Quantifying, characterizing, and controlling information flow in ultracold atomic gases

We study quantum information flow in a model comprised of a trapped impurity qubit immersed in a Bose-Einstein-condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We show that this system undergoes a transition from Markovian to non-Markovian dynamics, which can be controlled by changing key parameters such as the condensate scattering length. In this way, one can realize a quantum simulator of both Markovian and non-Markovian open quantum systems, the latter ones being characterized by a reverse flow of information from the background gas (reservoir) to the impurity (system).

Figure 1

Setup of the impurity-BEC system. The impurity is trapped in a double-well potential $V_A$ (solid) and immersed in a BEC confined by a shallow harmonic potential $V_B$ (dashed). The impurity occupies mostly the two states $|L\rangle$ and $|R\rangle$, in which the atom is localized in the left and right well, respectively. Finally, the distance between the two wells is $2L$.

Figure 2

Non-Markovianity measure ${\mathcal{N}}_{\text{deph}}$ as a function of the scattering length of the background gas $a_B$ with values of well separation $L=50$ nm (red dashed line), $L=75$ nm (blue dotted line), and $L=100$ nm (black solid line). The inset shows ${\mathcal{N}}_{\text{deph}}$ for very small values of the scattering length.

Figure 3

Non-Markovianity measure ${\mathcal{N}}_{\text{deph}}$ as a function of the scattering length of the background gas $a_B$ when the background gas is three-dimensional (red dashed line), quasi-two-dimensional (blue dotted line), and quasi-one-dimensional (black solid line). The inset shows a longer range of the scattering length $a_B$. In all figures, the well separation is $L=75$ nm.