Research

One of the greatest challenges in the field of topological matter is the determination of global topological invariants from local measurements such as local state density. The project concerns the use of machine learning methods to identify Chern numbers based on local state density measurements in two-dimensional topological superconductors. Solving the Chern number measurement problem will enable significant advances in the physics of topological materials. Purpose of the project is to use trained neural networks to determine Chern numbers for real samples produced by experimental groups. Such a perspective would open the possibility of determining the values ​​of topological invariants of new exotic two-dimensional materials without knowing their detailed microscopic model.

One of the greatest challenges in the field of topological matter is the determination of global topological invariants from local measurements such as local state density. The project concerns the use of machine learning methods to identify Chern numbers based on local state density measurements in two-dimensional topological superconductors. Solving the Chern number measurement problem will enable significant advances in the physics of topological materials. Purpose of the project is to use trained neural networks to determine Chern numbers for real samples produced by experimental groups. Such a perspective would open the possibility of determining the values ​​of topological invariants of new exotic two-dimensional materials without knowing their detailed microscopic model.

One of the direct applications of quantum technologies today are atomic clocks, which provide a universal frequency standard. The system of atomic clocks placed on Earth and Earth's orbit are the basis of the GPS geolocation system. The fundamentals of atomic clock is the precise measurement of atomic transitions in cesium-133 atoms. The accuracy of measuring atomic transitions can be significantly increased when atoms are prepared in a special quantum state, the so-called spin-squeezed states.

This research project focuses on the problem of producing and maintaining non-trivial quantum states (including Schrodinger's cat states, spin-squeezed states and GHZ (Greenberger-Horne-Zeilinger) states) in a one-dimensional optical lattice with ultracold atoms. Open questions are about life-time of such states, their robustness to atom loses and non-zero temperatures of the system.

The Atomic Laser is a coherent source of matter waves based on the ground state of Bose-Einstein condensate in an atomic trap. After partial opening of the trap emission of a coherent beam of matter waves take place, and the momentum-distribution is given by the ground state of the condensate. Coherent source of matter-waves is an important ingredient of atomic interferometers for quantum metrology. This project was devoted to study potential utilization of optical random lasers in order to narrow the width of the emitted matter waves in atomic lasers.

In the standard problem of one-dimensional Anderson location in the uncorrelated disorder all particles localize. The situation is different when the random potential has a finite correlation length. We showed a method of preparing a correlated random optical potential for atoms, which resulted in the appearance of a transparent momentum window: atoms with given momentum do not scatter at the random potential and propagate coherently through it.

It was proposed to use the nontrivial Anderson location for selective filtration of matter wave momentum, thus allowing the spectral width of a standard atomic laser to be narrowed down. The idea was to prepare Bose-Einstein condensate (BEC) in the initial state of the harmonic trap, then to open the trap and to evolve the condensate in a specially prepared random potential. This meant that the initial matter wave distribution in an atomic laser could become sharpen to the width of the momentum window with a divergent Anderson localization length.

Next, we showed the existence of a similar effect of band-pass filter of matter waves for atoms confined in periodically modulated optical lattice. We have shown the existence of a momentum whose location depends on experimental parameters, allowing for selective emission of matter waves.

Accurate temperature measurement in quantum systems is of fundamental importance for the construction of quantum computers, in which quantum states may lose their properties due to interactions with a thermal reservoir. In Phys. Rev. Lett. 114, 220405 (2015), the Authors presented fundamental limitations on the accuracy of temperature measurement of quantum systems from the point of view of quantum estimation theory. The authors showed what the energetic structure should have a Hamiltonian of a hypothetical quantum thermometer, which would show maximum sensitivity to changes in temperatures close to absolute zero. The energy structure of an ideal quantum thermometer should consist of one ground state and a degenerate excited state, while the energy gap should be proportional to the temperature, the accuracy of which we want to maximize.

We have shown that a simple system of several attracting ultracold fermion atoms in a one-dimensional harmonic trap has a very similar energy structure - such systems have been carried out experimentally for several years (Prof. Selim Jochim's group in Heilderberg, Science Vol. 332, 6027 (2011)).

System of several attracting fermions can serve as a quantum thermometer to measure temperatures order of the nanokelvin by measuring the probability of occupancy of the lowest states of the harmonic trap of atoms in the thermal state. The proposed quantum thermometer allows measurements to be made with an accuracy very close to the fundamental limitation on the precision of temperature measurements.

The Rydberg states of an atom are states with a large main quantum number, they are characterized by long life times (on the order of several milliseconds), the size of the atomic cloud on the order of micrometers and the long-range nature of van-der-Waals interactions. The Rydberg states constitute therefore, a promising platform for creating simulators of quantum systems known from matter physics condensed, incl. spin models as well as a platform for building quantum computers.

One of the promising experimental technique for utilization of Rydberg states in quantum simulations is called Rydberg-dressing. Rydberg-dressing, i.e. off-resonant coupling of the ground state atom to highly lying Rydberg state allows to induce long-range interactions between ultra-cold alkali atoms, which under 'normal' conditions only interact via contact interactions.

I have shown that the off-resonant coupling of condensate atoms with Rydberg states allows to effectively modify the scattering length of atoms in the condensate, and thus also their interactions. This is an alternative mechanism to the known Feshbach resonances. In addition, the Rydberg coupling based on laser light can be easily modified both in space and time, so that the interactions between atoms can be time and position-dependent - a very attractive experimentally method for studying exotic states of atomic condensates.

Project was devoted to a proposal for an experimental implementation of a quantum simulator for dynamics of soliton in the SSH model. In particular, so called Davydov soliton.

Davydov proposed a model to explain the almost lossless energy transport in quasi-one-dimensional molecular systems such as proteins or DNA strands [1]. A key element of Davydov's model is coupling between phonons propagating in a molecular chain and transported excitation. Propagation of excitation interacting with phonons results in the formation of a specific type of polaron, the so-called Davydov's soliton, which is responsible for energy transport in molecular chains.

Proposed setup is based on a one-dimensional optical lattice filled with Rydberg-dressed atoms, with one atom wearing the Rydberg angular state, and the other atoms wearing zero angular momentum states. The long-range nature of interactions allows the dressed state, carrying the angular momentum, to jump along the remaining atoms. The amplitude of such a transition depends on the distance between atoms, which, despite the confinement of mass centers in the optical minima, have quantum fluctuations of the position operators. Both effects - the long-range interaction and position quantum fluctuations make it possible to construct a simulator allowing direct observation of the Davydov soliton.

[1] A.S. Davydov, "Biology andquantum mechanics ”Permagon. Oxford, 1982