Adiabatic and nonadiabatic merging of independent Bose-Einstein condensates

Abstract

Motivated by a recent experiment [Chikkatur et al. Science, 296, 2193] 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 non-adiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still get a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the non-adiabatic 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 merging of condensates.

Density Profile of a Trapped Strongly Interacting Fermi Gas with Unbalanced Spin Populations

“…Despite a semiqualitative agreement, this finite temperature argument needs to be clarified by a more careful analysis, following, for instance, the work presented in Ref. [25]. Other scenarios can also be envisioned to explain the smooth crossover between the two phases, such as the existence of an intermediate phase-e.g., a gapless or FFLO phase as proposed in Ref.…”

Dynamics of Bose - Einstein condensates and the atom laser

“…Following [38], we have investigated this process in the context of a one-dimensional model. As we will see later on, despite its simplicity this model is capable of capturing many of the phenomena that take place during the merging process, and have not been addressed in earlier related theoretical work [38,39].…”

“…To be consistent with [38,39], as well as the experimental setup for condensate merging [35], we assume two nearly identical harmonic traps with confining frequency ω. As the two traps move towards each other, the global potential experienced by the trapped atoms can be modelled by a double-well potential of the form [33,41]…”

“…The function s(t) determines the details of the merging (i.e., speed and time scale T m ), which has to be adiabatic so that any kind of excitations due to movement of the traps are suppressed. To this end, the transport of the condensates must take place on a time scale much larger than the characteristic time-scale of excitations along the merging direction, as well as the time-scale of interatomic interactions [38,39]. Moreover, excitations can be minimized by appropriately choosing the profile of s(t).…”

“…Theoretical investigations and modelling of the process have so far been rather limited, with a number of relevant questions still open. More precisely, in related work [37,38,39], the influence of an initial phase difference between the two condensates on the dynamics of the merging, the question of the phase of the final condensate, as well as the type of phase-sensitive excitations were not addressed. These aspects are of vital interest as attested by their frequent recurrence in the relevant experimental literature [35,40].…”