Quantum Enhancement of Time Transfer between Remote Clocks
Lamine, B; Treps, N; Fabre, C
Laboratoire Kastler Brossel

Accurate spacetime positioning has become a crucial issue for future space experiment. The position in space (by ranging to a reference) or time (by clock synchronization with a reference) between two observers A and B may be achieved through the Einstein protocol which consists to repeatedly exchange light pulses. Each pulse carries along its propagation the light cone variable u=t-x/c which remains constant if dispersion effects can be ignored. The measurement of the time of arrival of each pulse allows a determination of either distance or clock synchronization. Let us consider ranging and assume that the two observers share synchronized clocks so that the observable to be monitored is a distance variation between A and B, obtained as the difference between the time of arrival of the pulse in B compare to a reference clock in B, divided by the speed of light.

Even if present resolution in time transfer is limited by classical noise, it is of interest to study the fundamental limits of time transfer associated with the quantum nature of the light probe used in the Einstein protocol. Indeed, it is already well known that ranging is submitted to the so called standard quantum limit which is inversely proportional to the inverse of the square root of the number of photon which shows that intense pulse is required.

In practice, the standard quantum limit can not be reached if the pulse is simply sent into an intensity detector because the electronic bandwidth severely restricts the resolution to the picosecond level. A way to avoid this limitation is to beat the incoming pulses with a local oscillator in order to interferometrically point the maximum of the pulse enveloppe with a resolution that is no more limited by the electronic bandwidth. An explicit protocol based on that idea using femtosecond pulses has already been proposed as a way to improve ranging sensitivity by J. Ye.

In this talk we propose a different scheme using mode locked femtosecond laser that combines both time-of-flight and phase measurement at the same time and leads to a higher sensitivity than existing protocol. The scheme is based on a homodyne detection where the temporal shape of the Local Oscillator (LO) is chosen such that information on the timing is extracted both from the phase and the enveloppe of the pulse. To do so, the temporal mode of the LO has to match the profile modification of the incoming pulses induced by a slight delay in its propagation. Such an adaptative measurement has already been successfully employed in the spatial domain to measure transverse beam displacement and tilt. Pulse shapers in the temporal domain are now currently available and our scheme could lead in principle to a precision as low as a few 10^-23 s for one second measurement time, roughly the same precision that the method proposed by J. Ye.

One of the big advantage of this scheme is that the SQL can be beaten in a rather straightforward manner using squeezed light propagating from A to B along with the pulse and do not require non local correlations compare to what is usually proposed in the literature. We show that the sensitivity is improved by the noise reduction factor of the squeezed light.

As a conclusion, the aim of this talk is to present a new time transfer protocol which allow measurement at the standard quantum level with mode locked femtosecond lasers and possibly allows a further improvement below the standard quantum limit using squeezing. This protocol could be used for ranging in space experiments where losses are small and high precision needed.