Exactly solvable models for multiatomic molecular Bose–Einstein condensates

Abstract

Abstract. I introduce two family of exactly solvable models for multiatomic heteronuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also showed.

Semiclassical quantization for a bosonic atom-molecule conversion system

“…It can be seen that the eigenvalues are symmetric around zero, and approximately equidistant at the boundaries of the spectrum, while they are closer together around the centre. The eigenvalues can be obtained analytically using a Bethe ansatz approach [12]. Figure 2 depicts the eigenvalues of the many-particle Hamiltonian (3) as a function of for v = 1, and two different particle numbers.…”

“…It can be seen that the eigenvalues are symmetric around zero, and approximately equidistant at the boundaries of the spectrum, while they are closer together around the centre. The eigenvalues can be obtained analytically using a Bethe ansatz approach [12].…”

“…Over the last decade there has been considerable interest in atom-molecule conversion in cold atoms and BECs [7][8][9][10][11][12][13][14][15][16][17]. Theoretically these systems are closely related to deformed SU (M ) algebras [18].…”

Bethe states for the two-site Bose–Hubbard model: A binomial approach

“…To explicitly write the BVS (19) or (20) we need to expand the powers of the D -operator (18). We thus consider the following n-th power binomial expansion for any two operators X and Ŷ , with n ≥ 2, proved by induction, …”

“…A particularly fruitful instrument in relation to ultracold physics are many-body atomic models related to BEC. In this direction the quantum inverse scattering method (QISM) [14][15][16][17][18] has been used to solve and study some prototypical many-body models that contribute to describe phenomena associated to BEC [19][20][21]. Some of these models, despite their simplicity, display a rich structure showing quantum phase transitions and interesting semi-classical behavior that have been studied in [22][23][24][25][26][27], and explored in different areas such as nuclear physics, condensed matter and atomicmolecular physics.…”