Abstract We propose and analyze a driven-dissipative quantum sensor that is continuously monitored close to a dissipative critical point. The sensor relies on the critical open Rabi model with the spin and phonon degrees of freedom of a single trapped ion to achieve criticality-enhanced sensitivity. Effective continuous monitoring of the sensor is realized via a co-trapped ancilla ion that switches between dark and bright internal states conditioned on a ‘jump’ of the phonon population which, remarkably, achieves nearly perfect phonon counting despite a low photon collection efficiency. By exploiting both dissipative criticality and efficient continuous readout, the sensor device achieves highly precise sensing of oscillating electric field gradients at a criticality-enhanced precision scaling beyond the standard quantum limit, which we demonstrate is robust to the experimental imperfections in real-world applications.
Abstract We propose and analyze a driven-dissipative quantum sensor that is continuously monitored close to a dissipative critical point. The sensor relies on the critical open Rabi model with the spin and phonon degrees of freedom of a single trapped ion to achieve criticality-enhanced sensitivity. Effective continuous monitoring of the sensor is realized via a co-trapped ancilla ion that switches between dark and bright internal states conditioned on a ‘jump’ of the phonon population which, remarkably, achieves nearly perfect phonon counting despite a low photon collection efficiency. By exploiting both dissipative criticality and efficient continuous readout, the sensor device achieves highly precise sensing of oscillating electric field gradients at a criticality-enhanced precision scaling beyond the standard quantum limit, which we demonstrate is robust to the experimental imperfections in real-world applications.
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.
Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 to 300 kHz is crucial for advancing both fundamental science and practical applications owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint because efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor based on an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with a sensitivity of 403.8 μV/(m Hz1/2) and a detection limit of 61.5 μV/m. In addition, this approach also shows remarkable robustness against noise. Our study helps realize practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.
Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.
The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser (nˉ<10) using a trapped 40Ca+ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of 14.15±0.77μV/m/Hz and a minimum detectable field variation of δEmin≈1.83μV/m. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.
Abstract 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 engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
Continuous monitoring of open quantum-optical systems offers a promising route towards quantum-enhanced sensing. In such sensing schemes, the ultimate precision limit is dictated by the quantum Cramér-Rao bound. However, reaching this fundamental bound with established continuous measurement techniques has remained an outstanding challenge. Here, we present an approach tailored to open quantum-optical sensors operating near dissipative critical points. The key insight of our approach is to exploit a synergy between the intrinsic critical dynamics and the unavoidable quantum measurement backaction of continuous homodyne detection. By carefully aligning the homodyne phase to the squeezing angle of the sensor state, quantum backaction can be evaded in the critical dynamics, thereby significantly boosting the attainable precision. We demonstrate the broad applicability of this approach across several sensor models and for both single- and multi-parameter estimation, showing that it consistently narrows the gap toward the ultimate precision bound.