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arXiv:1408.0067 · Physical Review A

Squeezed-light-enhanced atom interferometry below the standard quantum limit

Stuart S. Szigeti, Behnam Tonekaboni, W. Y. Sarah Lau, Samantha N. Hood, Simon A. Haine

Published Dec 22, 2014• 44 citations
arXivHTMLPDF

Abstract

We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e., low-frequency squeezing), (2) two-mode squeezed optical vacuum (i.e., high-frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.

DOI
10.1103/physreva.90.063630

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Optics Express•Jul 26, 2023•13 citations
We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e., low-frequency squeezing), (2) two-mode squeezed optical vacuum (i.e., high-frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.
We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys. Rev. A 90, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivity for lower QST efficiencies and with a sufficiently large degree of squeezing can attain near-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies. Furthermore, we use the quantum Fisher information to demonstrate the near optimality of our scheme.
We consider an optical interferometer with coherent light in one input and a squeezed vacuum in another. Such an interferometer is known to beat the standard quantum limit of sensitivity to the difference of phase shifts in its arms. We find the ultimate limit of precision for such an interferometer by calculating the quantum Fisher information of the mixed quantum state in one of the interferometer's outputs about the difference phase. We show that, in the vicinity of the black fringe, this information is asymptotically close to the quantum Fisher information about this phase for the two-mode readout. We conclude that the single-mode readout is optimal for phase estimation in squeezing-enhanced interferometry and allows for the Heisenberg scaling of precision. We also show that the optimal local measurement in the vicinity of the black fringe consists of amplifying the output field in a phase-sensitive way and measuring its photon number.
The canonical Mach-Zehnder interferometer fed with a coherent state and a squeezed-vacuum state of equal intensities is theoretically predicted to achieve Heisenberg scaling in phase sensitivity. However, this ultimate performance is unattainable using direct photon-number-difference detection due to a divergence arising precisely at the optimal equal-intensity regime. In this work, we introduce a dual-squeezing approach that overcomes this fundamental limitation. Our scheme employs an additional single-mode squeezer before detection, forming a paired configuration with the input squeezer used to generate the squeezed-vacuum state. We analytically demonstrate that the resulting dual-squeezing Mach-Zehnder interferometer enables Heisenberg-limited phase sensitivity with di rect photon-number-difference detection, while remaining robust against detection noise. Our work provides a feasible and robust route toward quantum-limited interferometric phase measurements
Atom interferometers measure the relative phase shifts between coherent matter-wave paths that arise from interactions with external fields or inertial forces. Due to their exceptional phase sensitivity, atom interferometers became an essential tool for precision measurements and fundamental physics experiments, finding applications in geodesy, gravimetry, and inertial navigation. However, their measurement precision is limited by quantum projection noise, which arises from the Heisenberg uncertainty principle, preventing the measurement of atomic states with absolute precision. The generation of entanglement between the atoms offers a path to surpass this so-called standard quantum limit, thereby enhancing the interferometer’s phase sensitivity beyond classical measurement bounds. This thesis reports on the development of an atom interferometer experiment designed to realize cavity-mediated, squeezed Mach-Zehnder-type interferometry with ultra-cold 87Rb atoms. The experiment combines cavity-aided spin-squeezing with cavity-mediated Mach-Zehnder interferometry to demonstrate entanglement-enhanced phase sensitivity. The experiment is centered on a triangular optical cavity that mediates all relevant atom-light interactions. The cavity provides optical trapping, spin-squeezing, and Raman beam-splitter operations, enabling to perform interferometry on a continuously trapped atomic ensemble. The thesis elaborates on the fundamental theoretical framework, the cavity design, and the full optical setup, including the detailed configuration of the developed laser stabilization methods. Experimentally, continuous loading methods were explored, resulting in an accumulation of up to 4 × 106 atoms in the dipole trap within a cycle time of 500 ms. The AC Stark shift compensation method developed for continuous loading was further applied for in-trap cooling to 10 µK, and optical pumping for efficient atomic state preparation. Coherent state control was verified via observation of microwave-driven Rabi oscillations, and used to characterize atom-cavity coupling. These presented results establish the experimental groundwork for the future development of cavity-mediated, entanglement-enhanced Mach-Zehnder-type atom interferometry.
Abstract A novel scheme for the enhancement of phase sensitivity based on a Mach–Zehnder interferometer (MZI) and intensity detection is proposed. With the input of bright entangled twin beams from four wave mixing (FWM), the phase sensitivity can beat shot noise limit (SNL) and approach Heisenberg limit. This scheme is special due to that only one of bright entangled twin beams enters into the MZI and the other one is employed for measurement. In addition, by altering the parametric strength of FWM and the implementation of maximum quantum squeezing, the optimal phase sensitivity can reach sub-SNL. Optical intensity depletion of photon detectors and internal intensity depletion of the MZI are also discussed. The scheme displays that by employing external resources, while one input of the MZI is an vacuum beam, the phase sensitivity still can beat SNL.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.