arXiv subjects

L. A. Toikka

Publications and source records attributed to L. A. Toikka.

13 recordsLinked to original sources

arXiv2019

Long Josephson junctions with exciton-polariton condensates

We demonstrate the possibility to build stable Josephson $π$-junction stripes with exciton-polariton condensates. The stability of the $π$-junction between arbitrary long polariton stripes is achieved at low pumping by balancing the snaking instability with counter-propagating flows towards the junction. Not dissimilar from a dark soliton, the instability becomes relevant at high pumping leading to formation of vortex dipoles. The resulting structures can be stabilised to produce static lattices of Josephson vortices in straight and ring geometries. Our results build towards realization of quantum technological applications based on the Josephson effect at room temperature.

cond-mat.quant-gas↗

arXiv2019

Disorder-induced two-body localised state in interacting quantum walks

We observe the onset of non-ergodicity from ballistic propagation of a two-body bound state in an interacting discrete-time quantum walk (DTQW) due to time-dependent disorder in the interaction. The effect of the disorder on the two-body state can be interpreted as Anderson-type localisation in a projected DTQW, but without saturation of entanglement entropy. We characterise the two-body localisation in terms of the rate of growth of entanglement entropy and compute the localisation length. We find indications for two distinct growth laws for the entanglement: a logarithmic law in the delocalised phase and a double logarithmic law in the localised phase. We discuss similarities with many-body localisation (MBL).

cond-mat.mes-hall↗

arXiv2019

Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids

By solving the Bogoliubov--De Gennes equations analytically, we derive the fermionic zero-modes satisfying the Majorana property that exist in vortices of a two-dimensional $s$-wave Fermi superfluid with spin-orbit coupling and Zeeman spin-splitting. The Majorana zero-mode becomes normalisable and exponentially localised to the vicinity of the vortex core when the superfluid is topologically non-trivial. We calculate the energy splitting due to Majorana hybridisation and identify that the $s$-wave Majorana vortices obey non-Abelian statistics.

cond-mat.quant-gas↗

arXiv2019

Many-body dynamical localisation of coupled quantum kicked rotors

The quantum motion of $N$ coupled kicked rotors is mapped to an interacting $N$-particle Anderson-Aubry-Andr$é$ tight-binding problem supporting many-body localised (MBL) phases. Interactions in configuration space are known to be insufficient for destroying Anderson localisation in a system in the MBL phase. The mapping we establish here predicts that a similar effect takes place in momentum space and determines the quantum dynamics of the coupled kicked rotors. Due to the boundedness of the Floquet quasi-energy spectrum there exists limitations on the interacting lattice models that can be mapped to quantum kicked rotors; in particular, no extensive observable can be mapped in the thermodynamic limit.

cond-mat.mes-hall↗

arXiv2018

Necessary and sufficient conditions for flat bands in $M$-dimensional $N$-band lattices with complex-valued nearest-neighbour hopping

We formulate the necessary and sufficient conditions for the existence of dispersionless energy eigenvalues (so-called `flat bands') and their associated compact localized eigenstates in $M$-dimensional tight-binding lattices with $N$ sites per unit cell and complex-amplitude nearest-neighbour tunneling between the lattice sites. The degrees of freedom $M$ can be traded for longer-range complex hopping in lattices with reduced dimensionality. We show the conditions explicitly for $(M = 1, N\leq4)$, $(M = 2, N = 2,3)$, and $(M = 3, N = 2,3)$, and outline their systematic construction for arbitrary $N$, $M$. If and only if the conditions are satisfied, then the system has one or more flat bands. By way of an example, we obtain new classes of flat band lattice geometries by solving the conditions for the lattice parameters in special cases.

cond-mat.mes-hall↗

arXiv2018

Accurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases

The interplay of spin-orbit coupling and Zeeman splitting in ultracold Fermi gases gives rise to a topological superfluid phase in two spatial dimensions that can host exotic Majorana excitations. Theoretical models have so far been based on a four-band Bogoliubov-de Gennes formalism for the combined spin-1/2 and particle-hole degrees of freedom. Here we present a simpler, yet accurate, two-band description based on a well-controlled projection technique that provides a new platform for exploring analogies with chiral p-wave superfluidity and detailed future studies of spatially non-uniform situations.

cond-mat.quant-gas↗

arXiv2017

Vortex dipole precession in a Fermi superfluid with Rashba spin-orbit coupling

We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana fermions -- in Fermi superfluids in the presence of spin population imbalance and two-dimensional SO coupling, which are both required to realize a topological atomic Fermi gas in experiments.

cond-mat.quant-gas↗

arXiv2017

Boson-vortex duality in compressible spin-orbit coupled BECs

Using a (1+2)-dimensional boson-vortex duality between non-linear electrodynamics and a two-component compressible Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, we obtain generalised versions of the hydrodynamic continuity and Euler equations where the phase defect and non-defect degrees of freedom enter separately. We obtain the generalised Magnus force on vortices under SO coupling, and associate the linear confinement of vortices due to SO coupling with instanton fluctuations of the dual theory.

cond-mat.quant-gas↗

arXiv2016

Exactly solvable model for a solitonic vortex in a compressible superfluid

Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved exactly in a model "slab" geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterizing the vortex cores, to the slab width. The key dynamical properties of the vortex, the inertial and physical masses, are well defined and renormalizable. They are calculated at leading order beyond the logarithmic accuracy that has limited previous approaches. Our results provide a solid framework for further detailed study of the vortex mass and vortex forces in strongly-correlated and exotic superfluids. The proposed geometry can be realised in quantum-gas experiments where high-precision measurements of vortex mass parameters are feasible.

cond-mat.quant-gas↗

arXiv2016

Analytic Vortex Dynamics in an Annular Bose-Einstein Condensate

We consider analytically the dynamics of an arbitrary number and configuration of vortices in an annular Bose-Einstein condensate obtaining expressions for the free energy and vortex precession rates to logarithmic accuracy. We also obtain lower bounds for the lifetime of a single vortex in the annulus. Our results enable a closed-form analytic treatment of vortex-vortex interactions in the annulus that is exact in the incompressible limit. The incompressible hydrodynamics that is developed here paves the way for more general analytical treatments of vortex dynamics in non-simply connected geometries.

cond-mat.quant-gas↗

arXiv2014

Reversible decay of ring dark solitons

We show how boundary effects can cause a Bose-Einstein condensate to periodically oscillate between a (circular) array of quantised vortex-antivortex pairs and a (ring) dark soliton. If the boundary is restrictive enough, the ring dark soliton becomes long-lived.

cond-mat.quant-gas↗

arXiv2013

Self-interference of a toroidal Bose-Einstein condensate

We demonstrate the role played by a ring trap and the associated ring geometry in inducing self-interference of a toroidal Bose-Einstein condensate. We start by showing how the existence of the self-interference can be inferred from the Wigner function representation of the ring. Then, using analytical expressions for the time-evolution of a freely expanding ring condensate with and without a persistent current, we show that the self-interference of the ring condensate is possible only in the absence of the persistent current. We conclude by proposing an experimental protocol for the creation of ring dark solitons using the toroidal self-interference.

cond-mat.quant-gas↗

arXiv2013

Creation and revival of ring dark solitons in a toroidal Bose-Einstein condensate

We propose a protocol for the simultaneous controlled creation of multiple concentric ring dark solitons in a toroidally trapped Bose-Einstein condensate. The decay of these solitons into a vortex-antivortex necklace shows revivals of the soliton structure, but eventually becomes an example of quantum turbulence.

cond-mat.quant-gas↗