Coherence spectroscopy has been intensively studied over the last several decades for various applications in science and engineering. The Rayleigh criterion defines the resolution limit of an interferometer, where many-wave interference beats the resolution limit of a two-slit system. On the other hand, the diffraction angle in a slit is reduced by the Kth power of the measured signal, resulting in the shot-noise limit. Here, the Kth power of the measured signal in an N-slit interferometer is studied for enhanced coherence spectroscopy to overcome the resolution limit of the original system. The Kth power to the individual intensities of the N-slit interferometer is numerically demonstrated for enhanced resolution satisfying the shot-noise limit. As a result, the Kth power of the intensity beats the resolution limit of the N-slit interferometer, in which the out-of-shelf spectrometer or wavelength meter can be a primary beneficiary of this technique. Due to the same resolution of the Heisenberg limit in quantum sensing as in the N-slit interference fringe, the proposed Kth power technique also beats the superresolution in quantum metrology.
Coherence spectroscopy has been intensively studied over the last several decades for various applications in science and engineering. The Rayleigh criterion defines the resolution limit of an interferometer, where many-wave interference beats the resolution limit of a two-slit system. On the other hand, the diffraction angle in a slit is reduced by the Kth power of the measured signal, resulting in the shot-noise limit. Here, the Kth power of the measured signal in an N-slit interferometer is studied for enhanced coherence spectroscopy to overcome the resolution limit of the original system. The Kth power to the individual intensities of the N-slit interferometer is numerically demonstrated for enhanced resolution satisfying the shot-noise limit. As a result, the Kth power of the intensity beats the resolution limit of the N-slit interferometer, in which the out-of-shelf spectrometer or wavelength meter can be a primary beneficiary of this technique. Due to the same resolution of the Heisenberg limit in quantum sensing as in the N-slit interference fringe, the proposed Kth power technique also beats the superresolution in quantum metrology.
The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.
Quantum sensing and metrology have been extensively investigated over the past several decades to surpass the classical shot noise limit and approach the Heisenberg limit. The hallmark of N00N state based quantum sensing is superresolution, characterized by the interference fringe pattern (1+cosNphi). However, practical implementations are severely constrained by the achievable photon number N, reduced fringe visibility, and vulnerability to photon loss. Recently, several coherence-based approaches without using N00N states have been explored as alternative routes to superresolution. Among them, the coherence de Broglie wavelength (CBW) approach is fully compatible with coherence optics. Here, we experimentally demonstrate CBW based superresolution up to N=3. In contrast to N00N state based schemes, the observed CBW fringes exhibit near unity visibility that is essentially independent of N and remain robust against photon loss. Although CBW does not attain the Heisenberg limited phase sensitivity, its phase sensitivity exhibits an N fold enhancement over conventional classical interferometric approaches. These results suggest that CBW provides a practical and scalable platform for superresolution based sensing and metrology.
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability density function of independently and identically distributed random variables. The Cramer-Rao lower bound (CRLB) indicates the minimum error of the Fisher information, generally known as the shot-noise limit. On the other hand, coherence has pushed the resolution limit further overcoming the diffraction limit using many-wave interference strictly confined to the first-order intensity correlation. However, practical implementation is limited by the lithographic constraints in, e.g., optical gratings. Recently, a coherence technique of superresolution has been introduced to overcome the diffraction limit in phase sensitivity using higher-order intensity correlations of a phase-controlled output field from an interferometer. Here, the superresolution is adopted for precision metrology in an optical spectrometer, whose enhanced frequency resolution is linearly proportional to the intensity-product order, overcoming CRLB. Unlike quantum sensing using entangled photons, this technique is purely classical and offers robust performance against environmental noises, benefiting from the interferometer's scanning mode for fringe counting.
There has been much recent interest in quantum optical interferometry for applications to metrology, subwavelength imaging, and remote sensing such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the Beer law for classical optical attenuation, and which provides sensitivity at the shot-noise limit. We show that coherent light coupled with photon-number-resolving detectors can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity no worse than shot noise in terms of the detected photon power.
We have derived a quantum LADAR scheme which exploits even coherent states of light, is shot noise limit in sensitivity and can resolve features much below Rayleigh diffraction limit. For a return power of n = 100, the resolution of our proposed scheme can reach 120 times higher than the classical diffraction limit in the sense of the well-define narrow feature. More importantly, our scheme has the super-resolving characteristics in the usual sense of word as there are multiple narrow peaks as would be the case in a N00N-states scheme.
Interference metrology is a method for achieving high precision detection by phase estimation. The phase sensitivity of a traditional interferometer is subject to the standard quantum limit, while its resolution is constrained by the Rayleigh diffraction limit. The resolution and sensitivity of phase measurement can be enhanced by using quantum metrology. We propose a quantum interference metrology scheme using the entangled squeezed vacuum state, which is obtained using the magic beam splitter, expressed as | ψ ⟩ = ( | ξ ⟩ | 0 ⟩ + | 0 ⟩ | ξ ⟩ ) / 2 + 2 / cosh r , such as the N00N state. We derive the phase sensitivity and the resolution of the system with Z detection, project detection, and parity detection. By simulation and analysis, we determine that parity detection is an optimal detection method, which can break through the Rayleigh diffraction limit and the standard quantum limit.