Probing two-particle exchange processes in two-mode Bose-Einstein condensates

Abstract

We study the fidelity decay and its freeze for an initial coherent state of two-mode Bose-Einstein condensates in the Fock regime considering a Bose-Hubbard model that includes two-particle tunneling terms. By using linear-response theory we find scaling properties of the fidelity as a function of the particle number that prove the existence of two-particle mode-exchange when a non-degeneracy condition is fulfilled. Tuning the energy difference of the two modes serves to distinguish the presence of two-particle mode-exchange terms through the appearance of certain singularities. We present numerical calculations that illustrate our findings, and propose exploiting a Feshbach resonance to verify experimentally our predictions.

Optimal and near-optimal probe states for quantum metrology of number-conserving two-mode bosonic Hamiltonians

“…with φ ∈ [0, 2π), i.e., |Ψ V are the well-known NOON states that appear in the context of attractive ultracold Bose gases (e.g., 7 Li) confined in a double-well potential [23,24]. The observable a † 1 a 1 a † 0 a 0 has, for N even, maximal eigenvalue N 2 /4 corresponding to state | N 2 , N 2 and, for N odd, maximal eigenvalue (N 2 − 1)/4 corresponding to the two-dimensional subspace spanned by the Dicke states |(N − 1)/2, (N + 1)/2 and |(N + 1)/2, (N − 1)/2 .…”

“…Therefore, the maximal variance of the observable J z is N 2 , occurs for the family of states |Ψ V given in Eq. (7).…”

“…with φ ∈ [0, 2π), i.e., |Ψ V are the well-known NOON states that appear in the context of attractive ultracold Bose gases (e.g., 7 Li) confined in a double-well potential [23,24]. The observable a † 1 a 1 a † 0 a 0 has, for N even, maximal eigenvalue…”

“…Methods for generating nonclassical states of the electromagnetic field or atomic ensembles by unitary or dissipative quantum dynamics are central to atom-field based quantum technologies, e.g., estimation of dynamical parameters beyond the standard quantum limit. In the realm of degenerate massive bosons (including, e.g., ultracold bosonic gases), studies on nonclassical states of N interacting bosons distributed among two orthogonal single particle states [1][2][3] have led to increased understanding of phenomena such as many-body entanglement [4], Schrödinger cat state formation [5,6], and coherent pair tunneling [7]. These systems also provide a foundation for the modern atomic clock [8].…”