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Quantum limit in time measurement with coherent pulses

par - 19 janvier 2009

Any measurement is limited by uncontrolled fluctuations, or noise, which limit its sensitivity. While most of the noise is of technical character, and can be in principle reduced below any arbitrarily small level by improving the experimental set-up (though it is usually difficult and time consuming in very high accuracy measurements), there also exists a more fundamental noise imposed by the quantum character of the physical world itself. The latter one can be reduced, or at least circumvented, not by reducing the experimental imperfections, but by a careful control of the quantum state of the system. This problematics is not new and has in particular been studied by the group back in the 90s as a way to improve sensitivity of gravitational wave detectors, which are quantum limited at high frequency. Meanwhile, the manipulation of quantum fluctuations (squeezed and, entangled states) to improve quantum-limited measurements led to successful demonstration experiments of sub-shot noise sensitivity in interferometric measurements and in high sensitivity absorption experiments. These squeezing techniques will certainly be used in the next generation of gravitational wave interferometric detectors.

In the time domain, frequency combs are invaluable tools because gradual developments in mode locked femtosecond laser have brought comb technology to the same level of sophistication than continuous lasers. Frequency combs consist in the coherent superposition of many frequency modes, giving rise to pulsed laser light with very long coherence length. They are by nature continuous laser beams and thus can be used for frequency metrology experiments where the integration time can be very long, reaching the second when actively locked. In addition, they carry a time-of-flight information in their time dependent amplitude which allows both absolute ranging measurements at intermediate distances as well as extremely precise relative measurement, in contrast with purely monochromatic beam which gives ranging only within a wavelength.

Schemes implemented to measure time delay can be divided into 2 families : those that perform a time-of-flight (noted tof) measurement (measuring the arrival time of a light pulse with fast photodetectors) and those that perform a phase measurement (within an interferometric system), each of them leading to a different standard quantum limit. The situation can be summarized in the following table.

u=t-x/c is the light cone variable, $\Delta\omega$ is the frequency spread, $\omega_0$ the central frequency of the light source and N is the number of incoming photons during the detection time. The last column of the table gives the ultimate sensitivity (SQL stands for Standard Quantum Limit) that can be reached using the respective technique (with shot noise limited light sources).

For the time being, the resolution in time transfer is limited by classical technical noises so that the previous SQL are not yet a limitation in time transfer. Nevertheless, with the recent developments in stabilization of frequency combs referenced to optical standard, it is getting closer and closer to these quantum limits. Both for a fundamental point of view and for future experiments, it is therefore necessary to compute the ultimate sensitivity in time transfer with coherent pulses.

Our project, developped in collaboration with the quantum optic group, is to propose a theoretical scheme that leads to a standard quantum limit smaller than both the time-of-flight and phase SQL. This scheme is based on a homodyne detection with a Local Oscillator shaped in a particular temporal mode. Then, the very low SQL can be overcome using appropriately squeezed frequency comb. Benefitting from the large number of photons and from the optimal choice of both the detection strategy and of the quantum resource, the proposed scheme represents a significant potential improvement in space-time positioning.

Quantum Improvement of Time Transfer between Remote Clocks, Brahim Lamine, Claude Fabre and Nicolas Treps Physical Review Letters 101 (2008) 123601 HAL

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