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arXiv:2310.12445 · Physical Review A

Antisymmetry-breaking-coupling–enhanced sensing of quantum reservoirs

Ji-Bing Yuan, Zhi-Min Tang, Ya‐Ju Song, Shi-Qing Tang, Zhao-Hui Peng, Xin-Wen Wang, Le‐Man Kuang

Published Jul 18, 2024• 3 citations
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Abstract

We investigate the use of a single generalized dephasing qubit for sensing a quantum reservoir, where the antisymmetry of the coupling between the qubit and its reservoir is broken. Our results indicate that, in addition to the decay factor encoding channel, the antisymmetry breaking coupling introduces another phase factor encoding channel. We propose an optimal measurement strategy for the generalized dephasing qubit, which enables the practical measurement precision to reach the theoretical ultimate precision quantified by the quantum signal-to-noise ratio (QSNR). As an application example, the generalized dephasing qubit is employed to estimate the $s$-wave scattering length of an atomic Bose-Einstein condensate. It is found that the QSNR contributed by the antisymmetry breaking coupling is at least two orders of magnitude higher than the QSNR contributed by the antisymmetry coupling at the millisecond timescale, and the optimal relative error can achieve a scaling $\ensuremath{\propto}1/(\ensuremath{\chi}t)$ in long-term encoding, where $\ensuremath{\chi}$ represents the relative driving strength and $t$ is the encoding time. Our work opens a way for supersensitive sensing of quantum reservoirs.

DOI
10.1103/physreva.110.012613

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We investigate the use of a single generalized dephasing qubit for sensing a quantum reservoir, where the antisymmetry of the coupling between the qubit and its reservoir is broken. Our results indicate that, in addition to the decay factor encoding channel, the antisymmetry breaking coupling introduces another phase factor encoding channel. We propose an optimal measurement strategy for the generalized dephasing qubit, which enables the practical measurement precision to reach the theoretical ultimate precision quantified by the quantum signal-to-noise ratio (QSNR). As an application example, the generalized dephasing qubit is employed to estimate the sss-wave scattering length of an atomic Bose-Einstein condensate. It is found that the QSNR contributed by the antisymmetry breaking coupling is at least two orders of magnitude higher than the QSNR contributed by the antisymmetry coupling at the millisecond timescale, and the optimal relative error can achieve a scaling \ensuremath∝1/(\ensuremathχt)\ensuremath{\propto}1/(\ensuremath{\chi}t)\ensuremath∝1/(\ensuremathχt) in long-term encoding, where \ensuremathχ\ensuremath{\chi}\ensuremathχ represents the relative driving strength and ttt is the encoding time. Our work opens a way for supersensitive sensing of quantum reservoirs.
We examine a system in which an impurity qubit is immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate whose collective excitations act as a depasing reservoir for the qubit. The relative dipole-dipole interaction strength is estimated by the probe qubit dephasing. The ultimate precision of this estimation is quantified by the quantum Fisher information, which can be obtained by means of measuring quantum coherence of the probe qubit. Our findings indicate that, in the interval where roton excitations appear, the quantum Fisher information oscillates periodically with the encoding time ttt, and the amplitude of these oscillations increases alongside the extension of ttt. Moreover, we analytically determine that the envelope curve formed by the local maximum points satisfies the functional relationship At+Bt1/2+CAt+Bt^{1/2}+CAt+Bt1/2+C during long-term encoding scenarios, where AAA, BBB, CCC are positive numbers. It is also revealed that the highly non-Markovian effects caused by the roton softening of the excitation spectrum allow long encoding time to serve as a resource for enhancing sensing precision. Our work provides a new pathway for enhancing the sensing precision of dephasing qubits.
We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength ηηη, the Ohmicity parameter sss, and the cutoff frequency ωcω_cωc​ to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio Q\mathcal{Q}Q. We show that the evolution of Q\mathcal{Q}Q with the scaled time ωctω_c tωc​t is independent of ωcω_cωc​, and peaks at an optimal time toptt_{\text{opt}}topt​, yielding optimal sensitivity Qopt\mathcal{Q}_{\text{opt}}Qopt​. We analyze how Qopt\mathcal{Q}_{\text{opt}}Qopt​ depends on ηηη, sss and the temperature TTT. Our results demonstrate that, for any Ohmic environment, provided that ωctopt≪1ω_c t_{\text{opt}} \ll 1ωc​topt​≪1, Qopt\mathcal{Q}_{\text{opt}}Qopt​ always reaches the upper bound: Qmax=0.648\mathcal{Q}_{\text{max}} = 0.648Qmax​=0.648 at zero temperature, and consistently attains Qmax/4\mathcal{Q}_{\text{max}}/4Qmax​/4 at high temperatures. Remarkably, we find that increasing the scaled temperature T/ωcT/ω_cT/ωc​ can enhance Qopt\mathcal{Q}_{\text{opt}}Qopt​ by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.
Quantum sensors have been shown to enable more precise measurements than classical sensors. By using entanglement and coherent evolution, the estimation error can be made to scale better in interrogation time, photon count, and other resources, achieving Heisenberg-limited scaling. However, environmental noise and hardware errors typically destroy the coherence of the sensitive quantum states. This motivates the use of fault-tolerant techniques to create more robust quantum sensing protocols. Such fault-tolerant quantum sensing approaches have been shown to enhance sensitivity for qubit systems, but many practical sensors require bosonic probes. In this paper, we propose a fault-tolerant protocol using bosons to estimate displacements in the presence of dephasing noise. We construct an optimal error-correcting code under a mean photon-number constraint. Controlled displacements couple the probe to a repetition-encoded qubit register, while repeated boson-parity measurements and resets remove probe noise without erasing the stored logical phase. Under circuit-level bit-flip noise, a distance-ddd code suppresses logical failures to order p(d+1)/2p^{(d+1)/2}p(d+1)/2. We show that, for a decay rate γAγ_AγA​, a total sensing time TTT and a mean photon number budget NNN, and for sufficiently small residual signals, the Fisher information scales as NT2NT^2NT2 over interrogation times of order γA−(d+1)/2γ_A^{-(d+1)/2}γA−(d+1)/2​. This is a significant improvement over the non-fault-tolerant approach that achieves Heisenberg scaling only for a total time O(γA−1)\mathcal O(γ_A^{-1})O(γA−1​).
We propose an approach to implement a supersensitive estimation of the key parameters of the Ohmic-family spectral density with coherent spin states as the quantum sensor. This method can dramatically improve the estimation precision of the reservoir coupling strength as well as the cutoff frequency of the spectral density, by using both the number of spins NNN and encoding time ttt as effective resources. The quantum Fisher information indicates that the estimation sensitivity of the spectral density can surpass the shot-noise limit for all the sub-Ohmic, Ohmic, and super-Ohmic reservoirs. In particular, for super-Ohmic reservoirs, the precision can achieve a scaling $\ensuremath{\propto}1/(Nt)$. We also present the measurement scheme which can saturate the quantum Cram\'er-Rao bound.
We investigate the sensing performance of a single-qubit quantum thermometer within a non-Markovian dynamical framework. By employing an exactly numerical hierarchical equations of the motion method, we go beyond traditional paradigms of the Born-Markov theory, the pure dephasing mechanism, and the weak-coupling approximation, which were commonly used in many previous studies of quantum thermometry. We find (i) the non-Markovian characteristics may boost the estimation efficiency, (ii) the sensitivity of quantum thermometry can be effectively optimized by engineering the proportions of different coupling operators in the whole sensor-reservoir interaction Hamiltonian, and (iii) a threshold, above which the strong sensor-reservoir coupling can significantly enhance the sensing precision in the long-encoding-time regime. Our results may have certain applications for high-resolution quantum thermometry.
Microwave squeezing represents the ultimate sensitivity frontier for superconducting qubit measurement. However, measurement enhancement has remained elusive, in part because integration with standard dispersive readout pollutes the signal channel with antisqueezed noise. Here we induce a stroboscopic light-matter coupling with superior squeezing compatibility, and observe an increase in the final signal-to-noise ratio of 24%. Squeezing the orthogonal phase slows measurement-induced dephasing by a factor of 1.8. This scheme provides a means to the practical application of squeezing for qubit measurement.