Tomasz Karpiuk

Soliton Trains in Bose-Fermi Mixtures

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.

Coherent forward scattering peak induced by Anderson localization.

Numerical simulations show that, at the onset of Anderson localization, the momentum distribution of a coherent wave packet launched inside a random potential exhibits, in the forward direction, a novel interference peak that complements the coherent backscattering peak. An explanation of this phenomenon in terms of maximally crossed diagrams predicts that the signal emerges around the localization time and grows on the scale of the Heisenberg time associated with the localization volume. Together, coherent back and forward scattering provide evidence for the occurrence of Anderson localization.

Spontaneous Solitons in the Thermal Equilibrium of a Quasi-1D Bose Gas

We show that solitons occur generically in the thermal equilibrium state of a weakly interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state, usually thought of as primarily phase-fluctuating. Thermal solitons are seen in uniform 1D, trapped 1D, and elongated 3D gases, appearing as shallow solitons at low quasicondensate temperatures, becoming widespread and deep as temperature rises. This behavior can be understood via thermal occupation of the type II excitations in the Lieb-Liniger model of a uniform 1D gas. Furthermore, we find that the quasicondensate phase includes very appreciable density fluctuations while leaving phase fluctuations largely unaltered from the standard picture derived from a density-fluctuation-free treatment.

Superfluid fountain effect in a Bose-Einstein condensate

We consider a simple experimental setup, based on a harmonic confinement, where a Bose-Einstein condensate and a thermal cloud of weakly interacting alkali atoms are trapped in two different vessels connected by a narrow channel. Using the classical field approximation, as described in J. Phys. B 40, R1 (2007) and optimized in Phys. Rev. A 81, 013629 (2010) for an arbitrary trapping potential, we theoretically investigate the analog of the celebrated superfluid helium fountain effect. We show that this thermo-mechanical effect might indeed be observed in this system. By analyzing the dynamics of the system, we are able to identify the superfluid and normal components of the flow as well as to distinguish the condensate fraction from the superfluid component. We show that the superfluid component can easily flow from the colder vessel to the hotter one while the normal component is practically blocked in the latter.

Imaging single Rydberg electrons in a Bose–Einstein condensate

The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment.

Coherent backscattering of ultracold matter waves: Momentum space signatures

Using analytical and numerical methods, it is shown that the momentum distribution of a matter wave packet launched in a random potential exhibits a pronounced coherent backscattering (CBS) peak. By analyzing the momentum distribution, key transport times can be directly measured. The CBS peak can be used to prove that transport occurs in the phase-coherent regime, and measuring its time dependence permits monitoring the transition from classical diffusion to Anderson localization.

On the stability of Bose–Fermi mixtures

We consider the stability of a mixture of degenerate Bose and Fermi gases. Even though the bosons effectively repel each other, the mixture can still collapse provided the Bose and Fermi gases attract each other strongly enough. For a given number of atoms and the strengths of the interactions between them, we find the geometry of a maximally compact trap that supports the stable mixture. We compare a simple analytical estimation for the critical axial frequency of the trap with results based on the numerical solution of hydrodynamic equations for the Bose–Fermi mixture.

Correspondence between dark solitons and the type II excitations of the Lieb-Liniger model

A one-dimensional model of bosons with repulsive short-range interactions, solved analytically by Lieb and Liniger many years ago, predicts existence of two branches of elementary excitations. One of them represents Bogoliubov phonons, the other, as suggested by some authors, might be related to dark solitons. On the other hand, it has been already demonstrated within a framework of the classical field approximation that quasi-one-dimensional interacting Bose gas at equilibrium exhibits excitations which are phonons and dark solitons. By showing that statistical distributions of dark solitons obtained within the classical field approximation match the distributions of quasiparticles of the second kind derived from fully quantum description we demonstrate that type II excitations in the Lieb-Liniger model are, indeed, quantum solitons.

Decay of multiply charged vortices at nonzero temperatures

Inspired by a recent experiment (Ryu 2007 et al Phys. Rev. Lett. 99 260401), we study the instability of multiply charged vortices in the presence of thermal atoms. We find various scenarios of the splitting of such vortices. The onset of the decay of a vortex is always preceded by an increase in the number of thermal (uncondensed) atoms in the system and manifests itself by the sudden rise of the amplitude of the oscillations of the quadrupole moment. Our calculations show that the decay time gets shorter when the multiplicity of a vortex becomes higher. (Some figures in this article are in colour only in the electronic version)

Constructing a classical field for a Bose-Einstein condensate in an arbitrary trapping potential: Quadrupole oscillations at nonzero temperatures

We optimize the classical field approximation of the version described by M. Brewczyk, M. Gajda, and K. Rz\k{a}\ifmmode \dot{z}\else \.{z}\fi{}ewski [J. Phys. B 40, R1 (2007)] for the oscillations of a Bose gas trapped in a harmonic potential at nonzero temperatures, as experimentally investigated by Jin et al. [Phys. Rev. Lett. 78, 764 (1997)]. Similar to experiment, the system response to external perturbations strongly depends on the initial temperature and the symmetry of perturbation. While for lower temperatures the thermal cloud follows the condensed part, for higher temperatures the thermal atoms oscillate rather with their natural frequency, whereas the condensate exhibits a frequency shift toward the thermal cloud frequency (