Researchers have developed a breakthrough method to perform fractional Fourier transforms of light pulses using quantum memory. This unique achievement includes the implementation of transformations in the ‘Schrödinger’s cat’ state, with potential applications in telecommunications and spectroscopy.
Researchers from the Faculty of Physics at the University of Warsaw, in collaboration with experts from the QOT Quantum Optics Technical Center, have developed an innovative technique that allows the fractional Fourier transform of light pulses to be performed using quantum memory.
This achievement is unique on a global scale, as the team presented the first experimental implementation of the aforementioned transformations in a system of this kind.Research results were published in prestigious journals physical review letter. In their research, the students tested a fractional His implementation of the Fourier transform using double light pulses, also known as the “Schrödinger’s cat” condition.
Pulse spectrum and time distribution
Waves such as light have unique properties: pulse duration and frequency (which in the case of light corresponds to its color). These properties are found to be interrelated through an operation called the Fourier transform, which makes it possible to switch from describing waves in time to describing spectra in frequency.
The fractional Fourier transform is a generalization of the Fourier transform that allows a partial transition from describing waves in time to describing them in frequency. Intuitively, this can be understood as a rotation of the considered signal’s distribution (eg, the periodic Wigner function) by a certain angle in the time-frequency domain.
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Students in the laboratory present the rotation of Schrödinger’s cat states. No cats were actually injured during the project.Credit: S. Kurzyna and B. Niewelt, University of Warsaw
This type of transform is very useful for designing special spectral-temporal filters to remove noise, allowing the creation of algorithms that can take advantage of the quantum properties of light to distinguish between pulses of different frequencies more accurately than ever before. It turns out. Method. This is especially important in spectroscopy, which helps study the chemical properties of materials, and in telecommunications, where information must be transmitted and processed with high precision and speed.
Lenses and Fourier Transforms?
A normal glass lens can focus the monochromatic light rays that fall on it to almost one point (focal point). Changing the angle of incidence of light on the lens changes the position of the focal point. This allows us to convert the angle of incidence to position, giving us the analogy of a Fourier transform in the space of orientation and position. Classical spectrometers based on diffraction gratings take advantage of this effect to convert the wavelength information of light into position so that spectral lines can be distinguished.
Time and frequency lens
Similar to glass lenses, time and frequency lenses can be used to effectively transform pulse durations into spectral distributions, i.e. Fourier transforms in time and frequency space. If you choose the power of such a lens correctly, you can perform fractional Fourier transforms. For light pulses, the action of time and frequency lenses corresponds to applying a quadratic phase to the signal.
To process the signal, the researchers used a quantum memory based on a cloud of rubidium atoms placed in a magneto-optical trap, more precisely a memory with quantum optical processing capabilities.Atoms were cooled to temperatures of tens of millions of degrees or more absolute temperature. The memory was placed in a changing magnetic field, allowing different frequency components to be stored in different parts of the cloud. The pulses are subjected to a time lens during writing and reading, and a frequency lens during storage.
Devices developed at UW allow us to implement such lenses in a programmable manner over a very wide range of parameters. Double pulsing is very prone to decoherence and is often compared to the famous Schrödinger cat. This is a macroscopic superposition of dead and living states, which is nearly impossible to achieve experimentally. Still, the team was able to implement high-fidelity operations against these vulnerable dual-pulse conditions.
This publication is the result of research in the Quantum Optical Devices Laboratory and the Quantum Memory Laboratory within the Center “Quantum Optical Technologies”, with master’s students Stanislaw Kurzina and Marcin Jastrzebski, Faculty Mr. Bartosz Nievert and Dr. Jan Novosielski participated. Mateusz Mazelanik, the head of the lab, Dr. Michal Parniak and his Prof. Wojciech Wasilewski. For the described results, Bartosz Niewelt also received a presentation grant award during his recent DAMOP his conference in Spokane, Washington.
The method must first be mapped to other wavelengths and parameter ranges before being directly applied to telecommunications. However, the fractional Fourier transform may prove important for optical receivers in state-of-the-art networks, including optical satellite links. Quantum optical processors developed at UW will make it possible to discover and test such new protocols in an efficient manner.
References: Bartosz Niewelt, Marcin Jastrzębski, Stanisław Kurzyna, Jan Nowosielski, Wojciech Wasilewski, Mateusz Mazelanik, and Michał Parniak, “An Experimental Implementation of the Optical Fractional Fourier Transform in the Time-Frequency Domain”, June 12, 2023, Available here. physical review letter.
DOI: 10.1103/PhysRevLett.130.240801
The “Quantum Optics Technologies” (MAB/2018/4) project is being implemented within the International Research Agenda Program of the Polish Science Foundation co-financed with the European Union under the European Regional Development Fund.