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We study the spin distillation of spinor gases of bosonic atoms and find two different mechanisms in ${}^{52}$Cr and $^{23}$Na atoms, both of which can cool effectively. The first mechanism involves dipolar scattering into initially unoccupied spin states and cools only above a threshold magnetic field. The second proceeds via equilibrium relaxation of the thermal cloud into empty spin states, reducing its proportion in the initial component. It cools only below a threshold magnetic field. The technique was initially demonstrated experimentally for a chromium dipolar gas [B. Naylor et al., Phys. Rev. Lett. 115, 243002 (2015)], whereas here we develop the concept further and provide an in-depth understanding of the required physics and limitations involved. Through numerical simulations, we reveal the mechanisms involved and demonstrate that the spin distillation cycle can be repeated several times, each time resulting in a significant additional reduction of the thermal atom fraction. Threshold values of magnetic field and predictions for the achievable temperature are also identified., Comment: 15 pages, 11 figures. Extended discussion and improved sectioning

We study the emergence of hysteresis during the process of quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 Bose Einstein condensate of ultracold atoms. We explicitly demonstrate the appearance of a hysteresis loop with various quench times showing that it is rate-independent for large magnetizations only. In other cases scaling of the hysteresis loop area is observed, which we explain by using the Kibble-Zurek theory in the limit of small magnetization. The effect of an external harmonic trapping potential is also discussed.

We study the effect of an external harmonic trapping potential on an outcome of the non-adiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that the dynamics of an untrapped system exhibits double universality with two different scaling laws appearing due to conservation of magnetization. We show that in the presence of a trap double universality persists. However, the corresponding scaling exponents are strongly modified by transfer of local magnetization across the system. The values of these exponents cannot be explained by the effect of causality alone, as in the spinless case. We derive the appropriate scaling laws based on a slow diffusive-drift relaxation process in the local density approximation.

We develop a method for investigating nonequilibrium dynamics of an ultracold system that is initially at thermal equilibrium. Our procedure is based on the classical fields approximation with appropriately prepared initial state. As an application of the method, we investigate the influence of thermal fluctuations on the quantum phase transition from an antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We find that at temperatures significantly lower than the critical condensation temperature $T_c$ the scaling law for the number of created spin defects remains intact., Comment: arXiv admin note: text overlap with arXiv:1309.6107

We study the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength. To do so, we derive a description similar to the stochastic Gross-Pitaevskii equation (SGPE) but keeping a fully quantum description of the low-energy fields using the positive-P representation. This allows us to treat both the quantum and thermal fluctuations together in an integrated way. A plain SGPE only allows for thermal fluctuations. The approach is applicable to such situations as finite temperature quantum quenches, but not equilibrium calculations due to the time limitations inherent in positive-P descriptions of interacting gases. One sees the appearance antibunching, the generation of counter-propagating atom pairs, and increased phase fluctuations. We show that the behavior can be estimated by adding the T=0 quantum fluctuation contribution to the thermal fluctuations described by the plain SGPE., Comment: 17 pages, 18 figures. Major revision, basically a reboot. Equations are now derived rather than heuristically postulated, and the example quench is now physically realistic. The calculations presented are new, but overall results are mostly qualitatively similar. A better understanding of the interplay between quantum and thermal fluctuations has been reached

The main obstacle in experimental realization of the Einstein-de Haas effect in a Bose-Einstein condensate is necessity of a very precise control of the extremely small (of the order of tens of $\mu$G) external magnetic field. In this paper we numerically study the response of a rubidium condensate to an optimized time-dependent magnetic field. We find a significant transfer of atoms from the initial maximally polarized state to the next Zeeman component at magnetic fields of the order of tens of milligauss. We propose an experiment in which such an optimization scheme could enable the observation of the Einstein-de Haas effect in a rubidium atom condensate.

We numerically study the dynamics of a spinor chromium condensate in low magnetic fields. We show that the condensate evolution has a resonant character revealing rich structure of resonances similar to that already discussed in the case of alkali-atoms condensates. This indicates that dipolar resonances occur commonly in the systems of cold atoms. In fact, they have been already observed experimentally. We further simulate two recent experiments with chromium condensates, in which the threshold in spin relaxation and the spontaneous demagnetization phenomena were observed. We demonstrate that both these effects originate in resonant dynamics of chromium condensate., Comment: 8 pages, 9 figures

We investigate the dynamics and outcome of a quantum phase transition from an antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We explicitly demonstrate double universality in dynamics within experiments with various quench time. Furthermore, we show that spin domains created in the nonequilibrium transition constitute a set of mutually incoherent quasicondensates. The quasicondensates appear to be positioned in a semi-regular fashion, which is a result of the conservation of local magnetization during the post-selection dynamics.

We consider a phase transition from antiferromagnetic to phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We demonstrate the occurrence of two scaling laws, for the number of spin fluctuations just after the phase transition, and for the number of spin domains in the final, stable configuration. Only the first scaling can be explained by the standard Kibble-\.Zurek mechanism. We explain the occurrence of two scaling laws by a model including post-selection of spin domains due to the conservation of condensate magnetization.

We demonstrate a method of controlled creation of spin domains in spin-1 antiferromagnetic Bose-Einstein condensates. The method exploits the phenomenon of phase separation of spin components in an external potential. By using an appropriate time dependent potential, a composition of spin domains can be created, as we demonstrate in the particular cases of a double well and a periodic potential. In contrast to other methods, which rely on spatially inhomogeneous magnetic fields, here the domain structure is completely determined by the optical fields, which makes the method versatile and reconfigurable. It allows for creation of domains of various sizes, with the spatial resolution limited by the spin healing length only.

We study a spinor condensate of Rb-87 atoms in F = 1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in mF = 1 component we observe a significant transfer of atoms to other, initially empty Zeeman states exclusively due to dipolar forces. Because of conservation of a total angular momentum the atoms going to other Zeeman components acquire an orbital angular momentum and circulate around the center of the trap. This is a realization of Einstein-de Haas effect in a system of cold gases. We show that the transfer of atoms via dipolar interaction is possible only when the energies of the initial and the final sates are equal. This condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. We found that there are many final states of different spatial density which can be tuned selectively to the initial state. We show a simple model explaining high selectivity and controllability of weak dipolar interactions in the condensate of Rb-87 atoms., Comment: 10 pages, 8 figures

We study a square plaquette of four optical microtraps containing ultracold $^{87}$Rb atoms in F=1 hyperfine state. In a presence of external resonant magnetic field the dipolar interactions couple initial $m_F=1$ component to other Zeeman sublevels. This process is a generalization of the Einstein-de Haas effect to the case when the external potential has only $C_4$ point-symmetry. We observe that vortex structures appear in the initially empty $m_F=0$ state. Topological properties of this state are determined by competition between the local axial symmetry of the individual trap and the discrete symmetry of the plaquette. For deep microtraps vortices are localized at individual sites whereas for shallow traps only one discrete vortex appears in the plaquette. States created in these two opposite cases have different topological properties related to $C_4$ point-symmetry.

We consider a spinor condensate of $^{87}$Rb atoms in F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in $m_F=0$ component we find that the system evolves towards a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin mixing contact potential. Our results show that because of a dynamical separation of magnetic components the spin mixing dynamics in $^{87}$Rb condensate is governed by dipolar interaction which plays no role in a single component rubidium system in a magnetic trap.