Fast conversion of Dicke states $|D_n^{\left(2\right)}\rangle$ to $|D_{n+1}^{\left(2\right)}\rangle$ by transitionless quantum driving

A scheme is proposed for fast conversion of two-atom Dicke states to three-atom Dickes state and three-atom Dicke states to four-atom Dicke states based on transitionless quantum driving. This scheme can be achieved within one step through appropriately regulating the Rabi frequencies of classical fields. The effects of decoherence induced by atomic spontaneous emission and leakage of the cavity are also taken into account. The numerical simulation result shows that this scheme is robust against both atomic spontaneous emission and cavity leakage. Furthermore, when multiple atoms are trapped in a cavity, the ($n+1$)-atom Dicke states can be derived directly from the $n$-atom Dicke states with the same principle, which provides a scalable way for the preparation of Dicke states in theory.

Figure 1

(a) Schematic illustration of $n$ identical neutral atoms interacting with a cavity. (b) Involved atomic energy-level configuration and the corresponding transitions. Here $|0\rangle$ and $|1\rangle$ are stable ground states and $|e\rangle$ is the excited state. The transition $|1\rangle \leftrightarrow |e\rangle$ is driven by classical field with time-dependent Rabi frequency ${\mathrm{\Omega }}_i$ ($i=1,2,...,n$), while the transition $|0\rangle \leftrightarrow |e\rangle$ is coupled to the cavity with coupling ${\lambda }_i$.

Figure 2

Comparison of the total interaction time required between shortcuts to the adiabaticity method and the STIRAP method. The parameters are $t_0=0.14t_f$, $t_c=0.19t_f$, $tan\alpha =1$, ${\mathrm{\Omega }}_0=0.1\lambda$, and $\mathrm{\Delta }=2\lambda$.

Figure 3

Fidelity of the conversion process governed by the Hamiltonian $H_I^{\prime }$ versus $\gamma /\lambda$ ($\kappa =\gamma$) and $\lambda t$. The parameters are $t_f=200/\lambda$, $t_0=0.14t_f$, $t_c=0.19t_f$, $tan\alpha =1$, ${\mathrm{\Omega }}_0=0.1\lambda$, and $\mathrm{\Delta }=2\lambda$.

Figure 4

Fidelity of the conversion process governed by the Hamiltonian $H_I^{\prime }$ versus $\gamma /\lambda$ and $\kappa /\lambda$ at $t=t_f$. The parameters are $t_f=200/\lambda$, $t_0=0.14t_f$, $t_c=0.19t_f$, $tan\alpha =1$, ${\mathrm{\Omega }}_0=0.1\lambda$, and $\mathrm{\Delta }=2\lambda$.