Analogy between a two-well Bose-Einstein condensate and atom diffraction

Abstract

We compare the dynamics of a Bose-Einstein condensate in two coupled potential wells with atoms diffracting from a standing light wave. The cor-

Resonances for coupled Bose-Einstein condensates

“…These features are significant at low particle numbers and for strong interactions. In previous work, we discussed some aspects of the dynamics of a two-well BEC in the strong-interaction regime [3]. This is close to the experimental situation for a BEC in a double-well trap, designed in Ref.…”

Classical versus quantum dynamics of the atomic Josephson junction

“…with initial conditions φ(0) = 0 and k(0) = −∆E/2, see Equation (27). Analytical solutions to (32) and (33) with the specified boundary conditions can be found in terms of special functions. For example, when the motion is below the separatrix we have…”

“…As their names suggest, these two phenomena can be viewed as analogues of well-known wave scattering effects in lattices. Indeed, Haroutyunyan and Nienhuis [33] have previously given an analysis of the mathematical connections between atomic double-well systems and atomic diffraction, including the Bragg scattering analogy. Our purpose here is rather to present an intuitive physical discussion and refer the interested reader to [33] for more formal details.…”

“…Indeed, Haroutyunyan and Nienhuis [33] have previously given an analysis of the mathematical connections between atomic double-well systems and atomic diffraction, including the Bragg scattering analogy. Our purpose here is rather to present an intuitive physical discussion and refer the interested reader to [33] for more formal details. Consider a beam of non-interacting quantum particles that form a plane wave incident upon a lattice whose interaction with the particles is given by the periodic potential V (x) = −V 0 cos Kx, as depicted in Figure 10.…”

Emulating a many-body topological transition with an aberrated optical cavity

“…The operator H BH is related to the Lipkin-Meshkov-Glick model [20] in nuclear physics and to Ising models with long-range interactions [21][22][23][24]. It is able to describe processes not captured by the mean-field approximation, such as squeezing of the number difference [25][26][27][28], Bloch oscillations and Bragg resonances [29,30], quantum revivals [31], and caustics in Fock space [32][33][34]. The first term in H BH accounts for on-site particle-particle interactions characterized by the "charging energy" E c , while the second describes hopping between sites at frequency J/ .…”