Quantum limits in coherent combination of optical signals

The standard approach to communication over large distances utilizes electromagnetic waves, typically of radio and microwave frequencies. Switching to yet higher frequencies, especially optical ones, theoretically could allow one to increase the communication rates. One of the most important advantages of optical communication is the access to lasers, which allow to substantially decrease beam divergence and concentrate the signal which is crucial in e.g. satellite communication. Moreover, optical frequencies allow for faster signal modulation i.e. more frequent sending of light pulses which increases the communication rates and additionally to avoid complicated formalities related to frequency allocation. However, construction of optical telescopes large enough to collect a substantial fraction of the light beam in the receiver is very costly when compared to standard radio frequency antennas. A way to solve this problem is to coherently combine light beams collected by several telescopes. In contrast to radio signals, which due to relatively low frequencies can be combined in postprocessing, optical signals need to be combined physically already at the receiver. In order to perform such a combination, one can utilize interference of light on a beam splitter and measure light intensity in the dark output port. In the ideal case, the optical signals collected by two telescopes interfere destructively in the dark output port of the beam splitter resulting in a measurement of zero intensity and all light leaves the device through the light output port. Unfortunately in practice light travels through the atmosphere which through turbulences causes the optical phase between the beams to fluctuate. This in turn leads to some part of the signal leaving through the dark port. The crucial step in beam combination is that from the measurement of intensity of light in this port one can infer the phase difference between the beams and correct it before the beam splitter therefore increasing the amount of light that interferes constructively and leaves the device through the light port for the subsequent time slots.

The aim of the project is to find and study the limits on the efficiency of coherent beam combination imposed by the laws of quantum mechanics in realistic scenarios including both detection noise and fluctuations of phase and intensity related to signal propagation. In a regime of weak signals, typical for satellite and deep-space communication, an additional factor affecting the beam combination performance is the fundamental quantum optical shot noise inherent to the process of photodetection. The source of this noise is the fact that at the most basic level light is composed of individual photons and the photodetection outcome is probabilistic in nature and depends on the photon number statistics of the quantum state of light in the pulse. Due to the discrete nature of this probability distribution it may happen that the registered number of photocounts is too low for valid phase correction in a timescale in which phase fluctuations would not change its value significantly.

A second goal of the project is to find ways to increase the efficiency of beam combination and approach the limits described above. Efficient procedures for phase correction and intensity estimation may allow to decrease the influence of these parameters fluctuations. Another part of the project will be to analyze if the use of nonclassical states of light or quantum detectors can improve the beam combination efficiency or allow to combine beams with lower intensity than possible classically. An analogous effect is known in quantum metrology, where e.g. squeezed states are used to improve precision of phase estimation in interferometric gravitational waves observatories like LIGO.

The answers to the above questions may be relevant in the design of optical communication systems in future satellites and deep-space missions beyond the orbit of the Moon. In particular in the latter scenario quantum effects may become especially relevant since the expected received signal strength is of the order of a single photon due to the large distance from Earth.