We consider a two-component interacting bosonic condensate with dominating intra-species repulsive density–density interactions. We study the phase diagram of the system at finite temperature with rotation, using large-scale Monte Carlo simulations of a two-component Ginzburg–Landau model of the system. In the presence of rotation, the system features a competition between long-range vortex–vortex interactions and short-range density–density interactions. This leads to a rotation-driven 'mixing' phase transition in a spatially inhomogeneous state with a broken symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and phase transitions split. This results in the formation of an intermediate state which breaks only symmetry. It represents two phase separated normal fluids with a difference in their densities.
We consider a two-component interacting bosonic condensate with dominating intra-species repulsive density–density interactions. We study the phase diagram of the system at finite temperature with rotation, using large-scale Monte Carlo simulations of a two-component Ginzburg–Landau model of the system. In the presence of rotation, the system features a competition between long-range vortex–vortex interactions and short-range density–density interactions. This leads to a rotation-driven 'mixing' phase transition in a spatially inhomogeneous state with a broken symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and phase transitions split. This results in the formation of an intermediate state which breaks only symmetry. It represents two phase separated normal fluids with a difference in their densities.
We consider a two-component immiscible Bose-Einstein condensate with dominating intra-species repulsive density-density interactions. In the ground-state phase of such a system only one condensates is present. This can be viewed as a spontaneous breakdown of Z2 symmetry. We study the phase diagram of the system at finite temperature beyond mean-field approximation. In the absence of rotation, we show that the system undergoes a first order phase transition from this ground state to a miscible two-component normal fluid as temperature is increased. In the presence of rotation, the system features a competition between vortex-vortex interaction and short range density-density interactions. This leads to a rotation-driven "mixing" phase transition in a spatially inhomogeneous state with additional broken U(1) symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and Z2 phase transitions split. This results in the formation of an intermediate state which breaks only Z2 symmetry. It represents two phase separated normal fluids with density imbalance.
Thermal fluctuations and melting transitions for rotating single-component superfluids have been intensively studied and are well understood. In contrast, the thermal effects on vortex states for two-component superfluids with density-density interaction, which have a much richer variety of vortex ground states, have been much less studied. Here, we investigate the thermal effects on vortex matter in superfluids with $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ broken symmetries and intercomponent density-density interactions, as well as the case with a larger SU(2) broken symmetry obtainable from the $[\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]$-symmetric case by tuning scattering lengths. In the former case we find that, in addition to first-order melting transitions, the system exhibits thermally driven phase transitions between square and hexagonal lattices. Our main result, however, concerns the case where the condensate exhibits SU(2) symmetry, and where vortices are not topological. At finite temperature, the system exhibits effects which do not have a counterpart in single-component systems. Namely, it has a state where thermally averaged quantities show no regular vortex lattice, yet the system retains superfluid coherence along the axis of rotation. In such a state, the thermal fluctuations result in transitions between different (nearly) degenerate vortex states without undergoing a melting transition. Our results apply to multicomponent Bose-Einstein condensates, and we suggest how to detect some of these unusual effects experimentally in such systems.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
Motivated by recent experimental advances, we study two-component spin-orbit coupled ultracold bosonic atoms in two dimensions on a square optical lattice. Using a Bose-Hubbard model with spin-conserving and non-spin-conserving nearest neighbour hoppings and spin-dependent on-site density-density interaction, our goal is to characterize phase separation and spin structure in the weakly interacting and deep Mott regimes. \nFor the weakly coupled regime, we decouple interactions through a real space uniform density mean field theory. At zero temperature, this gives an analytic condition for the phase separation transition driven by inter- relative to intracomponent interaction. Solving the self-consistent equations at finite temperature reveals entropic remixing in the phase separated regime and a more surprising entropy driven phase separation in the mixed regime. This is a consequence of complex interplay between interaction and spin-orbit coupling, and can be explained through the effect of component imbalance on the effective single-particle dispersion relation. We also provide an alternate explanation based on thermal occupation of eigenstates with a characteristic imbalance.\nIn the strongly interacting Mott regime, we derive an effective spin Hamiltonian describing the magnetic phases of the Mott insulator. The competition between anisotropic {Heisenberg} and Dzyaloshinskii-Moriya interactions gives rise to various ferromagnetic, antiferromagnetic, spiral, stripe, vortex, and skyrmion phases. On basis of classical Monte-Carlo simulations in the literature, we reconstruct the phase diagram with a classical variational approach, while magnon excitation spectra and quantum fluctuations are calculated with Holstein-Primakoff transformation and subsequent spin wave expansion. The analysis shows that states with ferromagnetic or antiferromagnetic ordering of boson species are protected against thermal fluctuations by a gap, and well described by classical states. States with equal superposition of boson species at each lattice site are subject to relatively large quantum fluctuations, which may cause breakdown of the states within their classical parameter space regions. The dispersion relations are gapless and linear around the minima to lowest order in the spin wave expansion.
Abstract At finite temperature, the stable equilibrium states of coupled two-component Bose Einstein condensations (BECs) with the same conformal mass in both non-rotating and rotating condition can be obtained by studying its real dynamics via holography. The equilibrium state is the state where the free energy reaches the minimum and does not change any more. In the case of no rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant η>ηc>0 η > η c > 0 . Under rotation, the quantum fluid reveals four equilibrium structures of vortex states by varying the η η from the miscible region to the phase separated region. Among the four structures, the vortex sheet solution is the most exotic one that appears in the phase separated region.
This thesis presents four research papers in the field of condensed-matter theory. Three of the papers make use of large-scale Monte-Carlo simulations to explore various aspects of Bose-Einstein condensates with multiple superfluid components. Papers I and II relate to a two-component Bose-Einstein condensate in three spatial dimensions under rotation. They explore the phase diagram and phase transitions of the model in two regimes, where either inter- or intra-component interactions dominates, as well as at a special SU(2)-symmetric point where all density-density interactions are of equal strength. We find that this rich phase diagram, in the coexisting regime, exhibits co-centered vortex lattices with hexagonal symmetry when the inter-component interaction is attractive. These lattices evolve into intercalated hexagonal lattices as the inter-component interaction is made repulsive, and further into intercalated square lattices as the repulsive interaction is increased in strength. In the phase-separated regime, we find striped vortex lattices for intermediate inter-component coupling strengths. For sufficiently strong inter-component coupling strengths one of the condensates is completely depleted, while the other develops a hexagonal vortex line lattice, as it is effectively a single-component condensate.\n\nPaper III investigates the phases and phase transitions of a similar model of a two-component condensate, now in two spatial dimensions with spin-orbit coupling and zero rotation. Here we find, for low inter-component coupling strength, that the effect of the spin-orbit interaction is to modulate the condensate fields by a single q-vector, a plane wave state. For increased inter-component couplings, but with intermediate spin-orbit coupling, we again find that one of the condensates will be depleted, making the remaining condensate effectively a single-component condensate. This completely removes the effect of the spin-orbit interaction. For both high inter-component and high spin-orbit interaction strengths, we find that the condensate forgoes the energy gained by depleting one condensate. It will rather modulate the condensate, but now with staggered condensate amplitudes. This state is a superposition of two states with modulation vectors q and - q, a standing wave state. We also explore the thermal phase transitions in the absence of spin-orbit couplings, here we find Kosterlitz-Thouless transitions in all components regardless of whether or not one component has collapsed, and independent on the value of the inter-component density-density interaction strength.\n\nThe last paper explores, in a purely analytical treatment, the effect of inter-band Josephson couplings on an N-component London superconductor. It utilizes a mathematical identity to re-express the model in terms of integer-valued superconducting currents, and we show that the inclusion of inter-band couplings introduces instanton-like events in these currents. These events effectively removes the current conservation in each individual superconducting current, as is expected when introducing the Josephson coupling. However, one particular combination of current, the sum of all the currents, remains conserved even with the Josepshon coupling. We argue that this converts the phase transitions of the neutral sector into crossovers, while leaving the charged phase transition unaffected. The fluctuations of the neutral sector will weaken, but may still influence the charged fluctuations sufficiently to preempt the remaining inverted-3DXY transition, making it first order. We also re-express the onset of the Higgs mass when entering the superconducting state as a blowout of loops of superconducting current.