Abstract Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus has potential in precision measurement applications. Although frequency measurements offer the hitherto highest precision due to the stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we demonstrate a WM-enhanced correlation spectroscopy technique capable of narrowing the resonance linewidth down to 0.1 Hz in a room-temperature atomic vapour cell. The potential of this technique for precision measurement is demonstrated through weak magnetic-field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly orthogonal manner, a sensitivity of 7 fT Hz−1/2 at a low frequency near DC is achieved using only one laser beam with 15 µW of power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian and shed new light on metrology and bio-magnetic field sensing.
Abstract Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus has potential in precision measurement applications. Although frequency measurements offer the hitherto highest precision due to the stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we demonstrate a WM-enhanced correlation spectroscopy technique capable of narrowing the resonance linewidth down to 0.1 Hz in a room-temperature atomic vapour cell. The potential of this technique for precision measurement is demonstrated through weak magnetic-field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly orthogonal manner, a sensitivity of 7 fT Hz−1/2 at a low frequency near DC is achieved using only one laser beam with 15 µW of power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian and shed new light on metrology and bio-magnetic field sensing.
Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus promise great potentials in precision measurements. Although frequency measurements offer the hitherto highest precision owing to stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we propose and demonstrate a WM-enhanced spectroscopy technique which is capable of narrowing the resonance to 0.1 Hz in a room-temperature atomic vapor cell. Potential of this technique for precision measurement is demonstrated through weak magnetic field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly-orthogonal manner, a sensitivity of 7 fT/Hz near DC is achieved, using only one laser beam of $\text{7 }\text{\mu W}$ power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian, and shed new light in metrology and bio-magnetic field sensing applications.
Background: Weak measurement involves weak coupling between the system and the measuring device (pointer) enables large amplification and high precision measurement of small physical parameters. The outcome of this special measurement procedure involving nearly mutually orthogonal pre- and post-selection of states in such weakly interacting systems leads to weak value that can become exceedingly large and lie outside the eigenvalue spectrum of the measured observable. This unprecedented ability of weak value amplification of small physical parameters has been successfully exploited for various metrological applications in the optical domain and beyond. Even though it is a quantum mechanical concept, it can be understood using the classical electromagnetic theory of light and thus can be realized in classical optics. Objective: Here, we briefly review the basic concepts of weak measurement and weak value amplification, provide illustrative examples of its implementation in various optical domains. The applications involve measuring ultra-sensitive beam deflections, high precision measurements of angular rotation, phase shift, temporal shift, frequency shift and so forth, and expand this extraordinary concept in the domain of nano-optics and plasmonics. Methods: In order to perform weak value amplification, we have used Gaussian beam and spectral response as the pointer subsequently. The polarization state associated with the pointer is used as pre and post-selection device. Results: We reveal the weak value amplification of sub-wavelength optical effects namely the Goos-Hänchen shift and the spin hall shift. Further, we demonstrate weak measurements using spectral line shape of resonance as a natural pointer, enabling weak value amplification beyond the conventional limit, demonstrating natural weak value amplification in plasmonic Fano resonances and so forth. The discussed concepts could have useful implications in various nano-optical systems to amplify tiny signals or effects. Conclusion: The emerging prospects of weak value amplification towards the development of novel optical weak measurement devices for metrological applications are extensively discussed.
Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analyzing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT / Hz 1/2 . Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents, to our knowledge, a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.
Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analysing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT/Hz1/2. Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.
Weak measurements, which offer a significant signal enhancement with pre- and post-selections, have proven to be powerful for precision metrology. However, the measured precision of the parameter of interest is always limited by the post-selection-induced probe loss, especially in the presence of technical noise. In this paper, we investigate the optimal pre- and post-selections of weak measurements for precision metrology in the presence of technical noise. While weak measurements apply more generally, we experimentally measure the spin splitting induced by the spin Hall effect of light (SHEL) to approach this issue. The highest measured precision of the spin splitting can be obtained with the post-selected state in the nonlinear intermediate regime. Surprisingly, the pre- and post-selections for the largest weak-value amplification are incapable of estimation of the spin splitting, since the amplified shift is independent of the spin splitting. Our results are not restricted to the SHEL and could be applied to other parameter estimations with weak measurements.
Detection of long-wavelength signal is of importance for diverse sensing and communication applications. Conventional metal antennas are limited in this regime, particularly when compactness and high sensitivity are both required. Despite intrinsic advantages for electric-field sensing across an ultra-broad range from DC to terahertz, Rydberg atoms still face challenges in practical long-wavelength signal detection, motivating the development of more sensitive and scalable approaches. In this work, we experimentally show that such a signal acting on the Rydberg state can be converted into a polarization variation of the probe laser, and realize signal extraction by appropriately utilizing the polarization degrees of freedom. Based on such a mechanism, we further design and implement a quantum weak measurement scheme, which clearly suppresses the technical noise and leads to considerable improvement of performance. Evaluation of the sensitivities across different post-selection angles demonstrates that the weak measurement results agree well with the theoretical model predictions. The advantages of our method are analyzed from multiple aspects, including characterizing the responses over different frequencies and comparing the responses of the weak measurement scheme and the traditional transmission-based method. After accounting for the screening effect of a measured ratio of 17% where the Rb 87 atoms experience a substantially reduced field inside the glass cell, the performance reaches 33 μV cm −1 Hz −1/2 in sensitivity and 1.0 μV cm −1 in minimal detectable field for an integration time of 1000 s, as perceived by the atoms.