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arXiv:1602.04072 · Scientific Reports

High-precision force sensing using a single trapped ion

Peter A. Ivanov, Nikolay V. Vitanov, Kilian Singer

Published Jun 16, 2016• 30 citations
arXivHTMLPDF

Abstract

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, our force sensing protocols can be made robust to the spin dephasing caused by the thermal and magnetic field fluctuations. In the quantum-Rabi probe, the residual spin-phonon coupling vanishes, which makes this sensing protocol naturally robust to thermally-induced spin dephasing. We show that the proposed techniques can be used to sense the axial and transverse components of the force with a sensitivity beyond the range, i.e. in the (xennonewton, 10(-27)). The Jahn-Teller protocol, in particular, can be used to implement a two-channel vector spectrum analyzer for measuring ultra-low voltages.

DOI
10.1038/srep28078

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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, our force sensing protocols can be made robust to the spin dephasing caused by the thermal and magnetic field fluctuations. In the quantum-Rabi probe, the residual spin-phonon coupling vanishes, which makes this sensing protocol naturally robust to thermally-induced spin dephasing. We show that the proposed techniques can be used to sense the axial and transverse components of the force with a sensitivity beyond the range, i.e. in the (xennonewton, 10(-27)). The Jahn-Teller protocol, in particular, can be used to implement a two-channel vector spectrum analyzer for measuring ultra-low voltages.
We propose force sensing protocols using a linear ion chain which can operate beyond the quantum standard limit. We show that oscillating forces that are off resonance with the motional trap frequency can be detected very efficiently by using quantum probes represented by various spin-boson models. We demonstrate that the temporal evolution of a quantum probe described by the Dicke model can be mapped on the nonlinear Ramsey interferometry which allows us to detect far-detuned forces simply by measuring the collective spin populations. Moreover, we show that the measurement uncertainty can reach the Heisenberg limit by using initial spin-correlated states, instead of motional entangled states. An important advantage of the sensing technique is its natural robustness against the thermally induced dephasing, which extends the coherence time of the measurement protocol. Furthermore, we introduce a sensing scheme that utilizes the strong spin-phonon coupling to improve the force estimation. We show that for a quantum probe represented by the quantum Rabi model the force sensitivity can overcome the one achieved by the simple harmonic oscillator force sensor.
Abstract We propose a scheme for detecting time-varying weak forces using a quantum probe consisting of a 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 critical coupling the measurement of the oscillator quadrature is optimal in a sense that saturates the fundamental Cramer–Rao bound. Furthermore, we study the force estimation in the presence of phonon squeezing and show that it can significantly improve the sensitivity reaching minimal detectable force of order of xN (1xN = 10 −27 N).
We propose a quantum sensing scheme for measuring weak forces based on a symmetry-breaking adiabatic transition in the quantum Rabi model. We show that the system described by the Rabi Hamiltonian can serve as a sensor for extremely weak forces with sensitivity beyond the yN /Hz/\sqrt{\text{Hz}}/Hz​ range. We propose an implementation of this sensing protocol using a single trapped ion. A major advantage of our scheme is that the force detection is performed by projective measurement of the population of the spin states at the end of the transition, instead of the far slower phonon number measurement used hitherto.
We present a technique to measure the amplitude of a center-of-mass (c.m.) motion of a two-dimensional ion crystal of ∼100 ions. By sensing motion at frequencies far from the c.m. resonance frequency, we experimentally determine the technique's measurement imprecision. We resolve amplitudes as small as 50 pm, 40 times smaller than the c.m. 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 c.m. 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 c.m. 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.
A trapped-ion harmonic oscillator represents a rich and well-controlled platform for tests of quantum physics, with applications to quantum simulations, quantum sensing, and quantum information processing. Owing to its net charge, the ion's motion is affected by changes in the electric potential. Consequently, electric field and potential curvature noise will limit the coherence of the ion's harmonic oscillation. While in some respects, this serves as a limitation in the performance of the trapped ion system (for example, in the fidelity of two-qubit gates or quantum simulations with motional quanta), it also opens an opportunity to use the ion as a precise field sensor and to use engineered quantum states of motion to enhance the sensitivity to these fields beyond the standard quantum limit (SQL). This thesis describes the implementation of such applications on a single beryllium ion confined in a Paul trap. In the thesis, I present the theory of an ideal harmonic oscillator and the implementation of this system using the motion of a single trapped ion, including producing special quantum states of motion; these states include the energy eigenstates of the harmonic oscillator, called number states, up to n=100, superpositions of number states of the form (1/√2)(|0> + |n>), with n up to 18, and coherently displaced number states with an average occupation up to approximately 300. I describe how we use these quantum states of motion for precise sensing of fluctuations of the harmonic oscillator frequency. The sensitivity of the (1/√2)(|0> + |n>) state ideally follows the 1/n Heisenberg scaling for frequency sensitivity. Additionally, I describe investigations of the spectrum of motional frequency noise using a series of coherent displacements of the motion of the ion, with features similar to Ramsey and dynamical decoupling sequences for two-level systems. While these displaced states don't improve sensitivity over the SQL, they can be simply and rapidly implemented with trapped ions. I discuss extensions to all of these experiments, including to multiple ions in a new trap designed to confine 3 or 4 ions in individually tunable potential wells.
We propose an adiabatic Ramsey interferometry technique for detecting weak nonlinearities with trapped ions. The method relies on using the quantum Rabi model as a probe, which is sensitive to nonlinear symmetry-breaking perturbations. We show that the couplings which arise either from anharmonic terms of the trapping potential or due to higher order terms in the Coulomb interaction expansion can be efficiently estimated by measuring the spin state probabilities alone. We show that the spin signal is amplified by the mean-phonon excitations, which results in the estimation precision reaching the super-Heisenberg limit. Notably, achieving such high-precision estimation does not require specific entangled state preparation and can be reached even for initial thermal motion state. Furthermore, we show that the super-Heisenberg scaling can be observed even in the presence of weak spin-dephasing.