Researchers from the Department of Physics at the University of Warsaw, in collaboration with experts from the QOT Center for Quantum Optical Technology, have pioneered an innovative technology that enables the fractional Fourier transformation of light pulses using quantum memory. This achievement is unique worldwide, as the team is the first to experimentally achieve the above transformation in such a system.
The research results were published in the famous journal Physical Review Letters. In their work, the students tested implementations of fractional Fourier transforms using double light pulses, also known as "Schrödinger's cat" states.
A wave (like light) has its own properties - pulse duration and frequency (in the case of light, corresponding to its color). It turns out that these properties are related to each other through an operation called the Fourier transform, which switches from describing the wave in terms of time to describing the wave spectrum in terms of frequency.
The fractional Fourier transform is a generalization of the Fourier transform that allows the transition from describing the time part of a wave to describing the frequency of the wave. Intuitively, it can be understood as rotating the distribution of the signal under consideration (for example, the time-periodic Wigner function) by a certain angle in the time-frequency domain.
This type of transformation has proven very useful in designing special spectral-temporal filters that not only remove noise but also create algorithms that exploit the quantum properties of light to distinguish pulses of different frequencies more precisely than traditional methods. This is particularly important in the fields of spectroscopy, which helps study the chemical properties of substances, and telecommunications, which require high-precision, high-speed transmission and processing of information.
An ordinary glass lens is able to focus a monochromatic light beam falling on it to almost a point (focal point). Changing the angle of incidence of light on the lens will change the position of the focus. This converts the angle of incidence into position, obtaining similar Fourier transforms in direction and position space. Classic spectrometers based on diffraction gratings exploit this effect to convert wavelength information of light into positional information, allowing us to distinguish spectral lines.
Similar to glass lenses, time and frequency lenses can also convert the duration of a pulse into a spectral distribution, or effectively perform a Fourier transform in time and frequency space. By correctly choosing the power of this lens, a fractional Fourier transform can be performed. In the case of light pulses, time and frequency lenses act as a secondary phase transformation of the signal.
To process the signals, the researchers used a quantum memory - or, more precisely, a memory with quantum light processing capabilities - based on a clump of rubidium atoms placed in a magneto-optical trap. Atoms are cooled to a specified temperature. The memory is placed in a changing magnetic field, allowing components of different frequencies to be stored in different parts of the atomic cloud. Pulses are subject to time lensing during writing and reading and frequency lensing during storage.
The device developed at the University of Washington can programmably implement such a lens over a very wide range of parameters. The double pulse is so prone to decoherence that it is often compared to the famous Schrödinger's cat - a macroscopic superposition that comes back from the dead and is almost impossible to achieve experimentally. Nonetheless, the team was able to faithfully manipulate these fragile double-pulse states.
This paper is the result of the work of the Quantum Optical Devices Laboratory and the Quantum Memory Laboratory of the "Quantum Optical Technology" Center. Two master's students participated in this work: Stanislaw Kurzyna and Marcin Jastrzebski, two undergraduates Bartosz Niewelt and Jan Nowosielski, Dr. Mateusz Mazelanik, and the laboratory leaders Dr. Michal Parniak and Professor Wojciech Wasilewski participated in this work. Due to these achievements, BartoszNiewelt also received a speaking grant award at the recent DAMOP conference in Spokane, Washington.
The method must first be mapped to other wavelengths and parameter ranges before being directly applicable to the telecommunications field. However, the fractional Fourier transform is crucial for optical receivers in state-of-the-art networks, including optical satellite links. A quantum light processor developed at the University of Washington can efficiently find and test this new protocol.