arXiv subjects

Jan Mostowski

Publications and source records attributed to Jan Mostowski.

12 recordsLinked to original sources

arXiv2023

Electron Localization in Rydberg States

We discuss the possibility of localizing an electron in a highly excited Rydberg state. The second-order correlation of emitted photons is the tool for the determination of electron position. This second-order correlation of emitted radiation and, therefore, the correlation of operators describing the acceleration of the electron allows for a partial localization of the electron in its orbit. The correlation function is found by approximating the transition matrix elements by their values in the classical limit. It is shown that the second-order correlation, depending on two times, is a function of the time difference and is a periodic function of this argument with the period equal to the period of the corresponding classical motion. The function has sharp maxima corresponding to large electron acceleration in the vicinity of the ``perihelion.'' This allows the localization of the electron in its consecutive approach to the perihelion point.

quant-ph↗

arXiv2021

Pauli crystals in harmonic trap and on a sphere

Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli exclusion principle. Measuring all particles at once, their positions tend to be close to vertices of non-trivial polyhedrons. Similar shapes are found for systems of particles bound to the surface of a sphere.

quant-ph↗

arXiv2021

Wigner Function for Harmonic Oscillator and The Classical Limit

The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function is shown using the quantum harmonic oscillator as an example. The Wigner function is found exactly for all states. The semi-classical wavefunctions for highly excited states are used as the approach to the classical limit. Therefore, one can found the classical limit of the Wigner function for highly excited states and shown that it gives the classical microcanonical ensemble.

quant-ph↗

arXiv2020

Pauli crystals -- interplay of symmetries

Recently observed Pauli crystals are structures formed by trapped ultracold atoms with the Fermi statistics. Interactions between these atoms are switched off, so their relative positions are determined by joined action of the trapping potential and the Pauli exclusion principle. Numericalmodeling is used in this paper to find the Pauli crystals in a two-dimensional isotropic harmonic trap, three-dimensional harmonic trap, and a two-dimensional square well trap. The Pauli crystals do not have the symmetry of the trap -- the symmetry is broken by the measurement of positions and, in many cases, by the quantum state of atoms in the trap. Furthermore, the Pauli crystals are compared with the Coulomb crystals formed by electrically charged trapped particles. The~structure of the Pauli crystals differs from that of the Coulomb crystals, this provides evidence that the exclusion principle cannot be replaced by a two-body repulsive interaction but rather has to be considered to be a specifically quantum mechanism leading to many-particle correlations.

cond-mat.quant-gas↗

arXiv2019

Quantum versus classical angular momentum

Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together with approximation to Clebsh-Gordan coefficients.

quant-ph↗

arXiv2017

On the observability of Pauli crystals

The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent [1]. These geometric structures, called Pauli crystals, are predicted for a system of $N$ identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of the system. Here we study how fragile Pauli crystals are when realistic experimental limitations are taken into account. The influence of the number of single-shots pictures available to analysis, thermal fluctuations and finite efficiency of detection are considered. The role of these sources of noise on the possibility of experimental observation of Pauli crystals is shown and conditions necessary for the detection of the geometrical arrangements of particles are identified.

cond-mat.quant-gas↗

arXiv2015

Single shot imaging of trapped Fermi gas

Recently developed techniques allow for simultaneous measurements of the positions of all ultra cold atoms in a trap with high resolution. Each such single shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single shot measurements in case of cloud of ultra-cold non-interacting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms.

cond-mat.quant-gas↗

arXiv2013

Ground states and dynamics of a trapped charged particle in the magnetic field

A system of two charged particles in a harmonic trap with additional magnetic field is considered. The problem is reduced to a single-particle one in relative coordinates. The ground- and lowest excited-state energies and wave functions are found. The ground state exhibits non-zero expectation value of the velocity (kinetic momentum) and the probability current density does not vanish as well. When the ground state becomes degenerate the expectation value of velocity becomes discontinuous. The effects associated with turning on of the magnetic field are studied by solving the appropriate time-dependent Schr\"odinger equation. No substantial differences between abrupt (discontinuous in time) and continuous switching on have been observed. Evolution of a wave packet which is initially Gaussian is also investigated. The wave packet loses its Gaussian nature and, after sufficiently large time, a system of diffractive maxima and minima is built.

quant-ph↗

arXiv2006

From a nonlinear string to a weakly interacting Bose gas

We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are included. An universal action has to be introduced in order to define particle number. The value of this action should be equal to the Planck constant. This constrain can be imposed by removing high frequency modes from the dynamics by introducing a cut-off. We show that the position of the cut-off has to be carefully adjusted. Finally, we show the proper choice of the cut-off ensures that all low frequency eigenenmodes which are taken into account are macroscopically occupied.

cond-mat.other↗

arXiv2005

Formation of soliton trains in Bose-Einstein condensates by temporal Talbot effect

We study the recent observation of formation of matter-wave soliton trains in Bose-Einstein condensates. We emphasize the role of the box-like confinement of the Bose-Einstein condensate and find that there exist time intervals for the opening the box that support the generation of real solitons. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in the experiment. Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.

cond-mat.other↗

arXiv2000

Exact versus mean-field description of the Bose-Einstein condensate: a model study

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactl y soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.

cond-mat.soft↗

arXiv2000

Destruction of Bose-Einstein condensate by strong interactions

We study exactly soluble system of trapped bosonic particles interacting by a model harmonic forces. The model allows for detailed examination of the order parameter (condensate wave function) as well as concept of the off-diagonal and diagonal order. We analyze the effect of interactions on the condensate and show that sufficiently strong interactions, attractive or repulsive, lead to destruction of the condensate. In the thermodynamic limit this destruction has a critical character. It is shown that the existence of the coherent state of bosons is related to existence of two length scales determined by one- and two-particle reduced density matrices. The condensate can exist only if the two length scales are of the same order. Interactions, both repulsive and attractive, change their relative size which may lead to destruction of coherence in the system and depletion of the condensate. We suggest that this scenario is model independent.

cond-mat.soft↗