Directional quantum state transfer in a dissipative Rydberg-atom-cavity system

Quantum state transfer is a basic task for quantum information processing, which can be easily executed using the coherent dynamics for a closed system instead of the dissipative dynamics for an open system. Here we propose a dissipation-assisted scheme to directionally transfer an arbitrary quantum state from the sender $A$ to the receiver $B$ by virtue of the Rydberg antiblockade mechanism, the laser-induced Raman transition, and the photon loss of an optical cavity. The prominent advantage of the current proposal is that it does not require accurate control over the relevant parameters of the system, as the target state is the steady state of the whole process. The effect of atomic spontaneous emission for the excited states is dramatically restricted by the adiabatic elimination, and a high population of the transferred state around $99\%$ is achievable with the current experimental technology.

Figure 1

(a) Setup for the dissipative scheme. Atoms $A$ and $B$ collectively interact with four classical lasers and one optical cavity. (b) Diagram of corresponding atomic energy levels.

Figure 2

The evolution of populations for ${\rho }_0$ and ${\rho }_R$ governed by the $H_X$ of Eq. (3). The relevant parameters are ${\mathrm{\Omega }}_1={\mathrm{\Omega }}_2=\delta =\mathrm{\Omega }, {\mathrm{\Delta }}_1=30\mathrm{\Omega }, {\mathrm{\Delta }}_2=90\mathrm{\Omega }, \alpha =sin\theta , \beta =cos\theta$, and $\theta =\pi /3$, where $\theta$ can be varied at will.

Figure 3

The populations as functions of $\mathrm{\Omega }t$ governed by the full master equation, Eq. (7), and the effective master equation, Eq. (8). The initial state is ${\rho }_0$ and the target state is ${\rho }_S$. The relevant parameters are set as ${\mathrm{\Omega }}_1={\mathrm{\Omega }}_2=\omega =g=\delta =\mathrm{\Omega }, {\mathrm{\Delta }}_1=30\mathrm{\Omega }, {\mathrm{\Delta }}_2=90\mathrm{\Omega }, \lambda =500\mathrm{\Omega }, \kappa =0.01g, \alpha =sin\theta , \beta =cos\theta$, and $\theta =\pi /3$. The inset is the populations of ${\rho }_S$ as functions of $\mathrm{\Omega }t$ with different $\theta$.

Figure 4

The evolutions of the populations for ${\rho }_S$ governed by the full master equation with different $\delta$, where the initial state is ${\rho }_0$ and the other parameters are the same as those in Fig. 3.

Figure 5

The population of the transferred state in atom B, $\langle \psi \left|\mathrm{Tr}{}_{A\&c}\left[\rho \right]\right|\psi \rangle$, with different $\kappa$, where the initial state is ${\rho }_0$. The parameters are ${\mathrm{\Omega }}_1={\mathrm{\Omega }}_2=\omega =g=\delta =\mathrm{\Omega }, {\mathrm{\Delta }}_1=20\mathrm{\Omega }, {\mathrm{\Delta }}_2=70\mathrm{\Omega }, \lambda =200\mathrm{\Omega }, \alpha =sin\theta , \beta =cos\theta$, and $\theta =\pi /3$.

Figure 6

The time evolutions of the populations for ${\rho }_S$ governed by a full master equation including the atomic spontaneous emission with different experimental parameters. The initial state is ${\rho }_0$ and the other parameters are chosen as ${\mathrm{\Omega }}_1={\mathrm{\Omega }}_2=\omega =\delta =g, {\mathrm{\Delta }}_1=30g, {\mathrm{\Delta }}_2=90g, \lambda =400g, {\gamma }_e=2\pi \times 3$ MHz, $\gamma =2\pi \times 1$ kHz, $\alpha =sin\theta , \beta =cos\theta$, and $\theta =\pi /3$.

Figure 7

The diagram of the generalized scheme to resist the collective dephasing from the environment, where the purpose is to transfer an arbitrary state, $|\psi \rangle ={\alpha |0\rangle }_L+{\beta |1\rangle }_L={\alpha |01\rangle }_P+\beta {|10\rangle }_P$, from system $A$ consisting of atoms 1 and 2 to system $B$ composed of atoms 3 and 4. (a) First, only apply all the operations identical to those of Fig. 1 to atoms 1 and 3. (b) Second, remove all the operations from atoms 1 and 3 to atoms 2 and 4.

Figure 8

The dynamics evolutions of populations for ${\rho }_S$ and ${\rho }_1$. The relevant parameters are equal to those of Fig. 3. In addition, the collective dephasing rate is chosen as ${\kappa }_d=0.1\mathrm{\Omega }$.