Entanglement creation with negative index metamaterials

We propose a scheme for creating a maximally entangled state comprising two field quanta. In our scheme, two weak light fields, which are initially prepared in either coherent or polarization states, interact with a composite medium near an interface between a dielectric and a negative index metamaterial. This interaction leads to a large Kerr nonlinearity, reduction of the group velocity of the light, and significant confinement of the light fields, while simultaneously avoiding amplitude losses of the incoming radiation. All these considerations make our scheme efficient.

Figure 1

Two weak light pulses create two surface polaritons near the interface between the dielectric $z>0$ and the metamaterial $z<0$. When electromagnetically induced transparency is established for both polaritons simultaneously, they will propagate along the interface with small group velocities ${\upsilon }_g<c$ and interact nonlinearly with each other.

Figure 2

Configuration of a six-level atom for creating double electromagnetically induced transparency for two weak fields $E_a$ and $E_b$. Here, the fields $E_a$ and $E_b$ are coupled resonantly with the transitions $|2\rangle \to |4\rangle$ and $|2\rangle \to |6\rangle$ and off-resonantly with the transitions $|3\rangle \to |5\rangle$ and $|1\rangle \to |5\rangle$ with detuning $\Delta$. Two classical control fields drive the transitions $|1\rangle \to |4\rangle$ and $|3\rangle \to |6\rangle$ [9].

Figure 3

Kerr coefficient $\chi (\times {10}^4)$ (dashed blue) and corresponding mutual phase shift $\phi$ in units of $\pi$ (solid red) as functions of the field frequency $\omega /{\omega }_0$.