Quantum-state transfer between tripod atoms over a dark fiber

In this work we introduce a model for quantum-state transfer between tripod atoms over a dark fiber. Two tripod atoms are confined in separate cavities linked by an optical fiber. The cavities and the fiber sustain two optical modes of opposite circular polarization. For each atom, the two ground states encode the quantum state to be transferred and are coupled to a common excited state by the cavity modes of opposite polarization. The remaining transition for each atom is used to control the transfer process. We demonstrate that by using laser pulses the dynamics of the system can be confined within a degenerate dark state subspace, with the different dark states interacting via nonadiabatic couplings. We solve analytically the dynamics in the dark state subspace, and determine the conditions on the pulse shape for the implementation of the quantum transfer. We identify a possible pulse shape which satisfies the required conditions, and demonstrate the quantum-state transfer via numerical simulations.

Figure 1

Optical cavity setup, and atom-light interaction scheme for the proposed implementation of quantum-state transfer.

Figure 2

Result of numerical simulations for the process implementing quantum-state transfer over a dark fiber. For each column, the top panel represents the pulse sequence, and the lower panel the time evolution of the populations of the states most relevant to the transfer process: the dashed line corresponds to the population of the $|-00\rangle |a00\rangle |00\rangle$ state, while the solid line is the population of the $|a00\rangle |-00\rangle |00\rangle$ state. The parameter of the calculations are: left column: $\tau =-150$, $\nu =20$, ${\Omega }_{1,0}={\Omega }_{2,0}=80$; center column: $\tau =0$, ${\Omega }_{1,0}={\Omega }_{2,0}=80$; right column $\tau =150$, ${\Omega }_{1,0}=-{\Omega }_{2,0}=80$. Furthermore, $g=21$, $w=300$, and $\nu =20$ for all simulation data sets.

Figure 3

Dependence on time of the eigenvalues of the $32\times 32$ Hamiltonian of the system. The relevant parameters are $w=300$, $\tau =150$, $g=21$, $t_0=1400$, ${\Omega }_{1,0}=-{\Omega }_{2,0}=80$, and $\nu =10$.

Figure 4

Result of numerical simulations for the quantum-state transfer over a dark fiber of the superposition $\left(\alpha \right|+00\rangle +\beta |-00\rangle )|a00\rangle |00\rangle$, with $\alpha =1/\sqrt{3}$, $\beta =-\sqrt{2/3}$. (a) The fidelity of transfer is plotted as a function of $\nu$. The different data sets differ for the value of $w$: filled circles correspond to $w=300$, open triangles to $w=200$, and open squares to $w=150$. The time delay between pulses is $\tau =150$ for all the data sets. (b) The fidelity is plotted as a function of the delay time $\tau$ between the pulses, for a cavity-fiber coupling $\nu =1$, and $w=300$. (c) The fidelity is calculated for pulses of different shape, as defined by Eq. (26), and plotted as a function of the parameter $A$, given by Eq. (19). For the data in panel (c), $\nu =1$, $\tau =150$, and $w=300$. The parameters common to all calculations are $g=21$, $t_0=1400$, and ${\Omega }_{1,0}=-{\Omega }_{2,0}=80$.