Two Atoms in a Double Well: An Exact Solution

Abstract

We propose to experimentally realize an odd parity eigenstate $|b⟩$ of two atoms in the double well. The occupation probability of this state shows evident dependence on the interaction, distinct from the result of two-mode model adopted in the Heidelberg experiment. The tunneling dynamics of two atoms starting from the $NOON$ state with infinite barrier height can be derived from the exactly solved model of $\delta$-barrier split double well based on a Bethe ansatz type hypothesis of the wave functions. We find that the single particle tunneling transfer the probabilities between double occupancy and single occupancy of each well.

5 pages, 3 figures, 6 pages Supplementary Material,

References in corpus (21)

• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Atom interferometry with Bose-Einstein condensates in a double-well potential
• Decoherence in Josephson Qubits from Junction Resonances
• Orbital superfluidity in the $P$-band of a bipartite optical square lattice
• Fermionization of two distinguishable fermions
• Collisions of matter-wave solitons
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout
• State preparation and dynamics of ultracold atoms in higher lattice orbitals
• Pairing in few-fermion systems with attractive interactions
• Few-boson dynamics in double wells: From single-atom to correlated-pair tunneling
• Counting atoms using interaction blockade in an optical superlattice
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Tunneling dynamics of few bosons in a double well
• Tunneling theory of two interacting atoms in a trap
• Excitations of Few-Boson Systems in 1-D Harmonic and Double Wells
• Boson Pairs in a One-dimensional Split Trap
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Hard-core Bose-Fermi mixture in one-dimensional split traps

Cited by in corpus (10)

• Exact dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential
• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• Counterflow dynamics of two correlated impurities immersed in a bosonic gas
• Many-body quantum dynamics of an asymmetric bosonic Josephson junction
• Effective two-mode description of a few ultra-cold bosons in a double-well potential
• Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction
• Topological states in the Kronig-Penney model with arbitrary scattering potentials
• Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction: Mean-field and many-body dynamics
• Interaction-controlled impurity transport in trapped mixtures of ultracold bosons
• Decay properties of unstable Tonks-Girardeau gases from a split trap