Quantum Cloning of a Coherent Light State into an Atomic Quantum Memory

A scheme for the optimal Gaussian cloning of coherent light states at the interface between light and atoms is proposed. The distinct feature of this proposal is that the clones are stored in an atomic quantum memory, which is important for applications in quantum communication. The atomic quantum cloning machine requires only a single passage of the light pulse through the atomic ensembles followed by the measurement of a light quadrature and an appropriate feedback, which renders the protocol experimentally feasible. An alternative protocol, where one of the clones is carried by the outgoing light pulse, is discussed in connection with eavesdropping on quantum key distribution.

Figure 1

Setup for the CV cloning of light into two atomic quantum memories. A light beam $L$ having a strong coherent component polarized along the $x$ axis propagates along the $z$ axis and passes through two atomic ensembles $A$ and $B$ polarized in the $x$ direction. The $z$ component of the Stokes vector of the output light beam is measured using wave plates (WPs), polarizing beam splitter (PBS) and two photodetectors ($\mathrm{D}$), and the atomic states are then displaced accordingly. The clones are stored in the atomic ensembles $A$ and $B$.

Figure 2

(a) Network for optimal symmetric Gaussian cloning of coherent states. The lines indicate the $\mathrm{C}\mathrm{\text{−}}\mathrm{N}\mathrm{O}\mathrm{T}$ gates, ● labels control mode and ⊕ indicates target mode. (b) Simplified cloning network where two $\mathrm{C}\mathrm{\text{−}}\mathrm{N}\mathrm{O}\mathrm{T}$ gates are replaced by the measurement of the $p_L$ quadrature followed by displacements of the atomic $p$ quadratures, as indicated by the open boxes.

Figure 3

Setup that produces one clone stored in an atomic quantum memory $A$ while the second “flying” clone is carried by the light beam $B$. BS is a balanced beam splitter and HD denotes homodyne detector. The clone in the light beam $B$ is squeezed in the $x$ quadrature by a factor of $\sqrt{2}$.