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arXiv:2604.05107

Quantum noise in ranging with optical pulses

Mylenne Manrique, Ilaria Gianani, Marco Barbieri, Valentina Parigi, Nicolas Treps

quant-phphysics.opticsSubmitted Apr 6, 2026• Announced Apr 8, 2026• 0 citations
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Abstract

Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal engineering and mdoe-sensitive detection sensitivity to distance at the standard limit can be achieved, however attaining improved uncertainties by the use of squeezing has not been explored. Here, we apply an effective Hamiltonian framework to the problem of ranging with quantum frequency combs in order to derive the associated precision bounds for distance estimation. We analyse the role of intensity anti-squeezing and temporal beam shaping, and find that quantum solutions may be appealing mostly for short-distance applications.

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Quantum noise in ranging with optical pulses

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Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal engineering and mode-sensitive detection, sensitivity to distance at the standard limit can be achieved; however, attaining improved uncertainties by the use of squeezing has not been explored. Here, we apply an effective Hamiltonian framework to the problem of ranging with quantum frequency combs in order to derive the associated precision bounds for distance estimation. The problem needs addressing of the pulse shape and its quantum properties at once. The analysis reveals that quantum solutions may be appealing mostly for short-distance applications.

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Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal engineering and mdoe-sensitive detection sensitivity to distance at the standard limit can be achieved, however attaining improved uncertainties by the use of squeezing has not been explored. Here, we apply an effective Hamiltonian framework to the problem of ranging with quantum frequency combs in order to derive the associated precision bounds for distance estimation. We analyse the role of intensity anti-squeezing and temporal beam shaping, and find that quantum solutions may be appealing mostly for short-distance applications.
Optical frequency combs combine ultrashort pulse duration and phase stability, making them powerful resources for high-precision ranging even when affected by atmospheric dispersion. It has been established that by classical modal engineering and mode-sensitive detection, sensitivity to distance at the standard limit can be achieved; however, attaining improved uncertainties by the use of squeezing has not been explored. Here, we apply an effective Hamiltonian framework to the problem of ranging with quantum frequency combs in order to derive the associated precision bounds for distance estimation. The problem needs addressing of the pulse shape and its quantum properties at once. The analysis reveals that quantum solutions may be appealing mostly for short-distance applications.
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.
Precision metrology is one application of optical frequency combs. Classical noise in their properties typically limits achievable measurement sensitivity. Amplitude and phase noise in optical frequency combs have already been studied extensively. So far, noise sidebands close to the carrier of either individual optical frequencies or of the mean field have been considered. This thesis develops methods to precisely characterize amplitude and phase noise down to the quantum limit. To this aim a transmissive, broadband passive cavity is developed. It filters and inter-converts amplitude and phase noise. The analysis of its signal by the use of homodyne detection provides a quantum limited measurement of phase noise. The application of ultrafast pulse shaping enables the measurement of the spectral correlations of amplitude and phase noise. Being represented by the use of covariance matrices, the entire noise correlations over the optical spectrum are characterized on the example of a Ti:Sapph oscillator. The measured noise correlations exhibit spectral structures, so-called modes. Their shape matches with the theoretical prediction. This concept known from multi-partite optical quantum systems is consequently applicable to classical noise in frequency combs. The knowledge of the intrinsic noise modes is likely provide an improvement of precision metrology experiments with combs.
Frequency combs enable precision measurements across timekeeping, spectroscopy, ranging and astronomy, and are now extending to integrated and field-deployable platforms. Realizing their full performance demands a comprehensive account of the quantum noise that arises when broadband optical fields are converted into finite-bandwidth electrical signals. Here we present a rigorous first-principles quantum-mechanical framework for optical frequency-comb metrology based on continuous-mode field quantization and a comb-line-resolved description of quantum fluctuations. The theory describes how quantum fluctuations of the comb field are transduced into electrical measurement noise. Formulated at the level of the comb field, the framework unifies the standard quantum limits of optical frequency division (OFD) and dual-comb spectroscopy (DCS) within a single treatment, and provides a general recipe for other comb-based measurements. On this footing, we identify practical, resource-efficient routes to quantum enhancement through engineered comb states, laying a foundation for the design of next-generation frequency combs operating at and beyond standard quantum limits.
We show that synchronously pumped Optical Parametric Oscillators are able to generate strongly squeezed trains of femtosecond pulses in “supermodes”, which are well defined superpositions of many modes of different frequencies. In some conditions, several supermodes can be simultaneously squeezed. In addition, we show that the use of such squeezed trains of pulses can improve time transfer between remote clocks and ranging techniques beyond the standard quantum limit provided they have an optimized temporal shape.