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arXiv:1407.8049 · Physical Review A

Nonlinear dressed states at the miscibility-immiscibility threshold

E. Nicklas, Wolfgang Muessel, Helmut Strobel, P. G. Kevrekidis, Markus K. Oberthaler

Published Nov 17, 2015• 19 citations
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Abstract

The dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a two-component Bose-Einstein condensate at the transition from miscible to immiscible with the additional control of linear interconversion. Excellent agreement is found between the detailed experimental time evolution and the corresponding numerical mean-field computations. Analyzing the dynamics of the system, we find clear indications of stationary states that we term nonlinear dressed states. A steady-state bifurcation analysis reveals a smooth connection of these states with dark-bright soliton solutions of the integrable two-component Manakov model.

DOI
10.1103/physreva.92.053614

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We report on the observation of controllable phase separation in a dual-species Bose-Einstein condensate with 85Rb and 87Rb. Interatomic interactions between the different components determine the miscibility of the two quantum fluids. In our experiments, we can clearly observe immiscible behavior via a dramatic spatial separation of the two species. Furthermore, a magnetic-field Feshbach resonance is used to change them between miscible and immiscible by tuning the 85Rb scattering length. The spatial density pattern of the immiscible quantum fluids exhibits complex alternating-domain structures that are uncharacteristic of its stationary ground state.

Physical Review Letters•Jul 24, 2008•493 citations
The dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a two-component Bose-Einstein condensate at the transition from miscible to immiscible with the additional control of linear interconversion. Excellent agreement is found between the detailed experimental time evolution and the corresponding numerical mean-field computations. Analyzing the dynamics of the system, we find clear indications of stationary states that we term nonlinear dressed states. A steady-state bifurcation analysis reveals a smooth connection of these states with dark-bright soliton solutions of the integrable two-component Manakov model.
We investigate application of nonlinearity management (NM, i.e., periodic variation of the strength of the intercomponent repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component Bose-Einstein condensate, both with and without linear mixing [Rabi coupling (RC)] between the components. To this end, we first identify, by means of a variational approximation and numerical solution, diverse stationary domain-wall (DW) structures supported by the system in the absence of management. The approximate analytical solutions for the DWs are found to be in excellent agreement with their numerical counterparts. An analytical estimate is also produced for the upshift of the MIM transition caused by the pressure of the trapping potential in the case of a confined system. An exact DW solution is produced for the system including the Pöschl-Teller potential, which is stable (unstable) if the potential is repulsive (attractive). Further, we find the spectrum of linear excitations in the spatially uniform mixed state, and thus establish parameter regions where the system is stable or unstable against demixing. In particular, RC upshifts the critical strength of the intercomponent repulsion for the onset of the MIM transition. Eigenfrequencies of excitations on top of DW states are identified from numerical simulations through monitoring the evolution of perturbed states. Weak NM applied at the DW eigenfrequency reveals features of the nonlinear resonance. Stronger NM, under which the system periodically crosses the MIM-transition point, restricts the miscibility.
In this work we experimentally study the rich interplay of a linear coupling and non-linear interactions between the two components of an elongated Bose-Einstein condensate of 87Rb. In the limit of strong linear coupling we generate dressed states and explore the effective interactions between them. We find that the miscibility of dressed states is opposite to that of the atomic states. If the characteristic energies of interactions and linear coupling are equal they give rise to a miscible-immiscible quantum phase transition. We study the linear response of the system to sudden quenches in the vicinity of the critical point by analyzing spin correlations in the system. A power law scaling of the characteristic length scales is observed on both sides of the phase transition and the scaling exponents agree with the mean field prediction. Temporal scaling is found on the miscible side in agreement with a prediction based on Bogoliubov theory. In addition, experimental results for finite-time quenches through the critical point are presented. The good control over amplitude and phase of the linear coupling field offers new possibilities for the study of both equilibrium and dynamical properties of phase transitions.
The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose–Einstein condensates is investigated. Motivated by the tunability of the atomic interactions in recent experiments, we explore in detail the impact that changes in the interaction strengths have on these bound pairs by considering significant deviations from the integrable limit. It is found that dark-bright soliton pairs exist as stable configurations in a wide parametric window spanning both the miscible and the immiscible regime of interactions. Outside this parameter interval, two unstable regions are identified and are associated with a supercritical and a subcritical pitchfork bifurcation, respectively. Dynamical manifestation of these instabilities gives rise to a redistribution of the bright density between the dark solitons, and also to symmetry-broken stationary states that are mass imbalanced (asymmetric) with respect to their bright soliton counterpart. The long-time dynamics of both the stable and the unstable balanced and imbalanced dark-bright soliton pairs is analyzed.
We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.
A one-dimensional mean-field model of a two-component condensate in the parabolic trap is considered, with the components corresponding to different spin states of the same atom. We demonstrate that the linear coupling (interconversion) between them, induced by a resonant electromagnetic wave, can drive the immiscible binary condensate into a miscible state. This transition is predicted in an analytical form by means of a variational approximation (for an infinitely long system), and is confirmed by direct numerical solutions of the symmetric and asymmetric models (the asymmetry accounts for a possible difference in the chemical potential between the components). We define an order parameter of the system as an off-centre shift of the centre of mass of each component. A numerically found dependence of the order parameter on the linear-coupling strength reveals a second-kind phase transition (in an effectively finite system). The phase transition looks very similar in two different regimes, namely, with a fixed number of atoms, or a fixed chemical potential. An additional transition is possible between double- and single-humped density distributions in the weak component of a strongly asymmetric system. We also briefly consider dynamical states, with the two components oscillating relative to each other. In this case, the components periodically separate even if they should be mixed in the static configuration.
We report on the observation of controllable phase separation in a dual-species Bose-Einstein condensate with 85Rb and 87Rb. Interatomic interactions between the different components determine the miscibility of the two quantum fluids. In our experiments, we can clearly observe immiscible behavior via a dramatic spatial separation of the two species. Furthermore, a magnetic-field Feshbach resonance is used to change them between miscible and immiscible by tuning the 85Rb scattering length. The spatial density pattern of the immiscible quantum fluids exhibits complex alternating-domain structures that are uncharacteristic of its stationary ground state.