The fractional Fourier Transform is a generalization of the Fourier Transform that enables a partial transition from a description of a wave in time to a description in frequency. Intuitively, it can be understood as a rotation of a circulation (for instance, the chronocyclic Wigner function) of the thought about signal by a specific angle in the time-frequency domain.
Students in the laboratory presenting rotation of Schrödinger feline states. No real cats were injured during the project. Credit: S. Kurzyna and B. Niewelt, University of Warsaw
It turns out that transforms of this type are extremely beneficial in the design of special spectral-temporal filters to remove sound and allow the development of algorithms that make it possible to utilize the quantum nature of light to distinguish pulses of different frequencies more specifically than traditional methods. This is especially important in spectroscopy, which assists study the chemical residential or commercial properties of matter, and telecommunications, which needs the transmission and processing of info with high precision and speed.
Lenses, and the Fourier Transform?
A common glass lens can focusing a monochromatic beam of light falling on it to nearly a single point (focus). Altering the angle of occurrence of light on the lens leads to a modification in the position of the focus. This allows us to convert angles of incidence into positions, getting the example of the Fourier Transform, in the area of positions and directions. A classical spectrometer based upon a diffraction grating usages this impact to transform the wavelength details of light into positions, allowing us to identify in between spectral lines.
Time and frequency lenses
To the glass time, frequency and lens lenses enable the conversion of a pulses duration into its spectral circulation, or effectively, perform a Fourier change in time and frequency area. The right selection of powers of such lenses makes it possible to carry out a fractional Fourier Transform. In the case of optical pulses, the action of time and frequency lenses represents using quadratic phases to the signal.
To process the signal, the scientists used a quantum memory– or more exactly a memory equipped with quantum light processing abilities– based on a cloud of rubidium atoms placed in a magneto-optical trap. The pulse was subjected to a time lens throughout reading and composing, and a frequency lens acted on it during storage.
The device developed at the UW allows the application of such lenses over a very wide variety of specifications and in a programmable way. A double pulse is really susceptible to decoherence, hence it is typically compared to the famous Schrödinger feline– a macroscopic superposition of being dead and alive, almost impossible to achieve experimentally. Still, the team had the ability to execute devoted operations on those vulnerable dual-pulse states.
The publication was the outcome of operate in the Quantum Optical Devices Laboratory and Quantum Memory Laboratory in the “Quantum Optical Technologies” center with the participation of two masters trainees: Stanislaw Kurzyna and Marcin Jastrzebski, 2 undergraduate trainees Bartosz Niewelt and Jan Nowosielski, Dr. Mateusz Mazelanik, and lab heads Dr. Michal Parniak and Prof. Wojciech Wasilewski. For the described outcomes, Bartosz Niewelt was likewise granted a discussion grant award throughout the recent DAMOP conference in Spokane, WA.
Before direct application in telecommunications, the technique needs to initially be mapped to other wavelengths and specification varieties. Fractional Fourier change, nevertheless, might show crucial for optical receivers in state-of-the-art networks, including optical satellite links. A quantum light processor established at the UW makes it possible to find and evaluate such new procedures in an effective way.
Referrals: “Experimental Implementation of the Optical Fractional Fourier Transform in the Time-Frequency Domain” by Bartosz Niewelt, Marcin Jastrzębski, Stanisław Kurzyna, Jan Nowosielski, Wojciech Wasilewski, Mateusz Mazelanik and Michał Parniak, 12 June 2023, Physical Review Letters.DOI: 10.1103/ PhysRevLett.130.240801.
The “Quantum Optical Technologies” (MAB/2018/4) task is performed within the International Research Agendas program of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
Researchers have actually developed a groundbreaking technique to carry out the fractional Fourier Transform of optical pulses using quantum memory. This distinct accomplishment included executing the improvement on a “Schrödingers cat” state, having potential applications in telecoms and spectroscopy.
Researchers from the University of Warsaws Faculty of Physics, in collaboration with experts from the QOT Centre for Quantum Optical Technologies, have pioneered an ingenious method that allows the fractional Fourier Transform of optical pulses to be performed utilizing quantum memory.
This achievement is special on the worldwide scale, as the group was the first to provide a speculative execution of the stated change in this kind of system. The results of the research study were published in the prestigious journal Physical Review Letters. In their work, the trainees tested the implementation of the fractional Fourier Transform utilizing a double optical pulse, also referred to as a “Schrödingers feline” state.
The spectrum of the pulse, and temporal distribution
Waves, such as light, have their own particular homes– pulse duration and frequency (matching, in the case of light, to its color). It turns out that these characteristics relate to each other through an operation called the Fourier Transform, which makes it possible to change from explaining a wave in time to describing its spectrum in frequencies.
In their work, the students tested the application of the fractional Fourier Transform utilizing a double optical pulse, likewise understood as a “Schrödingers feline” state.
This permits us to transform angles of occurrence into positions, obtaining the example of the Fourier Transform, in the space of positions and directions. To the glass time, lens and frequency lenses enable the conversion of a pulses duration into its spectral distribution, or successfully, perform a Fourier change in time and frequency space. The best choice of powers of such lenses makes it possible to carry out a fractional Fourier Transform. Fractional Fourier transform, nevertheless, could prove essential for optical receivers in cutting edge networks, consisting of optical satellite links.
