Entanglement generation in a system of two atomic quantum dots coupled to a pool of interacting bosons

We discuss entanglement generation in a closed system of one or two atomic quantum dots (qubits) coupled via Raman transitions to a pool of cold interacting bosons. The system exhibits rich entanglement dynamics, which we analyze in detail in an exact quantum mechanical treatment of the problem. The bipartite setup of only one atomic quantum dot coupled to a pool of bosons turns out to be equivalent to two qubits which easily get entangled from an initial product state. We show that both the number of bosons in the pool and the boson-boson interaction crucially affect the entanglement characteristics of the system. The tripartite system of two atomic quantum dots and a pool of bosons reduces to a qubit-qutrit-qubit realization. We consider entanglement possibilities of the pure system as well as of reduced ones by tracing out one of the constituents, and show how the entanglement can be controlled by varying system parameters. We demonstrate that the qutrit, as expected, plays a leading role in entangling the two qubits and the maximum entanglement depends in a nontrivial way on the pool characteristics.

Figure 1

Two atomic qubits coupled to a finite number of cold interacting bosons. The qubits are trapped by the tight potentials $V_1$ and $V_2$; the bosons are confined in an external potential $V_{\mathrm{bos}}$. $T$ is the optical transition assisted coupling between the qubits and the bosons.

Figure 2

(a) Time evolution of the concurrence of the bipartite setup for $n=10$, $E/T=0.01$ and the interaction $U/T=0$ (black curve 1); $U/T=0.06$ (red curve 2) and $U/T=0.1$ (blue curve 3). (b) Dependence of the entanglement period $t_{\mathrm{ent}}$ (dashed curves) and maximum concurrence $C_{\max }$ (solid curves) on the interaction $U/T$ for $n=10$ (circles) and $n=4$ (diamonds) bosons in the pool. Time $t$ and the entanglement period are expressed in units of $1/T$.

Figure 3

(a) Time-dependent concurrence $C$ of the tripartite setup for $E/T=0.01$, $n=10$, and interaction $U/T=0.2$. (b) The maximum value of concurrence $C_{\max }$ of the tripartite system versus interaction $U/T$ for $n=4$ (dotted black line), $n=10$ (dashed red line), and $n=30$ (solid blue line) bosons in the pool.

Figure 4

Entanglement period $t_{\mathrm{ent}}$ versus interaction for $n=4$ (black squares), $n=10$ (red circles), and $n=30$ (blue diamonds) interacting bosons in the pool. The product $t_{\mathrm{ent}}U/T$ versus $U/T$ is shown in the inset.

Figure 5

(a) Time dependence of the entanglement of formation $E_f$ for $U/T=0.2$ and $n=10$. (b) The maximum values of the entanglement of formation $E_{\max }$ (dashed curves) and the negativity $N_{\max }$ (solid curves) versus the interaction $U/T$ for $n=4$ (black curves 1 and 1${}^{\prime }$), $n=10$ (red curves 2 and 2${}^{\prime }$), and $n=30$ (blue curves 3 and 3${}^{\prime }$) bosons in the pool.

Figure 6

(a) Time dependence of the entanglement of formation $E_f$ for $U/T=0.2$ and $n=10$. (b) The maximum values of the entanglement of formation $E_{\max }$ (dashed curves) and the negativity $N_{\max }$ (solid curves) versus interaction $U/T$ for $n=4$ (black squares), $n=10$ (red circles), and $n=30$ (blue diamonds) bosons in the pool.