Fragility of fragmentation in Bose-Einstein condensates

Abstract

A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or translationally symmetric is fragmented as a direct result of these symmetries. A corresponding mean-field unfragmented state, with an identical energy to leading order in the number of particles, can generally be constructed. As a consequence, vanishingly weak symmetry-breaking perturbations destabilize the fragmented state, which would thus be extremely difficult to realize experimentally, and lead to an unfragmented condensate.

Fragmented Many-Body Ground States for Scalar Bosons in a Single Trap

“…We have checked the robustness of the fragmentation obtained on the A 3 > 0 side upon increasing the interlevel coupling up to $ OðN 0 Þ, as well as for variations of the values of the single-particle energies 0 and 1 to the same order. The degree of fragmentation is therefore stable for small perturbations on the single-particle level, different to what was found in [16,17], where the origin of fragmentation is distinct from our interaction-couplings based mechanism. Finally, because the energy contribution of the A 3 term is negative, for a concrete realization with sufficiently small A 3 the fragmented state has to be at a (local) minimum of the energy in the parameter space of the orbitals É i .…”

“…We demonstrate that by tuning the four interaction matrix elements relative to each other, various many-body states-coherent and fragmented states, as well as coherent superpositions of degenerate macroscopically distinct quantum states [13]-can be accessed in a single trap. In addition, the fragmented states are not susceptible to decay to a nonfragmented (coherent) state because of a perturbation on single-particle level [16,17], due to the fragmentation being based to the values of the interaction couplings.We begin with a general quadratic plus quartic Hamiltonian for two interacting modes,The interaction coefficients are given by0 ÞV int ðr À r 0 ÞÉ k ðr 0 ÞÉ l ðrÞ. It is of major importance for the discussion to follow that we include pair exchange between the two modes due to scattering of pairs of bosons /A 3 , in addition to the standard density-density type terms / A 1 , A 2 , A 4 .…”

“…We demonstrate that by tuning the four interaction matrix elements relative to each other, various many-body states-coherent and fragmented states, as well as coherent superpositions of degenerate macroscopically distinct quantum states [13]-can be accessed in a single trap. In addition, the fragmented states are not susceptible to decay to a nonfragmented (coherent) state because of a perturbation on single-particle level [16,17], due to the fragmentation being based to the values of the interaction couplings.…”

Number-squeezed and fragmented states of strongly interacting bosons in a double well

“…No analysis of number squeezing has yet been made within the eight-mode model or with full threedimensional computational simulations, although a onedimensional truncated Wigner approximation has been used to estimate on-site [26] and inter-site number fluctuations [28]. Regarding fragmentation, much theoretical effort has also gone into understanding this phenomenon using two-mode models [8][9][10][75][76][77]. As is the case with squeezing, these models are inadequate to fully capture the behavior of the system with respect to fragmentation at large interaction strengths.…”

Emergence of a new pair-coherent phase in many-body quenches of repulsive bosons

“…This conclusion is gained from highly symmetric (e.g., rotationally invariant) situations, for example, in antiferromagnetic spinor condensates [5] or rotating gases [6]. The fragmented condensate states occurring for these symmetrical Hamiltonians are extremely fragile against decay into a coherent state (a single condensate) by small perturbations coupling the single-particle modes [7], breaking, e.g., rotational symmetry. As a consequence, the fragmented states are also extremely sensitive to small time-dependent perturbations like number fluctuations and generally excitations above the fragmented condensate ground state.…”