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arXiv:1506.07993

Spontaneous-symmetry-breaking assisted quantum sensors

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

Published Jun 26, 2015• 7 citations
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Abstract

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 $/\sqrt{\text{Hz}}$ 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.

DOI
10.48550/arxiv.1506.07993

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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 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.
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 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.
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 show that the quasiadiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, which leads to the collapse of the wave function into one of two possible ground states. The scaling of the final-state properties with the number of atoms and with the intensity of the symmetry-breaking field can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.
Symmetry is crucial for gaining insights into the fundamental properties of physical systems, bringing possibilities in studying exotic phenomena such as quantum phase transitions and ground-state entanglement. Here, we experimentally simulate a highly controllable extended quantum Rabi model, capable of tuning into the ultrastrong or deep coupling regime, in a spin-motion-coupled trapped ion. We observe that the phonon driven by such a model with Z_{2} symmetry preserved (broken) would experience double (single) excitation in the ultrastrong coupling regime. Quantum phenomena such as strong ground-state entanglement and quantum superposition in systems occur with parity symmetry, and these phenomena disappear following the symmetry breaking. We also find sensitive responses for the two-level system entropy and phonon Wigner function in the deep coupling regime, depending on the parameter across the symmetry transition point. This Letter offers the prospect of exploring symmetry-controlled quantum phenomena and their applications in high-precision quantum technologies.