Research topics Recent highlights

ON-2.6 Recent research highlights

December 2015 Real-space collapse of a polariton condensate

Microcavity polaritons are two-dimensional bosonic fluids with strong nonlinearities, composed of coupled photonic and electronic excitations. Here we report the unique phenomenology that is observed when a pulse of light impacts the polariton vacuum: the fluid which is suddenly created does not splash but instead coheres into a very bright spot.
Caption: Experimental images of a collapsing condensate.
Real-space collapse of a polariton condensate

L. Dominici, M. Petrov, M. Matuszewski, D. Ballarini, M. De Giorgi, D. Colas, E. Cancellieri, B. Silva Fernández, A. Bramati, G. Gigli, A. Kavokin, F. Laussy, D. Sanvitto
Nature Commun. 6, 8993 (Dec 2015)

February 2016 Entanglement storage by classical fixed points in the two-axis countertwisting model

We analyzed a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen.
Caption: Time evolution of the Husimi function with rotation at an optimal moment of time.
Entanglement storage by classical fixed points in the two-axis countertwisting model

D. Kajtoch, K. Pawłowski, E. Witkowska
Phys. Rev. A 93, 022331 (Feb 2016)

February 2016 A tractable prescription for large-scale free flight expansion of wavefunctions

Carrying out the free flight expansion of an ultracold bosonic cloud released from the trap is a pain when the needed numerical lattice doesn't fit in the memory of your computer. An algorithm has been found to avoid this memory problem, and carry our even very large expansions.
Caption: Free expansion of a thermal cloud containing large density fluctuations and solitons.
A tractable prescription for large-scale free flight expansion of wavefunctions

P. Deuar

February 2016 Spin squeezing in dipolar spinor condensates

We studied the effect of dipolar interactions on the level of spin squeezing in a spin-1 Bose-Einstein condensates by using the single mode approximation. The biaxial nature of dipolar interactions allows for dynamical generation of spin-squeezed states in the system. We calculated numerically the spin squeezing parameter showing that it is possible to reach the strongest squeezing set by the two-axis countertwisting model.
Caption: The inverse of the squeezing parameter ξ-2. The qualitative change of the squeezing parameter around 3α/β = 1 corresponds to changing stability of the mean-field fixed points between a stable center to an unstable saddle, or vice versa.
Spin squeezing in dipolar spinor condensates

D. Kajtoch, E. Witkowska
Phys. Rev. A 93, 023627 (Feb 2016)

January 2016 Two-flavour mixture of a few fermions of different mass in a one-dimensional harmonic trap

We study a system of two species of fermions of different mass confined in a one-dimensional harmonic trap. It is shown that a mass difference between fermionic species induces a separation in the density of the lighter flavour independently of the number of particles. The separation is robust to the interactions with a thermal environment.
Caption: Single particle density of heavy (blue) and light (red) fermions calculated for the ground state for different numbers of particles.
Two-flavour mixture of a few fermions of different mass in a one-dimensional harmonic trap

Daniel Pęcak, M. Gajda, T. Sowiński
New J. Phys. 18, 013030 (Jan 2016)

December 2015 Accuracy of classical field calculations and optimal cutoffs

We have determined the regime of acuracy for classical field descriptions of ideal and some weakly interacting gases, based on the criterion that many observables should be accurately reproduced, including density fluctuations and kinetic energy. Optimal cutoffs and accuracy are also found as a function fo temperature.
Caption: Optimal cutoffs (green) and maximum error RMS (blue) as a function of dimensionless temperature (tau) and cutoff (fc).
Classical field records of a quantum system: Their internal consistency and accuracy

J. Pietraszewicz, P. Deuar
Phys. Rev. A 92, 063620 (Dec 2015)

September 2015 The Wigner Stochastic Gross-Pitaevskii Equation

A fuller version of the popularly used Stochastic Gross-Pitaevskii Equation (SGPE) has been derived, that takes into account also quantum fluctuatons in the gas, and is directly sensitive to the absolute number of atoms in the cloud. Antibunching, atomic shot noise and quantum phase fluctuations can be obtained. Unlike some earlier attempts in this direction, the equations are stable and allow one to obtain stationary thermal states.
Caption: Soliton evolution in a thermal gas described by the WSGPE.

P. Deuar, N. Proukakis, T. Świsłocki
In preparation.

July 2015 Quantum dynamics generated by the two-axis countertwisting Hamiltonian

We studied the quantum dynamics generated by the two-axis countertwisting Hamiltonian from an initial spin coherent state in a spin-1/2 ensemble. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of four neutrally stable and two saddle unstable fixed points. The presence of the latter is responsible for a high level of squeezing.
Caption: Time evolution of the Quantum Fisher Information (top), Husimi function (bottom left) and Wigner function (bottom right).
Quantum dynamics generated by the two-axis countertwisting Hamiltonian

D. Kajtoch, E. Witkowska
Phys. Rev. A 92, 013623 (Jul 2015)

VIDEO (mp4)

March 2010 Einstein - de Haas effect on a plaquette of optical lattice sites

When several vortices localised in optical lattice sites in a 87Rb spinor gas in the F=1 state interact via dipole-dipole magnetic spin interactions we observe the formation of a global inter-site vortex on a 2x2 plaquette when the lattice potential is partially lowered.
Caption: Formation of a global vortex in a 2x2 plaquette after partial lowering of the lattice height.
Tunable dipolar resonances and Einstein-de Haas effect in a 87Rb-atom condensate

T. Świsłocki, T. Sowiński, J. Pietraszewicz, M. Brewczyk, M. Lewenstein, J. Zakrzewski, M. Gajda
Phys. Rev. A 83, 063617 (Jun 2011)

January 2010 Scattering of radiation by a system of point dipoles on a ring. Exact solution

The problem of scattering of radiation by a system on N quasi-point like dipoles located on a circle (equidistantly in the polar angle) in two spatial dimensions has been solved. A closed-form expression for the electric fields at the points where the dipoles are located has been given via a partial wave decomposition. The scattering and focusing properties have been investigated for both dielectric and metallic scatterers.
Caption: Radiation patterns of plane waves scattered by a system of metallic wires located on a circle. (left) 18 000 wires, (right) 1200 wires.
Scattering of radiation by a system of point dipoles on a ring. Exact solution in two dimensions

M. Janowicz
J. Mod. Opt. 57, 366 (Mar 2010)

November 2009 Precision calculations of the incoherent halo of atoms in a supersonic BEC collision

The incoherently scattered atoms are found to lie in a spheroidal shell at smaller velocities than the incoming BECs. In a broad collaboration with the experiment in Orsay, France, and theorists in Warsaw and Brisbane, Australia, the details of the processes have been understood and verified by comparing the experimental data with mircoscopic many-body calculations using the positive-P method, and a time-adaptive Bogoliubov approach that is used to investigate the removal or addition of chosen sub-processes.
Caption: (top-left) experimental data for a slice through the scattered atom halo (top-right) simulation (bottom) matching of experimental (black) and simulated (red) shell radii
Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics

V. Krachmalnicoff, J.-C. Jaskula, M. Bonneau, G.B. Partridge, D. Boiron, C.I. Westbrook, P. Deuar, P. Ziń, M. Trippenbach, K.V. Kheruntsyan
Phys. Rev. Lett. 104, 150402 (Apr 15 2010)

May 2009 Collective diffusion of a one-dimensional lattice gas adsorbate

The collective diffusion coefficient in a one-dimensional lattice gas adsorbate was calculated using a variational approach, for the case of long-range interparticle interactions. The diffusion coefficient depends strongly on the relationship between the substrate lattice constant and the characteristic length of the interparticle interaction potential. At fixed density, it also has an oscillating character as a function of the characteristic interaction length due to the interplay between the distances allowed by the substrate lattice structure those that minimize the total interaction energy.
Caption: Density dependence of the diffusion coefficient in terms of θ=1/l the inverse of the nearest-neighbor pair length l, and lattice constant a, for several values of the Fermi wavevector qF of the surface electrons.
Diffusion of particles interacting via long-range and oscillating forces in one dimension
F. Krzyżewski, M.A. Załuska-Kotur
Phys. Rev. B 80, 155410 (Oct 2009)

March 2009 Controlled Quantum/Semiclassical hybrid methods for simulating many-body quantum dynamics

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly, while remaining reliable. A demonstration is made for the collision of sodium BECs with 150 000 atoms.
Caption: A comparison of predictions of scattered particle number using various methods (independent hybrid predictions are labeled HA and HB).
Simulation of Complete Many-Body Quantum Dynamics Using Controlled
Quantum-Semiclassical Hybrids

P. Deuar
Phys. Rev. Lett. 103, 130402 (Sep 25 2009)

January 2009 Dipolar interactions dominate the 87Rb spinor gas

The thermalisation of the 87Rb spinor bose gas in the F=1 state was simulated using the classical-field method. It was found that even at small magnetic fields of the order of 1mG or less, the process is dominated by the dipole-dipole magnetic spin interactions, rather than spin mixing contact interactions.
Caption: A sequence of time-frames showing fluctuations of the spin textures in the gas in thermal equilibrium.
Spinor condensate of 87Rb as a dipolar gas

T. Świsłocki, M. Brewczyk, M. Gajda, K. Rzążewski
Phys. Rev. A 81, 033604 (Mar 2010)

January 2009 Optimal high-energy cutoff in c-field methods found

The quantitative details of the different c-field simulation methods for Bose gases are noticeably dependent on details of the high-energy cutoff employed - a technical parameter. We have determined the optimal cutoff for trapped Bose gases, in the sense that choosing this value and letting the gas thermalise very closely reproduces the true thermal distribution. Surprisingly, this cutoff corresponds to about half a particle on average per mode at the high-energy end of the scale, a value much lower than heretofore used in most variants of the c-field method.
Caption: Probability distribution of having Nex bosons outside the ground state in a 1D trap. Solid black: exact distribution; Red: classical field with optimised cutoff; dashed black: classical field with 0.9 and 1.1 times optimal cutoff.
Bose statistics and classical fields
E. Witkowska, M. Gajda, K. Rzążewski
Phys. Rev. A 79, 033631 (Mar 2009)

September 2008 Scattering of narrow beams and short pulses on dielectric spheres

The scattering of gaussian beam electromagnetic pulses by a hard dielectric sphere is shown to be well approximated by a superposition of plane waves. Furthermore, the scattering of short pulses composed of discrete frequency waves on a hard or dielectric sphere is described. This extends the Lorenz-Mie theory for scattering of plane waves.
Caption: Time evolution of very long and very narrow electromagnetic pulse.
Scattering of narrow stationary beams and short pulses on spheres
W. Żakowicz
EPL 85, 40001 (Feb 2009)

September 2008 Gain-loss asymmetry for emerging stock markets

Stock indices for European emerging markets are analyzed using the investment horizon approach. Gain-loss asymmetry is observed for all analyzed data, but with a different character for emerging and for established markets. When optimal investment horizon is plotted as a function of absolute return value, for established markets gain curve lies typically above loss curve, whereas in the case of emerging markets the situation is the opposite. In the latter case one has to wait longer for loss than for gain of the same return value. We propose a measure quantifying the gain-loss asymmetry that clearly exhibits a difference between emerging and established markets.
Caption: Distribution of investment horizons (with fitted function) for return rate 0.04 of one of the polish mutual funds.
New results on gain-loss asymmetry for stock markets time series
M. Grudziecki, E. Gnatowska, K. Karpio, A. Orłowski, M.A. Załuska-Kotur
Acta Phys. Pol. A 114, 569 (Sep 2008)

August 2008 Dynamical Casimir effect in oscillating media

It was shown that pairs of photons are produced in an oscillating homogenous medium with constant material coefficients, and that there are parametric resonance regions where there is an exponentially growing number of photons. This process may be viewed as another manifestation of the dynamical Casimir effect. However, in contrast to the standard dynamical Casimir effect, photon production here takes place in the entire volume and is not due to time dependence of the boundary conditions or material constants.
Caption: Behavior of the real and imaginary parts of the characteristic exponent ν for photons produced at frequency ω in the first two resonance regions. Medium oscillation frequency is Ω.
Dynamical Casimir effect in oscillating media
I. Białynicki-Birula, Z. Białynicka-Birula
Phys. Rev. A 78, 042109 (Oct 2008)

June 2008 Decay of multiply charged vortices in a BEC

The decay of multiply charged vortices in the presence of thermal atoms in a BEC were studied using the classical field method. The onset of the decay of a vortex is always preceded by the increase of a 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.
Caption: (top-left) Isodensity plots for two typical vortex configurations, (bot-left) z-integrated densities, (top-right) condensate density, (bot-right) non-condensate density.
Decay of multiply charged vortices at nonzero temperatures
T. Karpiuk, M. Brewczyk, M. Gajda, K. Rzążewski
J. Phys. B 42, 095301 (May 14 2009)

June 2008 Distillation of a Bose-Einstein condensate

In a two-trap system, with the atoms initially in a BEc in the higher-energy trap, experiments have shown that eventually the atoms make their way into the lower energy trap even when the potential barrier between the two traps is far too high for tunelling from the condensate to occur. Using classical field simulations, we have shown that this can occur via a process where the thermal cloud of the initial condensate rises out of the trap, moves over the barrier, and condenses eventually in the lower energy trap. This is highly analogous to distillation, or in a colder setting to the Helium fountain.
Caption: Condensate fractions in the high-potential (green) and low-potential (red) wells, as a function of time. Note the lower condensate fraction in the low-potential well.
Distillation of a one-dimensional Bose-Einstein condensate
A. Górecka, M. Gajda
Phys. Rev. A 79, 053624 (May 2009)

March 2008 Segregation in a noninteracting binary mixture

The process of stripe formation in a system consisting of particles of two sizes on sites is analyzed numerically, for the case when there are no direct interactions. However, the sites can be occupied by up to four neighboring large particles but smaller objects cannot overlap. The system orders, forming stripes, under external, constant, or oscillating driving forces if its density is large enough. It is shown that this process happens with logarithmic like time dependence.
Caption: Successive stages of separation of large (red) and small (green) particles. Free sites are visible as white spots.
Segregation in a noninteracting binary mixture
F. Krzyżewski, M.A. Załuska-Kotur
Phys. Rev. E 77, 031502 (Mar 2008)

February 2008 Spontaneous collective effects in a Fabry-Perot cavity

The spontaneous emission of radiation from two two-level atoms in a Fabry-Perot cavity is considered, with a modulated transition frequency of the atoms. This modulation leads to a radical change of the spontaneous emission dynamics, including decoherence properties of entangled atomic states. It could be used to dynamically control the collective effects in spontaneous emission in cavities. To achieve this, the modulation should (1) be able to periodically detune the atoms from the resonance with the cavity, and (2) fulfil a resonant condition between the modulation frequency and modulation depth.
Caption: A parametric plot of the evolution of R+iI = α1α2 for α1|e>|g> and α2|g>|e> amplitudes that illustrates the dynamics of degradation of the relative phase between the atoms. a is a detuning from the resonance frequency modulation value.
Light localization in left-handed media
M. Rusek, A. Orłowski, J. Mostowski
Acta Phys. Pol. A 112, 409 (Oct 2007)

October 2007 Light localization in left-handed media

Localized waves in disordered left-handed materials are studied using a generalized coupled-dipole model. Resonances in an open system consisting of randomly distributed electric and magnetic dipoles are investigated. A new type of long-lived resonance modes localized at the boundary of the system is found. They resemble evanescent waves responsible for a super-focusing phenomenon by a left-handed lens.
Caption: Field energy density in a resonance mode of the two-dimensional medium consisting of randomly distributed dipoles.
Light localization in left-handed media
M. Rusek, A. Orłowski, J. Mostowski
Acta Phys. Pol. A 112, 409 (Oct 2007)

March 2007 Domain growth in the interacting adsorbate

Domain growth dynamics is studied in a one-dimensional Potts model. We show that an exponent of a power-like time domain growth is determined not only by the conservation or nonconservation of the order parameter, but also by the asymmetry of single particle jumps. Domains that have an anisotropic pattern, such as (2X1), have a tendency to grow faster in a certain direction than they do in others. As a result, dynamical behavior of systems which start in the same configurations and eventually reach the same equilibrium states is completely different.
Caption: Examples of the domain pattern resulting from (2x1) ordering.
Domain growth in the interacting adsorbate: Nonsymmetric particle jump model
M.A. Załuska-Kotur, S. Krukowski, A. Łusakowski, Ł.A. Turski
Phys. Rev. B 75, 115412 (Mar 2007)