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.
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.
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.
One-axis twisting (OAT) and two-axis twisting (TAT) are well-known methods for achieving entanglement-enhanced quantum metrology, and their time-reversal echo offers a potent tool for approaching the Heisenberg limit even with detection noise. However, flipping the sign of interaction to implement the time-reversal echo is generally challenging. Here, we propose an echo protocol based on synthetic TAT from interaction-fixed OAT in a pseudospin-1/2 ensemble to achieve time-reversal quantum metrology. By applying modulation pulses around two different orthogonal directions, the effective TAT and its echo can be realized without changing the interaction. We demonstrate that this protocol not only outperforms the OAT echo scheme in both metrological gain and evolution time but is also robust against detection noise. Our protocol presents a TAT echo scheme that effectively avoids flipping the sign of interaction, providing a viable method for improving precision and robustness of quantum metrology.
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
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.
We consider the role of detection noise in quantum-enhanced metrology in collective spin systems and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. We then present an interaction-based readout utilizing the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis countertwisting, twist-and-turn squeezing, quantum nondemolition measurements, and adiabatically scanning through a quantum phase transition. We demonstrate that our method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum-sensing devices in the presence of unavoidable detection noise.
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.