Atomic Quantum Dots Coupled to a Reservoir of a Superfluid Bose-Einstein Condensate

We study the dynamics of an atomic quantum dot, i.e., a single atom in a tight optical trap which is coupled to a superfluid reservoir via laser transitions. Quantum interference between the collisional interactions and the laser induced coupling results in a tunable dot-bath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spin-boson model with Ohmic coupling, which exhibits a dissipative phase transition and allows us to directly measure atomic Luttinger parameters.

Figure 1

Schematic setup of an atomic quantum dot coupled to a superfluid atomic reservoir. The Bose liquid of atoms in state $a$ is confined in a shallow trap $V_a(\mathbf{x})$. The atom in state $b$ is localized in tightly confining potential $V_b(\mathbf{x})$. Atoms in states $a$ and $b$ are coupled via a Raman transition with effective Rabi frequency $\Omega$. A large on-site interaction $U_{bb}>0$ allows only a single atom in the dot.

Figure 2

The oscillation frequency $\tilde{\Delta }$ and the damping rate $\Gamma$ as functions of the coupling strength $\alpha$. For the damping in the range $1/2<\alpha <1$ we used the approximate expression $\Gamma =(1/2-\alpha )\tan (\pi \alpha ){\Delta }_r(\alpha )$ [22]. The dissipative phase transition shows up as a jump of size $m_s$ in the occupation as the detuning $\delta$ is changed from small negative to positive values.