Pu Jian, Jonathan Roslund, Roman Schmeissner, Valérian Thiel, Claude Fabre and Nicolas Treps
Metrology is the science of measuring, and any measurement is a comparison to a given scale. Precise measurements require long term stable reference standards to permit to measure a mean value out any kind of disturbing noise. Light can be such a reference scale, as its properties allow reaching very high precision and sensitivity levels.
Regardless to its generation, the precise properties of light are limited by noise effects emerging from the quantization of light. Any optical measurement is therefore limited by these unavoidable fluctuations, namely the shot noise - or quantum limit. It is important to know what the ultimate sensitivity that can be possibly achieved in a measurement using a light beam is, and how this sensitivity could be enhanced by using quantum resources.
For many years, our group has been studying these limits both theoretically and experimentally. We have in particular recently studied the general theoretical bounds on the estimation of an arbitrary parameter encode in a light beam, and how this parameter can be optimally retrieved in a detection system [Pinel 2012].
The first implementations of these optimal measurement schemes have been carried out in the spatial domain : we have studied the quantum limits in image processing [Fade 2008, Delaubert 2008] and demonstrated experimentally optimal measurements of beam displacement and beam tilt [Delaubert 2006].
The theoretical and experimental study of these limits is the issue of the project FRECQUAM supported by the ERC, combining optical frequency combs as a metrological tool with the framework of quantum optics. It unites in some sense the two parts of the 2005 Nobel Price for optical frequency combs and quantum optics.
Optical frequency combs consist of a large number of individual optical frequency components with a fixed phase relation over a long coherence time. Being a frequency ruler they are equivalent to a regular train of femtosecond light pulses. The extraordinary stability of their properties permitted measurements with unprecedented precision and makes them perfect tools for high precision metrological applications.
We have studied the theoretical limits of sensitivity in the estimation of parameters encoded in an optical frequency comb, for example a time delay or a dispersion parameter. This lead to the proposal of metrological experiments at the quantum limit, like space-time positioning [Lamine 2008] or dispersion measurement in air [Jian 2012].
In order to experimentally reach the quantum limits in these experiments, we develop and investigate the noise properties of several optical devices : quantum projective measurements, namely the balanced homodyne detection, are used as high sensitivity detection schemes ; passive filtering cavities play an important role in removing classical noise from the frequency combs ; pulse shaping techniques are needed to access the information carried in various temporal modes in balanced homodyne detection.
Further investigations try to generalize the underlying theoretical concept and concern the possible definition of observables on frequency combs parameters.
[Jian 2012] P. Jian, O. Pinel, C. Fabre, B. Lamine, N. Treps, « Real-time distance measurement immune from atmospheric parameters using optical frequency combs », Opt Express 20, 27133 (2012).
[Pinel 2012] O. Pinel, J. Fade, D. Braun, Pu Jian, N. Treps, C. Fabre, « Ultimate sensitivity of precision measurements with intense Gaussian quantum light : a multi-modal approach », Phys. Rev A Rapid Com.85, 010101 (2012)
T. Amri, J. Laurat, C. Fabre « Characterizing Quantum Properties of a measurement apparatus : insights from the retrodictive approach” Phys. Rev. Letters 106, 020502 (2011)
[Delaubert 2008] V. Delaubert, N. Treps, C. Fabre, H. Bachor, P. Réfrégier, “Quantum limits in image processing” Europhys. Letters 81 44001 (2008)
[Lamine 2008] B. Lamine, C. Fabre, N. Treps, “Quantum improvement of time transfer between remote clocks” , Phys Rev. Letters 101 123601 (2008)
[Fade 2008] J. Fade, N. Treps, C. Fabre, P. Réfrégier « Optimal precision of parameter estimation in images with sub-Poissonian quantum fluctuations “ Eur. Phys. Journal D 50, 215 (2008)
V. Delaubert, Gao Bo, N. Treps, C. Fabre, "’Optical storage of high density information beyond the diffraction limit : a quantum study’, Phys. Rev. A 73, 013820 (2006)
V.Delaubert, N.Treps, M.Lassen, C.C.Harb, C.Fabre, P.K.Lam, H-A.Bachor, “homodyne detection as an optimal small displacement and tilt measurements”, Phys. RevA74, 053823 (2006)