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arXiv:2309.02291 · Physical Review Research

Revisiting the impact of dissipation on time-reversed one-axis-twist quantum-sensing protocols

Martin Koppenhöfer, Aashish A. Clerk

Published Dec 22, 2023• 8 citations
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Abstract

Spin squeezing can increase the sensitivity of interferometric measurements of small signals in large spin ensembles beyond the standard quantum limit. In many practical settings, the ideal metrological gain is limited by imperfect readout of the sensor. To overcome this issue, protocols based on time reversal of unitary one-axis-twist (OAT) spin-squeezing dynamics have been proposed. Such protocols mitigate readout noise and, when implemented using cavity feedback, have been argued to also be robust against dissipation as long as the collective cooperativity of the system is sufficiently large [Davis et al., Phys. Rev. Lett. 116, 053601 (2016)]. Here, we perform a careful systematic study of dissipative effects on three different implementations of a OAT twist-untwist sensing scheme (based on symmetric as well as asymmetric cavity feedback and on a Tavis-Cummings interaction). Our full treatment shows that the three approaches have markedly different properties and resilience when subject to dissipation. Moreover, the metrological gain for an implementation using symmetric cavity feedback is more sensitive to undesired dissipation than was previously appreciated.

DOI
10.1103/physrevresearch.5.043279

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Spin squeezing can increase the sensitivity of interferometric measurements of small signals in large spin ensembles beyond the standard quantum limit. In many practical settings, the ideal metrological gain is limited by imperfect readout of the sensor. To overcome this issue, protocols based on time reversal of unitary one-axis-twist (OAT) spin-squeezing dynamics have been proposed. Such protocols mitigate readout noise and, when implemented using cavity feedback, have been argued to also be robust against dissipation as long as the collective cooperativity of the system is sufficiently large [Davis et al., Phys. Rev. Lett. 116, 053601 (2016)]. Here, we perform a careful systematic study of dissipative effects on three different implementations of a OAT twist-untwist sensing scheme (based on symmetric as well as asymmetric cavity feedback and on a Tavis-Cummings interaction). Our full treatment shows that the three approaches have markedly different properties and resilience when subject to dissipation. Moreover, the metrological gain for an implementation using symmetric cavity feedback is more sensitive to undesired dissipation than was previously appreciated.
Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.
One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.
Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics $U(\ensuremath{\phi})$ (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of $\ensuremath{\phi}$ even when the nonlinearities are applied for times much shorter than required to produce Schr\"odinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator $\stackrel{P\vec}{n}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{J}$. We consider the following physical settings: all-to-all interactions generated by one-axis twisting Jz2{J}_{z}^{2}Jz2​ (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cram\'er-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of LLL without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an LLL layer quantum alternating operator ansatz.
Harnessing dissipation in the presence of strong symmetries has recently emerged as a promising route for generating entanglement in atomic clocks. However, previous proposals relied on regimes where cavity photons can be adiabatically eliminated, significantly limiting their applicability to experimentally relevant cavity-QED regimes that lie in or near the resolved vacuum Rabi splitting regime. Here we show that symmetry-protected dissipative spin squeezing can be realized even when cavity photons actively participate in the dynamics, extending the experimental relevance of the protocol. We study a three-level ensemble of 87Sr^{87}\mathrm{Sr}87Sr atoms coupled to an optical cavity in the resolved vacuum Rabi splitting regime and demonstrate that, with smooth ramps of the drive amplitude and detunings, the driven-dissipative dynamics enters a stable low-photon regime in which nonadiabatic cavity excitations and sector-resolving photon leakage can be controlled. Within this low-photon operating window, sector-resolving photon leakage is suppressed and the sector-dependent geometric phase realizes effective one-axis twisting. At the end of the protocol the entanglement can also be efficiently transferred directly onto the long-lived clock states by turning the drive off. For experimentally realistic parameters, we theoretically show that more than 25 dB25\,\mathrm{dB}25dB of squeezing can be generated for 10510^5105 atoms, closely saturating the ideal one-axis twisting scaling ξmin⁡2∝N−2/3ξ_{\min}^2 \propto N^{-2/3}ξmin2​∝N−2/3. At fixed cooperativity, the optimized squeezing remains broadly comparable to the unresolved-regime implementation, while the resolved-regime implementation reaches comparable squeezing on a substantially shorter physical timescale. These results establish symmetry-protected dissipative dynamics as a practical route to beyond the standard-quantum-limit performance in optical-clock platforms.
Quantum metrology protocols exploiting ensembles of N two-level systems and Ramsey-style measurements are ubiquitous.However, in many cases excess readout noise severely degrades the measurement sensitivity; in particular in sensors based on ensembles of solid-state defect spins.We present a dissipative "spin-amplification" protocol that allows us to dramatically improve the sensitivity of such schemes, even in the presence of realistic intrinsic dissipation and noise.Our method is based on exploiting collective (i.e., superradiant) spin decay, an effect that is usually seen as a nuisance because it limits spin-squeezing protocols.We show that our approach can allow a system with a highly imperfect spin readout to approach standard-quantum-limit-like scaling in N within a factor of 2, without needing to change the actual readout mechanism.Our ideas are compatible with several state-of-the-art experimental platforms where an ensemble of solid-state spins (NV centers, SiV centers) is coupled to a common microwave or mechanical mode.
Quantum-enhanced sensing with atomic ensembles has predominantly focused on qubit-based protocols, despite the growing ability of many experimental platforms to coherently control and entangle multi-level systems. Here, we investigate quantum-enhanced sensing with qutrit ensembles by introducing three experimentally feasible qutrit generalisations of the one-axis twisting (OAT) model that involve entangling operations only between two levels, while the third level primarily acts as a spectator. We characterize the metrological utility of the dynamically generated states using the quantum Fisher information toolbox. We find numerically that all three models offer considerable freedom in encoding direction for quantum-enhanced sensing, with up to 6 out of 8 possible directions exhibit near-Heisenberg scaling after a short evolution time. We discuss experimental access to this enhanced metrological precision via effective time-reversal protocols. Furthermore, we examine the practical issues of estimation ambiguity and local dissipation, and show that they can be largely overcome by optimizing the sensor operating point. Finally, we show that the measurement incompatibility in estimating multiple parameters simultaneously encoded in different directions with near-Heisenberg scaling of precision is suppressed at the zero operating point as the system size increases. In the process, we find that one of the models enables near-Heisenberg scaling metrology with a pair of commuting generators, a possibility that arises from the su(3)su(3)su(3) algebra and is thus absent in qubit-ensemble based sensors of collective SU(2)SU(2)SU(2) rotations.