Oleksandr Fialko

Kibble-Zurek Scaling and its Breakdown for Spontaneous Generation of Josephson Vortices in Bose-Einstein Condensates

Atomic Bose-Einstein condensates confined to a dual-ring trap support Josephson vortices as topologically stable defects in the relative phase. We propose a test of the scaling laws for defect formation by quenching a Bose gas to degeneracy in this geometry. Stochastic Gross-Pitaevskii simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches, consistent with the Kibble-Zurek mechanism. Slow quenches show stronger quench-time dependence that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime. Interference of the two atomic fields enables clear long-time measurement of stable defects and a direct test of the Kibble-Zurek mechanism in Bose-Einstein condensation.

Soliton magnetization dynamics in spin-orbit-coupled Bose-Einstein condensates

Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark soliton excitations that show periodic density dynamics in real space. In addition to the density feature, solitons also carry a localized pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.

Fate of the false vacuum: Towards realization with ultra-cold atoms

Quantum decay of a relativistic scalar field from a false vacuum is a fundamental idea in quantum field theory. It is relevant to models of the early Universe, where the nucleation of bubbles gives rise to an inflationary universe and the creation of matter. Here we propose a laboratory test using an experimental model of an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated radio-frequency coupling of the spin components. Numerical simulations demonstrate the spontaneous formation of true vacuum bubbles with realistic parameters and time-scales.

Quantum Tunneling of a Vortex between Two Pinning Potentials

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.

Oscillons in coupled Bose-Einstein condensates

Long-lived, spatially localized, and temporally oscillating nonlinear excitations are predicted by numerical simulation of coupled Gross-Pitaevskii equations. These oscillons closely resemble the time-periodic breather solutions of the sine-Gordon equation but decay slowly by radiating Bogoliubov phonons. Their time-dependent profile is closely matched with solutions of the sine-Gordon equation, which emerges as an effective field theory for the relative phase of two linearly coupled Bose fields in the weak-coupling limit. For strong coupling the long-lived oscillons persist and involve both relative and total phase fields. The oscillons decay via Bogoliubov phonon radiation that is increasingly suppressed for decreasing oscillon amplitude. Possibilities for creating oscillons are addressed in atomic gas experiments by collision of oppositely charged Bose-Josephson vortices and direct phase imprinting.

The decay and collisions of dark solitons in superfluid Fermi gases

We study soliton collisions and the decay of solitons into sound in superfluid Fermi gases across the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer (BEC–BCS) crossover by performing numerical simulations of the time-dependent Bogoliubov–de Gennes equations. This decay process occurs when the solitons are accelerated to the bulk pair-breaking speed by an external potential. A similar decay process may occur when solitons are accelerated by an inelastic collision with another soliton. We find that soliton collisions become increasingly inelastic as we move from the BEC to the BCS regime, and the excess energy is converted into sound. We interpret this effect as being due to the evolution of Andreev bound states localized within the soliton.

Spin-Orbit Coupled Bose Gases at Finite Temperatures

Spin-orbit coupling is predicted to have a dramatic effect on thermal properties of a two-component atomic Bose gas. We show that in three spatial dimensions it lowers the critical temperature of condensation and enhances thermal depletion of the condensate fraction. In two dimensions we show that spin-orbit coupling destroys superfluidity at any finite temperature, modifying dramatically the cerebrated Berezinskii-Kosterlitz-Thouless scenario. We explain this by the increase of the number of low-energy states induced by spin-orbit coupling, enhancing the role of quantum fluctuations.

Fragility of the fractional quantum spin Hall effect in quantum gases

We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle motion to the lowest Landau level. While interaction between same-spin particles leads to incompressible correlated states at fractional filling factors as known from the fractional quantum Hall effect, these states are destabilized by interactions between opposite spin particles. Exact results for two particles with opposite spin reveal a quasi-continuous spectrum of extended states with a large density of states at low energy. This has implications for the prospects of realizing the fractional quantum spin Hall effect in electronic or ultra-cold atom systems. Numerical diagonalization is used to extend the two-particle results to many bosonic particles and trapped systems. The interplay between an external trapping potential and spin-dependent interactions is shown to open up new possibilities for engineering exotic correlated many-particle states with ultra-cold atoms.

Quantum simulations of the early universe

A procedure is described whereby a linearly coupled spinor Bose condensate can be used as a physically accessible quantum simulator of the early universe. In particular, an experiment to generate an analog of an unstable vacuum in a relativistic scalar field theory is proposed. This is related to quantum theories of the inflationary phase of the early universe. There is an unstable vacuum sector whose dynamics correspond to the quantum sine-Gordon equations in one, two or three space dimensions. Numerical simulations of the expected behavior are reported using a truncated Wigner phase-space method, giving evidence for the dynamical formation of complex spatial clusters. Preliminary results showing the dependence on coupling strength, condensate size and dimensionality are obtained.

Nucleation in Finite Topological Systems During Continuous Metastable Quantum Phase Transitions

Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit global breaking of the rotational symmetry. This could be realized with current experimental technology.