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arXiv:2012.08915 · Physical Review Research

Adiabatic sensing technique for optimal temperature estimation using trapped ions

Aleksandrina V. Kirkova, Weibin Li, Peter A. Ivanov

Published Mar 15, 2021• 16 citations
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Abstract

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 nonlinear 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 configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition.We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cramér-Rao bound for a quantum oscillator at thermal equilibrium.

DOI
10.1103/physrevresearch.3.013244

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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 nonlinear 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 configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition.We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cramér-Rao bound for a quantum oscillator at thermal equilibrium.
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).
The measurement of phonon numbers in laser-cooled ions is pivotal for determining whether an ion is in its ground state. Commonly employed experimental techniques include the analysis of red-to-blue sideband ratios and the adiabatic evolution on the red-sideband transition. We introduce a theoretical approach utilizing composite pulses that enables the direct measurement of the population in a specific Fock state, eliminating the need for state evolution fitting. This method offers a more straightforward quantification of higher Fock state populations compared to the red-sideband adiabatic evolution technique. By applying quantum optimal control strategies, we enhance the fidelity of the unitary operations executed by the composite pulses. By utilizing numerical calculation methods of quantum optimal control, we have overcome the limitations of analytical calculations that require weak coupling and first-order Lamb-Dicke expansion, allowing our method to achieve sufficient accuracy in strong coupling regime. Furthermore, we also present a data processing method that allows the estimated value of the phonon number to be closer to the true value. An illustrative example of its efficacy in high Fock state measurement is provided.
I propose an efficient method for measuring nonlinear coupling between the collective axial breathing mode and the radial rocking mode induced by the mutual Coulomb repulsion in linear ion crystal. The quantum sensing technique is based on the laser-induced coupling between one of the vibrational modes and the internal ion's spin states which allows to estimate the nonlinear coupling either by measuring the phonon probability distribution or by directly observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of nonlinear phonon coupling the off-resonance interaction between the ion spin states and the axial breathing mode leads to spin-dependent phonon squeezing of the radial rocking mode. Thus the nonlinear coupling can be estimated by measuring population distribution of the motional squeezed state. Furthermore, I show that the off-resonance interaction between the spin and the radial rocking mode creates a spin-dependent beam splitter operation between the two vibrational modes. Thus the parameter estimation can be carried out by detecting the ion spin populations. Finally, I show that the measurement uncertainty precision can reach the Heisenberg limit by using an entangled state between the two collective modes.
Understanding how thermal fluctuations modify or suppress quantum-enhanced sensing is a central problem in quantum metrology. Closely related questions arise in quantum thermodynamics, particularly regarding the relation between the work induced by a signal and the information acquired by a sensor. Here, we establish general relations among the sensitivity of thermal quantum states, as quantified by different quantum Fisher information metrics, their temperature dependence, and the work induced by a unitary signal. We further show that, at high temperature, all monotone QFI metrics coincide to leading order with a universal quantity that can be expressed as the variance of a simple observable and itself defines a lesser-known QFI metric. This emergent uniqueness is reminiscent of the uniqueness of classical Fisher information in information geometry. In continuous-variable systems, the infinite-temperature limit is finite and generically non-zero for quadratic Gaussian signals, while it diverges for higher-degree signals. Remarkably, for any purely quadratic signal generator, the infinite-temperature QFI is at least twice the zero-temperature SLD QFI or, equivalently, at least eight times the ground-state variance of the generator. Consequently, the Cramér--Rao lower bound on the estimator variance is reduced by at least a factor of two. We illustrate these results using harmonic chains of bosonic modes relevant to trapped-ion platforms and quantum field-theoretic models.
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 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 n[over ¯]~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 are useful for characterizing ultrafast entangling gates between multiple trapped ions.