Motivated by a recent experiment [Chikkatur et al., Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate). In the nonadiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still obtain a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the nonadiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on the merging of condensates.
Motivated by a recent experiment [Chikkatur et al., Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate). In the nonadiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still obtain a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the nonadiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on the merging of condensates.
In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.
We studied the creation of coherent atomic ensembles by various means, allof which are either already demonstrated experimentally or within reach ofcurrent experiments. We investigated the dynamics of the outcoupling of acoherent beam from an atomic Bose-Einstein condensate. Since this problemis well treated in present literature, we focused on another aspect of proposedatom-laser schemes, the pumping. To this end, we investigated the merging ofindependent condensates and paid particular attention to the role of the relativephase. We found that it emerges as a key parameter during the merging process,almost solely defining the resulting dynamics. More concretely, the phasedifference determines the depth of an adiabatically formed soliton as well as thedynamics of a dipole oscillation of the atomic cloud, which builds up during themerging process. Under the assumption of a coherent cooling, such as evaporationof higher energy atoms from the ensemble, we were able to empiricallyfind an analytic formula for the phase of the final condensate. We studied themerging as an independent process, not necessarily linked to the atom laseritself. Our results might shed light onto new, non-destructive ways of readingout phase-differences between condensates as it is necessary in matter-wavespectroscopy. Although not related to our work, it is worth mentioning thatin the mean-time, a different pumping mechanism was demonstrated. It relieson two electronic transitions, with a reservoir condensate and a separate lasingcondensate [74]. We turned towards a different way of producing matter wavepulses altogether, namely superradiance from condensates, which shows otherpromising aspects, such as well defined populations and momenta of the createdpulses. We constructed a quantum treatment for the early stages of the process,which, as we have shown, is not well described within the available mean-fieldmodels. This semi-classical model can, however, produce quantum expectationvalues by means of averaging over randomly seeded trajectories. We used thisrelations to investigate the statistics of delay– and passage-times of superradiantpulses. Beyond the mean-field treatment of the problem, the quantum modelpredicts long range order as well as atomic bunching in the side-modes and enhancedcross-correlations between forward and backwards scattered atoms. Inthe strong pulse regime, the two counter-propagating clouds become entangledand the number difference between them is squeezed.4.6.2 OutlookThe experimental verification of our results is within reach of current experiments,and the tools available to probe Bose-Einstein condensates are advancingat a fast rate. As far as our studies are concerned, there are still open questions.We found that, in general, the merging of condensates is related to the formationof a soliton. The decay of such a structure is a topic of current debate, but theconsensus that this depends highly on the geometry of the trapping potentialsused seems reached.We investigated the early stage of superradiance from condensates and it isnatural to ask what is to expect for later stages, or in other situations wheredepletion of the primary condensate, population of higher order side-modes or120interaction between end-fire modes become relevant. Our results suggest thatthe exotic correlations we found decay with time, but this is not conclusive
We study the formation of vortices in a Bose-Einstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental setup of Scherer et al. [Phys. Rev. Lett. 98, 110402 (2007)], where three BECs are created in a magnetic trap that is segmented into three regions by a repulsive optical potential; the BECs merge together as the optical potential is removed. First, we study the two-dimensional case; in particular, we examine the effects of the relative phases of the different fragments and the removal rate of the optical potential on the vortex formation. We find that many vortices are created by instant removal of the optical potential regardless of relative phases, and that fewer vortices are created if the intensity of the optical potential is gradually ramped down and the condensed fragments gradually merge. In all cases, self-annihilation of vortices of opposite charge is observed. We also find that for sufficiently long barrier ramp times, the initial relative phases between the fragments leave a clear imprint on the resulting topological configuration. Finally, we study the three-dimensional system and the formation of vortex lines and vortex rings due to the merger of the BEC fragments; our results illustrate how the relevant vorticity is manifested for appropriate phase differences, as well as how it may be masked by the planar projections observed experimentally.
The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as dispersive shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.