Bosons condensed in two modes with flavor-changing interaction

Abstract

A quantum model is considered for N bosons populating two orthogonal single-particle modes with tunable energy separation in the presence of flavour-changing contact interaction. The quantum ground state is well approximated as a coherent superposition (for zero temperature) or a mixture (at low temperature) of two quasi-classical states. In a mean field description, the systems realizes one of these states via spontaneous symmetry breaking. Both mean field states, in a certain parameter range, possess finite angular momentum and exhibit broken time-reversal symmetry in contrast to the quantum ground state. The phase diagram is explored at the mean-field level and by direct diagonalisation. The nature of the quantum ground state at zero and finite temperature is analyzed by means of the Penrose Onsager criterion. One of three possible phases shows fragmentation on the single-particle level together with a finite pair order parameter. Thermal and quantum fluctuations are characterized with respect to regions of universal scaling behavior.The non-equilibrium dynamics shows a sharp transition between a self-trapping and a pair-tunneling regime. A recently realized experimental implementation is discussed with bosonic atoms condensed in the two inequivalent energy minima X± of the second band of a bipartite two-dimensional optical lattice.

Orbital many-body dynamics of bosons in the second Bloch band of an optical lattice

“…A detailed treatment of the underlying two-mode model is found in Ref. [22]. Remarkably, the observed ascending trend of ν osc is well reproduced by the model although band relaxation, heating, and particle loss are neglected here.…”

“…This results in the intriguing consequence that even tiny energy scales as that of weak contact interactions play a decisive role in determining the structure of the lowest energy state in each band. The presence of degenerate local orbitals enables contact interaction processes, which change the orbital character of the colliding atoms [22]. Multi-flavor Bose-Einstein condensates (BEC) with complex interaction-induced phase textures can emerge [8,11,12,17] including examples with non-trivial topological properties [23,24].…”

“…We selectively populate one out of the two degenerate global energy minima in the second band of an optical square lattice with a BEC and observe the subsequent dynamics, which displays a damped oscillation of population between both energy minima. This oscillation is exclusively driven by two kinds of collisional interactions, i.e., the on-site collisions of atoms in either of the three local orbitals s, p x , and p y , respectively, and a flavor-changing collision mimicking a pair tunneling process [22,27,28], where two atoms colliding, e.g. in the p x -orbital at some lattice site, are both transferred to the p y -orbital or vice versa.…”

Logarithmic quantum time crystal

“…where â † 1 ( â1 ) and â † 2 ( â2 ) are the creation (annihilation) operators of two modes and N is the total number of bosons. This simple theoretical model can now be realized in experiments [21]. In the above, we have set the strength of single particle hopping as the unit of energy and therefore γ is a dimensionless parameter characterizing the interaction strength and the pair hopping.…”

Logarithmic Quantum Time Crystal

“…This simple theoretical model can now be realized in experiments. [22] Here, we have set the strength of single particle hopping as the unit of energy and therefore 𝛾 is a dimensionless parameter characterizing the interaction strength and the pair hopping. In addition, for simplicity, we set ≡ 1.…”