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

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.Comment: 4 pages, 4 figures, new result

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.Comment: This article belongs to the Special Issue "Symmetries and the Pauli Exclusion Principle

Hydrogen atom in phase space: The Wigner representation

We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.Comment: 8 pages (including figures

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.Comment: 7 pages, 4 figure

Spontaneous emission in a Fabry-Perot cavity: frequency modulation and collective effects

Abstract The spontaneous emission of radiation from two two-level atoms in a Fabry-Perot cavity is considered. The transition frequency of the atoms is assumed to be modulated. It is shown that the frequency modulation leads to radical change of the spontaneous emission dynamics, including the decoherence properties of the entangled atomic states. Two ingredients are necessary in order to achieve this. Firstly, the modulation should be able to periodically detune the atoms from the resonance with the cavity. Secondly, the dynamics of spontaneous emission is efficiently modified if a resonant condition between the modulation frequency and modulation depth is fulfilled. Thus, frequency modulation can be used to dynamically control the collective effects in spontaneous emission in cavities