A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramér-Rao limit of detection without any assumptions on the nature of the light source.
A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramér-Rao limit of detection without any assumptions on the nature of the light source.
We develop a quantum sensing framework for the phase independent detection of weak coherent optical displacements based on SU(1,1) interferometry. Unlike conventional quantum measurement protocols that require prior knowledge of the signal phase and coherent homodyne detection, the proposed approach estimates the displacement magnitude independently of its phase. We show that, under ideal lossless conditions, a conventional SU(1,1) interferometer employing only total intensity detection saturates the quantum Cramer Rao bound for displacement magnitude estimation. We further derive the analytical expression of the quantum Cramer Rao bound and the sensitivity of the conventional SU(1,1) interferometer with total intensity detection and systematically investigate its performance in the presence of optical loss. The proposed phase-independent intensity detection scheme achieves comparable performance over experimentally relevant operating regimes while eliminating the need for local oscillators, phase locking, and quadrature tracking. These results establish SU(1,1) based intensity detection as a practical platform for phase independent quantum sensing.
Summary form only given. Optical techniques are widely used in many areas of science and technology to make accurate measurements. The precision of these measurements suffers from limits due to the unavoidable quantum fluctuations of light. When the light is in the quasi-classical coherent state, this limit is called ”standard quantum limit” and scales as 1/√N with N the number of photons. While better scaling can be achieved with exotic quantum states, coherent light is experimentally interesting as we are able to produce it with large N. We consider light as a probe for the measurement of a parameter p that affects the medium or the length through which the light propagates. We derived the ultimate limit of sensitivity, the so-called quantum Cramér-Rao bound, for the measurement of p [1]: for u(ω, p) the normalized mean field mode of the light, the minimal fluctuation of p that can be measured is given in Fig. 1. We also showed that this ultimate limit of sensitivity can be reached experimentally in a homodyne detection scheme, where the intense local oscillator is taken in the mode wp o ∂u ∂p, called detection mode associated with p. This measurement scheme can be applied to space-time positioning experiments such as ranging or clock synchronization [2]. The basic method for space-time positioning relies on the exchange of regular light pulses between two emitters. For coherent broadband light pulses, such as the ones delivered by a mode-locked femtosecond laser, of central frequency ω0 and of spectral width Δω, the quantum limits of the measurements of the delay t are given by δtphase = 2√Nω0 1 for interferometric measurements and δttof = 2√NΔω 1 for time-of-flight measurements. However, these two methods do not reach the quantum Cramer-Rao bound; this ultimate limit is achieved by a homodyne detection with local oscillator w(ω) o iωu(ω), and is given by 1 δtmin = (1) 2√N . Δω2 + ω2 0 For usual characteristics of a Titane:Sapphire femtosecond laser and 1 ms integration time, δtmin = 10-23s. We demonstrate this limit experimentally by using pulse shaping techniques to shape the local oscillator in the detection mode. We also study the influence of the intensity and phase noise of a mode-locked femtosecond laser on this limit. This technique can also be applied in the case of ranging in a dispersive medium such as air. In this case, dispersive effects due to environmental parameters such as pressure, temperature or humidity affect the precision of measurements. Usually, this problem is tacked by measuring separately the environmental parameters or using several wavelengths, which can be difficult and require post-processing. We show that using the same technique as previously shown, the parasitic effects due to the medium in a distance measurement can be canceled by shaping properly the local oscillator [3]: we choose for the local oscillator a mode that is orthogonal to the environmental effects, so the homodyne detection is insensitive to them, at the expense of a lower sensitivity. This scheme is an all-optical and real-time measurement of distance in a dispersive medium.
With the rapid advancement of science and technology, phase measurement plays a crucial role in various fields such as optics, communication, and radar. Traditional phase measurement methods, relying on classical light sources, produce results following the central limit theorem, limiting measurement precision to the standard quantum limit. However, recent in-depth studies of quantum theory and quantum enhanced experimental techniques are breaking this barrier. The use of specially designed non-classical light sources for phase measurement not only provides the possibility of breaking through the limits of measurement precision but also meets the growing demand for high-precision measurements.This paper started from a statistical perspective, introduced key indicators for evaluating measurement precision, including the Cramér-Rao Boundary (CRB) and Fisher Information, and extends to experimental approaches beyond the standard quantum limit. Subsequently, by introducing quantum light sources such as squeezed states, entangled states, and methods like harmonic amplification to achieve amplifier the phase and optical detection, the paper provides a comprehensive review of recent research achievements in super-resolution phase measurement techniques. Finally, we select several technological categories with a promising engineering outlook, analyze the technical challenges limiting their maturity, and provide a prospective outlook.
Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.
Quantum techniques, developed in recent decades, provide new approaches to achieving high-precision measurements beyond the classical bounds. In this paper, we theoretically demonstrate a metrology method for improving the sensitivity of the interferometric optical gyroscope, robust against the loss, by using coherent-light stimulated two-mode squeezed beams as the light source. The detection protocol is based on a simple intensity measurement, and the quantum noise is far below the shot-noise limit. The enhancement factors for different coherent light fields are analyzed in detail. Additionally, the influence of loss during the propagation in the optical path is studied, and the conditions for achieving sub-shot-noise measurement sensitivity are obtained. We also find that the phase sensitivity of the proposed gyroscope scheme becomes closer to the quantum Cramér-Rao bound with increasing of the photon number of the coherent beams.