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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum limited measurements with optical frequency combs

Pu Jian, Olivier Pinel, Jonathan Roslund, Roman Schmeissner, Brahim Lamine, Claude Fabre, Nicolas Treps

Published May 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-iqec.2013.6801755

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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.
The measurement and manipulation of coherent optical fields have been transformed by the optical frequency comb. Today, the optical frequency comb grants measurements precise enough to count individual cycles of light as well as the generation of nearly any coherent electromagnetic field from the ultraviolet through the infrared. These capabilities have enabled the most precise realizations and comparisons of time, precision spectroscopy over broad bandwidths, and the ability to convert stable signals between optical and microwave fields–seamlessly connecting the entire electromagnetic spectrum from hertz (100 ) to petahertz (1015). These applications involve the interference of a frequency comb with another coherent light source, such as another frequency comb or a single-frequency continuous-wave laser. However, coherent light represents only one type of light. The vast majority of light emanates from “black bodies” such as stars, which is in a thermal state as opposed to a coherent state, and carries profound information about the universe and humanity’s place within it. Other types of light defy classical electromagnetism and are known as non-classical or quantum light. Such quantum light may play central roles in quantum communication, quantum computation, and quantum-enhanced metrology. In this thesis, the use of the optical frequency comb in the interferometric measurement of thermal and quantum light is investigated, with a focus on assessing fundamental limits to the sensitivity of such measurements. In order to measure thermal light, a technique called dual-comb correlation spectroscopy is explored. This technique entails heterodyne measurement of the field of thermal light and subsequent correlation of the field in time. This process reveals the spectrum of thermal light at high resolution and across broad bandwidths. New theoretical work uncovers previously unknown fundamental limits on sensitivity when measuring realistically weak thermal light. Experimental investigation verifies this scaling and is accompanied by a demonstration of spectroscopy at the equivalent power spectral density of our Sun, realizing a greater than 1000-fold sensitivity increase over past demonstrations of this technique. These insights pave the way for expansion of this technique to comb-based spatial correlation of thermal fields. This advancement would allow for extended baseline synthetic aperture hyperspectral imaging throughout the optical spectrum, facilitating novel and profound observations of the universe. The use of frequency combs for the measurement of quantum light is also investigated. This scenario breaks typical quantum optics assumptions, such as large, mode-matched local oscillators, and necessitates new quantum measurement operators. Such measurement operators are derived, which not only describe homodyne measurements on any quantum state of light with a frequency comb local oscillator, but also indicate that the shot noise limit generally reached in comb-based measurements of coherent light (such as in continuous-wave laser heterodyne and dual-comb spectroscopy) does not correspond to the quadrature or coherent state-overlap description standard in quantum optics. Efforts to experimentally reach this “standard” quantum limit demonstrate a significant improvement in the signal-to-noise ratio over the conventional comb-based shot noise limit, paving the way for lower-power portable optical clocks and quantum-enhanced frequencycomb metrology.
Optical techniques are widely used in many areas of science and technology to make accurate measurements and diagnostics, from microscopy, spectroscopy, chemical analysis, to gravitational wave detection and ranging. There are many reasons for this: light allows us to extract information in a remote and non-destructive way, it carries information in a massively parallel way, and perhaps more importantly, optical measurements can reach very high precision and sensitivity levels. It is therefore important to know what is the ultimate limit of sensitivity that can be possibly achieved in the estimation of a physical parameter p that is encoded in a light beam of fixed mean photon number N. This limit is imposed by the unavoidable quantum fluctuations of light and depends on the quantum state of light that conveys the information about p. When the light is in a coherent state, this limit is called ‘standard quantum limit’ and scales as 1/N1/2.
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.
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.
Accurate time-delay measurement has become a crucial issue for space positioning experiments which require increasing precision over large distances. The femtosecond frequency comb has been found to be a good source for its advantages of a large nonambiguity range and coherence length up to tens of kilometers or more. A scheme combining homodyne detection and frequency combs was proposed [B. Lamine et al., Phys. Rev. Lett. 101, 123601 (2008)] that leads to a timing sensitivity reaching the shot-noise limit; with a squeezed frequency comb as the input field, the measured timing sensitivity can be further improved to the level of the sub-shot-noise limit. Based on this scheme and a squeezed frequency comb that was measured to have a phase squeezing of 1.5 dB at an analyzing frequency of 2 MHz, a narrow-band interferometric timing measurement is implemented. The minimum measurable timing variation modulation at 2 MHz is reduced from a shot-noise-limited value of $(2.8\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s to $(2.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s.