Balancing high sensitivity with a broad dynamic range is a fundamental challenge in measurement science, as improving one often compromises the other. While traditional quantum metrology has prioritized enhancing local sensitivity, a large dynamic range is crucial for applications such as atomic clocks, where extended phase interrogation times contribute to wider phase range. In this Letter, we introduce a novel quantum deamplification mechanism that extends dynamic range at a minimal cost of sensitivity. Our approach uses two sequential spin-squeezing operations to generate and detect an entangled probe state, respectively. We demonstrate that the optimal quantum interferometer limit can be approached through two-axis countertwisting dynamics. Further expansion of dynamic range is possible by using sequential quantum deamplification interspersed with phase encoding processes. Additionally, we show that robustness against detection noise can be enhanced by a hybrid sensing scheme that combines quantum deamplification with quantum amplification. Our protocol is within the reach of state-of-the-art atomic-molecular-optical platforms, offering a scalable, noise-resilient pathway for entanglement-enhanced metrology.
Balancing high sensitivity with a broad dynamic range is a fundamental challenge in measurement science, as improving one often compromises the other. While traditional quantum metrology has prioritized enhancing local sensitivity, a large dynamic range is crucial for applications such as atomic clocks, where extended phase interrogation times contribute to wider phase range. In this Letter, we introduce a novel quantum deamplification mechanism that extends dynamic range at a minimal cost of sensitivity. Our approach uses two sequential spin-squeezing operations to generate and detect an entangled probe state, respectively. We demonstrate that the optimal quantum interferometer limit can be approached through two-axis countertwisting dynamics. Further expansion of dynamic range is possible by using sequential quantum deamplification interspersed with phase encoding processes. Additionally, we show that robustness against detection noise can be enhanced by a hybrid sensing scheme that combines quantum deamplification with quantum amplification. Our protocol is within the reach of state-of-the-art atomic-molecular-optical platforms, offering a scalable, noise-resilient pathway for entanglement-enhanced metrology.
Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states, accounting for common-mode phase noise spanning the full 2π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit. Specifically, we identify optimal squeezed states that minimize the differential phase variance, scaling as N−2/3, while eliminating bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér-Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
Quantum metrology explores optimal quantum protocols for parameter estimation. In the context of optical atomic clocks, conventional protocols focus on optimal input states and measurements to achieve enhanced sensitivities. However, such protocols are typically limited by phase slip errors inflicted due to the decoherence of the local oscillator. Here, we study schemes to extend the dynamic range and overcome phase slip noise through weak measurements with ancilla qubits. Using coherent spin states, we find optimal weak measurements protocols: we identify optimal measurement strength for any given interrogation time and number of atoms. Then, we combine weak and projective measurements to construct a protocol that asymptotically saturates the noiseless precision limits and outperforms previously proposed methods for phase slip noise suppression.
In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1 / N . Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of 1 / N , while increasing the quantum noise by N and amplifying the phase by a factor of N . Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N . Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of 2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.
In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1/N. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N, while increasing the quantum noise by N, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of N atoms, behaving as a single entity with an N-fold increase in Compton frequency. The resulting N-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an N-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
Entanglement-enhanced atom interferometry has the potential of surpassing the standard quantum limit and eventually reaching the ultimate Heisenberg bound. The experimental progress is, however, hindered by various technical noise sources, including the noise in the detection of the output quantum state. The influence of detection noise can be largely overcome by exploiting echo schemes, where the entanglement-generating interaction is repeated after the interferometer sequence. Here, we propose an echo protocol that uses two-axis countertwisting as the main nonlinear interaction. We demonstrate that the scheme is robust to detection noise and its performance is superior compared to the already demonstrated one-axis twisting echo scheme. In particular, the sensitivity maintains the Heisenberg scaling in the limit of a large particle number. Finally, we show that the protocol can be implemented with spinor Bose-Einstein condensates. Our results thus outline a realistic approach to mitigate the detection noise in quantum-enhanced interferometry.
Quantum metrology harnesses nonclassical resources including squeezed states and quantum entanglement to overcome fundamental limitations imposed by the shot-noise limit (SNL). While conventional optical interferometers for phase detection typically operate in the MHz-frequency regime due to technical noise constraints at lower frequencies, numerous practical applications demand operation in the kHz regime or below. Here, we present a truncated SU(1,1) interferometric configuration that achieves enhanced phase sensitivity in the low-frequency (kHz) domain by exploiting quantum entanglement generated through two-mode squeezed states. Our approach incorporates quantum sideband control to achieve quantum correlations across multiple low-frequency bands while simultaneously suppressing technical noise. Through precise locking of optimal phase, we demonstrate a significant improvement in signal-to-noise ratio within the kHz range, with phase sensitivity surpassing the SNL by 2.0 ± 0.2 dB. These experimental results provide crucial validation for extending entanglement-enhanced optical interferometry into low-frequency metrological applications and establish novel methodologies for optical modulation and sideband-based quantum information processing and quantum sensing protocols.