crystal has been evaluated and co…
We introduce quantum sensing protocol for detection spatially varying fields by using two coupled harmonic oscillators as a quantum probe. We discuss a physical implementation of the sensing technique with two trapped ions coupled via Coulomb mediated phonon hopping. Our method relies on using the coupling between the localized ion oscillations and the internal states of the trapped ions which allows to measure spatially varying electric and magnetic fields. First we discuss an adiabatic sensing technique which is capable to detect a very small force difference simply by measuring the ion spin…
Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on 2D crystal arrays of approximately one hundred $^9$Be$^+$ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and …
Gravity generated by large masses has been observed using a variety of probes from atomic interferometers to torsional balances. However, gravitational coupling between small masses has never been observed so far. Here, we demonstrate sensitive displacement sensing of the Brownian motion of an optically trapped 7-mg pendulum motion whose natural quality factor is increased to $10^8$ through dissipation dilution. The sensitivity for an integration time of one second corresponds to the displacement generated by the gravitational coupling between the probe and a mm separated 100 mg mass, whose po…
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an en…
We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation …
We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Using suitably chosen internal electronic state-dependent displacements based on bi-chromatic laser fields we map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out using fluorescence detection. Combining the two readout results provides full information about the symmetric characteristic function. We characterize the performance of the technique by applying it to a rang…
Entangling gates in trapped-ion quantum computing have primarily targeted stationary ions with initial motional distributions that are thermal and close to the ground state. However, future systems will likely incur significant non-thermal excitation due to, e.g., ion transport, longer operational times, and increased spatial extent of the trap array. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Molmer-Sorenson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shar…
We propose a design for a superconducting nonlinear interferometer operating at microwave frequencies which allows the measurement of the optical nonlinearity η, with a precision which scales better than the Heisenberg-like limit as δηsimilar to R^{-3/2}, with R the quantification of resources. By designing the nonlinear optical element to possess physically moving parts we are able to use the superconducting nonlinear interferometer to measure the physical displacement r, of the moving parts to a spatial precision of δ(rt) on the order of 10^{-21}m/Hz
Homodyne and heterodyne detection represent "twin-pillars" of quantum displacement sensing using optical cavities, having permitted major breakthroughs including detection of gravitational waves and of the motion of quantum ground-state cooled mechanical oscillators. Both can suffer disadvantages as diagnostics in quantum optomechanics, either through symmetrisation (homodyne), or loss of correlations (heterodyne). We show that, for modest heterodyne beat frequencies ($Ω\sim ω_M/10 \gg Γ$), judicious construction of the autocorrelation of the measured current can either recover (i) a spectrum …
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…
Optimal Displacement Sensing with Spin-Dependent Squeezed States
University of Amsterdam（阿姆斯特丹大学）；QuSoft；University of Sydney（悉尼大学）；Sydney Nano Institute, University of Sydney（悉尼大学悉尼纳米研究所）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Center for Quantum Information, Communication and Computing, Indian Institute of Technology Madras（马德拉斯印度理工学院量子信息、通信与计算中心）
We present a method of sensing AC magnetic fields. The method is based on the construction of a robust qubit by the application of continuous driving fields. Specifically, magnetic noise and power fluctuations of the driving fields do not operate within the robust qubit subspace, and hence, robustness to both external and controller noise is achieved. We consider trapped-ion based implementation via the dipole transitions, which is relevant for several types of ions, such as the $^{40}{\rm{Ca}}^{+}$, $^{88}{\rm{Sr}}^{+}$, and the $^{138}{\rm{Ba}}^{+}$ ions. Taking experimental errors into acco…
Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism correspond…
We introduce quantum sensing schemes for measuring very weak forces with a single trapped ion. They use the spin-motional coupling induced by the laser-ion interaction to transfer the relevant force information to the spin-degree of freedom. Therefore, the force estimation is carried out simply by observing the Ramsey-type oscillations of the ion spin states. Three quantum probes are considered, which are represented by systems obeying the Jaynes-Cummings, quantum Rabi (in 1D) and Jahn-Teller (in 2D) models. By using dynamical decoupling schemes in the Jaynes-Cummings and Jahn-Teller models, o…
We describe a simple protocol for the single-step generation of $N$-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full $N$-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this $N$-body gate operation allows the single-step implementation of a family of $N$-bit gate operations …
We sense the motion of a trapped atomic ion using a sequence of state-dependent ultrafast momentum kicks. We use this atom interferometer to characterize a nearly-pure quantum state with $n=1$ phonon and accurately measure thermal states ranging from near the zero-point energy to $\bar{n}\sim 10^4$, with the possibility of extending at least 100 times higher in energy. The complete energy range of this method spans from the ground state to far outside of the Lamb-Dicke regime, where atomic motion is greater than the optical wavelength. Apart from thermometry, these interferometric techniques a…
Ultra-high sensitivity detection of quantum-scale displacements in cavity optomechanics optimises the combined errors from measurement back-action and imprecisions from incoming quantum noises. This sets the well-known Standard Quantum Limit (SQL). Normal quantum cavity optomechanics allows cooling and detection of a single degree of freedom, along the cavity axis. However, a recent breakthrough that allows quantum ground-state cooling of levitated nanoparticles [Delic et al, arxiv:1911.04406], is uniquely 3D in character, with coupling along the $x$, $y$ and $z$ axes. We investigate current e…
We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. As this method is reversible and state selective it effectively implements a controlled-squeeze gate. We show how to use this resource, that can be useful for quantum information processing with continuous variables, in order to prepare coherent superpositions of states which are squeezed along complementary quadratures. We show that these states, which we denote as "${\mathcal X}$-states", exhibit high sensitivity to small displacements along two …
Direct observation of the optical Magnus effect with a trapped ion
ETH Zürich（苏黎世联邦理工学院）；Paul Scherrer Institut (PSI)（保罗谢尔研究所）；Institute for Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；University of Amsterdam（阿姆斯特丹大学）；Department of Physics, University of Trieste（的里雅斯特大学物理系）；QuSoft
We demonstrate super-resolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a sub-diffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped $^{40}\mathrm{Ca}^+$ ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of $4.2(1)\,μ$m we reach a spatia…
We propose a scheme for detecting time-varying weak forces using quantum probe consisting of single spin and quantum oscillator under the effect of collective dissipation. We study the force estimation in the steady-state regime where the information of the force is extracted by measuring observable of the oscillator such as quadrature and mean phonon excitation. We quantify the force sensitivity in terms of quantum Fisher information and show that it diverges approaching the critical spin-boson coupling making the system sensitive to very small force perturbation. We show that close to the cr…
Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing \cite{RMPforce2003, Rugar2004, YazdiIEEE}. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. Examples for such mechanical oscillators include micro-fabricated cantilevers \cite{YazdiIEEE}, carbon nanotubes \cite{NanotubeForce} as well as single trapped ions \cite{Bollinger, Udem} . The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator thus inc…
We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal f…
We demonstrate control of the absolute phase of an optical lattice with respect to a single trapped ion. The lattice is generated by off-resonant free-space laser beams, we actively stabilize its phase by measuring its ac-Stark shift on a trapped ion. The ion is localized within the standing wave to better than 2\% of its period. The locked lattice allows us to apply displacement operations via resonant optical forces with a controlled direction in phase space. Moreover, we observe the lattice-induced phase evolution of spin superposition states in order to analyze the relevant decoherence mec…
We show how to measure a steady-state magnon population in a magnetostatic mode of a ferromagnet or ferrimagnet, such as yttrium iron garnet. We adopt an optomechanical approach and utilize the magnetoelasticity of the ferromagnet. The magnetostrictive force dispersively couples magnons to the deformation displacement of the ferromagnet, which is proportional to the magnon population. By further coupling the mechanical displacement to an optical cavity that is resonantly driven by a weak laser, the magnetostrictively induced displacement can be sensed by measuring the phase quadrature of the o…
Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this work, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and p…
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology, including both phase and displacement sensing. We identified the optimal graph states for the two sensing modalities and showed that Heisenberg scaling of the accuracy for both phase and displacement sensing can be achieved with local homodyne measurements.
We present an implementation of quantum logic gates via internal state dependent displacements of ions in a linear Paul trap caused by optical dipole forces. Based on a general quantum analysis of the system dynamics we consider specific implementations with alkaline earth ions. For experimentally realistic parameters gate infidelities as low as $10^{-4}$ can be obtained.
Magnetic resonance in an ensemble of laser-cooled trapped Rb atoms is excited using a micro- cantilever with a magnetic tip. The cantilever is mounted on a multi-layer chip designed to capture, cool, and magnetically transport cold atoms. The coupling is observed by measuring the loss from a magnetic trap as the oscillating cantilever induces Zeeman state transitions in the atoms. Interfacing cold atoms with mechanical devices could enable probing and manipulating atomic spins with nanometer spatial resolution and single-spin sensitivity, leading to new capabilities in quantum computation, qua…
We consider the interaction of a magnetically trapped Bose-Einstein condensate of Rubidium atoms with the stationary microwave radiation field sustained by a coplanar waveguide resonator. This coupling allows for the measurement of the magnetic field of the resonator by means of counting the atoms that fall out of the condensate due to hyperfine transitions to non-trapped states. We determine the quantum efficiency of this detection scheme and show that weak microwave fields at the single-photon level can be sensed with an integration time on the order of a second.
Detection of the weakest forces in nature and the search for new physics are aided by increasingly sensitive measurements of the motion of mechanical oscillators. However, the attainable knowledge of an oscillator's motion is limited by quantum fluctuations that exist even if the oscillator is in its lowest possible energy state. Here we demonstrate a widely applicable technique for amplifying coherent displacements of a mechanical oscillator with initial magnitudes well below these zero-point fluctuations. When applying two orthogonal "squeezing" interactions before and after a small displace…
Noise-Limited Sensitivity in Cavity Optomechanical Molecular Sensing Enabled by Quantum Zero-Point Displacement Coupling and Strong Photon-Phonon Interaction for Chiral Detection
Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.
Integrated technologies greatly enhance the prospects for practical quantum information processing and sensing devices based on trapped ions. High-speed and high-fidelity ion state readout is critical for any such application. Integrated detectors offer significant advantages for system portability and can also greatly facilitate parallel operations if a separate detector can be incorporated at each ion-trapping location. Here we demonstrate ion quantum state detection at room temperature utilizing single-photon avalanche diodes (SPADs) integrated directly into the substrate of silicon ion tra…
Quantum Vector Signal Analyzer: Wideband Electric Field Sensing via Motional Raman Transitions
University of California Los Angeles（加州大学洛杉矶分校）；Challenge Institute for Quantum Computation, University of California Los Angeles（加州大学洛杉矶分校量子计算挑战研究所）；Center for Quantum Science and Engineering, University of California Los Angeles（加州大学洛杉矶分校量子科学与工程中心）
Quantum mechanics dictates that the precision of physical measurements must be subject to certain constraints. In the case of inteferometric displacement measurements, these restrictions impose a 'standard quantum limit' (SQL), which optimally balances the precision of a measurement with its unwanted backaction. To go beyond this limit, one must devise more sophisticated measurement techniques, which either 'evade' the backaction of the measurement, or achieve clever cancellation of the unwanted noise at the detector. In the half-century since the SQL was established, systems ranging from LIGO…
Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially,…
State-dependent Gaussian gate set using an optical tweezer for trapped ions
ETH Zürich（苏黎世联邦理工学院）；Paul Scherrer Institut (PSI)（保罗谢尔研究所）；Institute for Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Department of Physics, University of Trieste（的里雅斯特大学物理系）；Quantum Center, ETH Zurich（苏黎世联邦理工学院量子中心）
