The QOT Centre for Quantum Optical Technologies and University of Warsaw’s Faculty of Physics have developed an innovative method for performing the fractional Fourier Transform of optical pulses, which is only possible with quantum memory.
This achievement stands out globally as the first to demonstrate an experimental application of the transformation in this kind of system. The research was published in the prestigious Physical Review Letters, where it was tested using a double optical pulse, also known as ‘Schrödinger’s cat’ state, to implement the fractional Fourier Transform.
The pulse’s spectrum and duration.
Waves, including light, possess their own unique characteristics such as pulse duration and frequency (which corresponds to the color of light). The Fourier Transform is a process that allows for the transition from describing emulsions in time to expressing the spectrum of an oscillator in frequencies.
The fractional Fourier Transform is a generalization of the Fouriers’ description of time waves that leads to describing them in frequency as if it were merely reflected an angle in the time–frequency domain, and can be interpreted in hindsight as rotation of arbitrary distribution.
The use of transforms like this is particularly beneficial in the development of specialized noise-reducing spectral-temporal filters and algorithms that utilize the quantum nature of light to detect pulses of different frequencies with greater accuracy. This is especially crucial in fields such as chemistry, physics, and telecommunications, which require fast and precise information transmission.
What is the Fourier Transform associated with lenses?
By adjusting the angle of incidence of light on an ordinary glass lens, a monochromatic beam of white light can be focused to almost 0°. This transforms the focus of the image into its position, which allows us to derive the Fourier Transform from angles of illumination to positions. A classical spectrometer built on diffraction grating uses this effect to convert wavelength information of pure photon emission into positions, making it possible to differentiate between spectra and rays.
The lenses of time and frequency
Time and frequency lenses, like glass lenses in the same way, can transform a pulse’s duration into its spectral distribution or perform inverse Fourier transform within time and frequencies. The selection of powers in these lenses allows for fractional FourIER Transform, while the application of quadratic phases to optical pulses is equivalent.
The researchers utilized a quantum memory, which is based on atoms of rubidium that were placed in ‘a magneto-optical trap’ and cooled to temperatures often millions above absolute zero. They then placed the memory in an evolving magnetic field, where components of different frequencies could be stored; subsequently, he read and wrote the pulse using specialized equipment (a time lens) while the other components were being read or written, and another lens used to store the information, with the latter acting as if it was acted on it during storage.
The UW-developed device enables the use of such lenses across a wide range of parameters and in programmable ways. A double pulse is highly decoherent, making it comparable to the famous Schrödinger cat. However, the team was able to perform faithful operations on fragile dual-pulse states.
The publication was a result of research conducted at the Quantum Optical Devices Laboratory and QuantUM Memory Laboratory, which had members from Stanislaw Kurzyna, Marcin Jastrzebski, Bartosz Niewelt, Jan Nowosielski (undergraduate) and Dr. Mateusz Mazelanik (lab head), as well as Drexel Parniak and Prof. Wojciech Wasilewski (17th grade), who were awarded ‘presentation award’ for their work during the recent DAMOP conference in Spokane, WA
Prior to its direct use in telecommunications, the method must be mapped to other wavelengths and parameter ranges. The crucial role of fractional Fourier transform is essential for optical receivers in advanced networks, including optical satellite links. A quantum light processor developed at the UW facilitates the efficient discovery and testing of these novel protocols.
Physical Review Letters, cited on 12 June 2023, contains an article titled “Experimental Implementation of the Optical Fractional Fourier Transform in the Time-Frequency Domain” by Bartosz Niewelt, Marcin Jastrzbski, Stanisaw Kurzyna, Jan Nowosielski (from Polish obsessive list) and Mateusz Mazelanik, Micha Parniak.
The publication’s DOI is 10.1031/PhysRevLett.130.240801.
The Foundation for Polish Science’s “Quantum Optical Technologies” (MAB/2018/4) project is carried out as part of the International Research Agendas program, which is co-funded by the European Union through the EU Regional Development Fund.