Scheme for entanglement generation in an atom-cavity system via dissipation

We propose a dissipative scheme to generate a maximally entangled state for two $\Lambda$-type atoms trapped in an optical cavity. Different from the unitary-dynamics-based scheme, our work shows that both atomic spontaneous emission and cavity decay are no longer detrimental, but necessary for entanglement generation. The scheme is independent of initial states and does not require precise time control. A final numerical simulation with two groups of experimental parameters indicates that the present scheme is feasible and the performance could be better than the unitary-dynamics-based scheme.

Figure 1

(a) The schematic of two $\Lambda$-type atoms A and B trapped into an optical cavity. $\kappa$ and and $\gamma$ stand for the cavity decay rate and atomic spontaneous emission rate, respectively. (b) Energy level structure of the $\Lambda$-type atom. Here we have assumed the excited state $|2\rangle$ spontaneously decays into two ground states with branching rate $\gamma /2$.

Figure 2

Level configuration and transitions in the dressed state picture. After choosing the frequency suitably, microwave field causes resonant transitions among states $|00\rangle |0\rangle ,|S\rangle |0\rangle$, and $|11\rangle |0\rangle$. And classical laser field causes resonant transition from state $|00\rangle |0\rangle$ to state $|T_1^{+}\rangle$, but causes nonresonant transitions from $|T\rangle |0\rangle$ to the states in the single excitation subspace.

Figure 3

Populations of $|T\rangle |0\rangle ,|S\rangle |0\rangle ,|00\rangle |0\rangle$, and $|11\rangle |0\rangle$ versus time in units of $g^{-1}$ with the initial state $|11\rangle |0\rangle$. The parameters are chosen as $\Omega =0.015g,{\Omega }_{\mathrm{MW}}=0.4\Omega ,\Delta =-g$, and $\kappa =\gamma =0.1g$.

Figure 4

(a) Fidelity of $|T\rangle |0\rangle$ versus $\kappa$ and $\gamma$ at the time $4\times {10}^4/g$. The parameters are chosen as $\Omega =0.015g,{\Omega }_{\mathrm{MW}}=0.4\Omega$, and $\Delta =-g$. (b) Fidelity of $|T\rangle |0\rangle$ versus $\kappa$ and $\gamma$ at the time $4\times {10}^5/g$. Curves in the figure denotes $C=300$, 100, 50, 30, 20, and 15 (from left to right), respectively.

Figure 5

(a) Fidelity of $|T\rangle |0\rangle$ at the time $4\times {10}^5/g$ versus the relative fluctuations $\delta g/g$ or $\delta \Delta /\Delta$. (b) Fidelity of $|T\rangle |0\rangle$ versus the relative fluctuations $\delta \Omega /\Omega$ and $\delta {\Omega }_{\mathrm{MW}}/{\Omega }_{\mathrm{MW}}$. The rest of the parameters are the same as in Fig. 3.

Figure 6

Fidelity of $|T\rangle |0\rangle$ with two groups of experimental parameters versus time in units of $g^{-1}$. The green (solid) and blue (dashed) lines are plotted with the typical experimental parameters extracted from the Refs. [32, 33, 34] and Ref. [35], respectively.