Spin cat states are promising candidates for achieving Heisenberg-limited quantum metrology. It is suggested that spin cat states can be generated by adiabatic evolution. However, due to the limited coherence time, the adiabatic process may be too slow to be practical. To speed up the state generation, we propose to use machine optimization to generate desired spin cat states. Our proposed scheme relies only on experimentally demonstrated one-axis twisting interactions with piecewise time-modulation of rotations designed via machine optimization. The required evolution time is much shorter than the one with adiabatic evolution and it does not make large modification to the existing experimental setups. Our protocol with machine optimization is efficient and easy to be implemented in state-of-the-art experiments.
Spin cat states are promising candidates for achieving Heisenberg-limited quantum metrology. It is suggested that spin cat states can be generated by adiabatic evolution. However, due to the limited coherence time, the adiabatic process may be too slow to be practical. To speed up the state generation, we propose to use machine optimization to generate desired spin cat states. Our proposed scheme relies only on experimentally demonstrated one-axis twisting interactions with piecewise time-modulation of rotations designed via machine optimization. The required evolution time is much shorter than the one with adiabatic evolution and it does not make large modification to the existing experimental setups. Our protocol with machine optimization is efficient and easy to be implemented in state-of-the-art experiments.
Abstract Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\frac{\ensuremath{\pi}}{2}$ pulses, and a population measurement, which can be realized via current experimental techniques. Compared with the twisting echo scheme on spin squeezed states, our scheme with spin cat states is more robust against detection noise. Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with non-Gaussian entangled states.
We propose a scheme for the generation of optimal squeezed states for Ramsey interferometry. The scheme consists of an alternating series of one-axis twisting pulses and rotations, both of which are straightforward to implement experimentally. The resulting states show a metrological gain proportional to the Heisenberg limit. We demonstrate that the Heisenberg scaling is maintained even when placing constraints on the amplitude of the pulses implementing the one-axis twisting and when taking into account realistic losses due to photon scattering.
We use machine optimization to develop a quantum sensing scheme that achieves significantly better sensitivity than traditional schemes with the same quantum resources. Utilizing one-axis twisting dynamics to generate quantum entanglement, we find that, rather than dividing the temporal resources into separate "state-preparation" and "interrogation" stages, a complicated machine-designed sequence of rotations allows for the generation of metrologically useful entanglement while the parameter is interrogated. This provides much higher sensitivities for a given total time compared to states generated via traditional one-axis twisting schemes. This approach could be applied to other methods of generating quantum-enhanced states, allowing for atomic clocks, magnetometers, and inertial sensors with increased sensitivities.
Achieving higher precision in quantum metrology demands the optimization of both entangled-state preparation and readout processes. However, direct machine optimization using variational dynamics becomes impractical and time consuming, particularly with a large particle number. Here, we develop a heuristic recursive screening-breeding algorithm designed to efficiently optimize variational dynamics for scalable quantum metrology. Leveraging the similarity between optimal variables for adjacent particle numbers, the algorithm recursively updates variables from few to many particles, significantly reducing computational overhead. This enables the identification of optimized dynamics for entangled state preparation and readout, even with a large particle number. As a proof of concept, we apply the algorithm to efficiently optimize twist-and-turn dynamics for spin cat state preparation, interaction-based readout, and time-reversal metrology. Notably, in well-recursive cases, optimized variables can be approximated via fitting without recursion. Our recursive optimization algorithm establishes an efficient framework for scalable quantum metrology protocols, providing a practical avenue for quantum sensing with many-body systems.
Generating macroscopic quantum entanglement is central to quantum metrology. While traversing a quantum critical point yields Heisenberg-limited precision, adiabatic schemes are restricted by slow dynamics and decoherence. Here, we propose a non-adiabatic Floquet protocol in a single-cavity Bose-Einstein condensate to circumvent these limitations. By applying rapid rotations and phase jumps, we dynamically synthesize effective Two-Axis Twisting (TAT) interactions from native longitudinal couplings. To evaluate this beyond mean-field limits, we develop an exact finite-state automaton Matrix Product Operator (MPO) encoding that strictly bounds the virtual dimension to O(1), enabling exact DMRG and TDVP simulations for large systems. Tracking non-equilibrium Floquet TAT dynamics and environmental decoherence for N=103 ensembles, we demonstrate that the quench rapidly generates Heisenberg-limited spin squeezing (ξR2∼1/N). The microsecond timescale of this protocol decouples the generation process from typical millisecond decoherence, with phenomenological models revealing an optimal extraction time near t≈3.26μs. This work establishes a feasible route for realizing Heisenberg-limited metrology in current cavity-QED platforms.