Russian physicists were able to subtract ten photons from the thermal state of light – a set of photons that behave consistently like a bosonic gas – and measure its parameters after this operation. The measurement results are in good agreement with theoretical values, according to an article published in Physical Review A…

In quantum optics, scientists prepare and measure various quantum states of light. These states can be described using a density matrix that defines how the photon wave functions are related. For example, in the case of the Fock state, it is just a set of n photons, in the case of a coherent state it is the sum of all possible Fock states, taken with some coefficients. Quantum states can belong to one of several basic classes – for example, displaced or squeezed states.

Wigner functions of states with different numbers of split off photons
KG Katamadze et. al. / Phys. Rev. A

Quantum thermal states of light play a special role among them. In this case, the values ​​of the Bose-Einstein distribution are on the diagonal of the density matrix, and the off-diagonal elements are equal to zero. On the one hand, such states are relatively easy to obtain. On the other hand, they can be used to study effects based on classical and quantum correlation. It is worth noting that one of the first experiments in quantum optics was carried out with the thermal states of light, and since then they have been used in many interesting applications, for example, in ghost imaging or “thermal laser”.

At the same time, the addition and subtraction of photons from the light field is of great interest in quantum optics. For example, in this way it is possible to check the commutation relations of the operators that describe the creation and annihilation of photons. Or enhance the light without adding unnecessary noise. For the first time, states from which one or two photons were subtracted were investigated in 2008 by scientists from Italy and Great Britain. There was also work on obtaining states from which up to eight photons were subtracted.

Physicists from Moscow State University and the Institute of Physics and Technology of the Russian Academy of Sciences set up an experiment in which they obtained states with 10 subtracted photons. To do this, they used the following experimental setup. Light from a cw helium-neon laser (wavelength of about 633 nanometers) was directed into an optical fiber and split into two beams. The smaller part was directed to a rotating matte disk (GGD in the figure), which randomly modulated the amplitude and phase of the laser radiation and turned the light into quasi-thermal. Then the photons were “pinched off” from this beam with the help of a separator. Finally, the number of split off photons was measured using a COUNT-100C-FC detector (APD in the figure), and the state of the remaining beam with subtracted photons was compared with the initial state of another beam (homodyne detection). The main difference between the experiment and the previous ones is that one APD detector could sequentially record several photons at once. This is what made it possible to study states with a large number of split off photons.

Schematic of the experimental setup KG Katamadze et. al. / Phys. Rev. A

As a result, scientists experimentally found the probability distribution for states with different numbers of photons subtracted. They calculated the same distribution theoretically and compared it with experiment. It turned out that it depends on only two parameters – the average number of photons μ and the coherence parameter a, which, in turn, are completely determined by the number of photons subtracted from the state. By approximating the experimental dependence with distributions with different parameters a and μ, physicists found out which values ​​are best suited for describing states, and then compared them with the theoretically calculated values. It turned out that, on the whole, they are in good agreement, although the coherence parameter is slightly underestimated in comparison with theory.

Dependence on the number of subtracted photons of the average number of photons μ and the coherence parameter a
KG Katamadze et. al. / Phys. Rev. A

In addition, for each state, physics calculated the fidelity of experimental versus theoretical distributions. Roughly speaking, this number shows how well two distributions match. It turned out that the average purity is 99.6 – 99.9 percent. Generally speaking, this is a very high value.

Source: nplus1.ru