Single Photons from Coupled Quantum Modes

Single photon emitters often rely on a strong nonlinearity to make the behavior of a quantum mode susceptible to a change in the number of quanta between one and two. In most systems, the strength of nonlinearity is weak, such that changes at the single quantum level have little effect. Here, we consider coupled quantum modes and find that they can be strongly sensitive at the single quantum level, even if nonlinear interactions are modest. As examples, we consider solid-state implementations based on the tunneling of polaritons between quantum boxes or their parametric modes in a microcavity. We find that these systems can act as promising single photon emitters.

Figure 1

(a) Variation of $g_{2,11}(0)$ with $E_1$ and $E_2$. (b) Dependence of the equal time correlation function and average populations on $E_2$ for $E_1=0.07\mathrm{meV}$. (c) $g_{2,11}(t)$ for the optimum parameters from (a). (d) $g_{2,11}(0)$ from Eq. (5) (solid line) and comparison to the single mode case (dotted line). In all panels $\Gamma =0.2\mathrm{meV}$ and in (a–c) $F=0.1\mathrm{meV}$.

Figure 2

Eigenstates from the diagonalization of the Hamiltonian Eq. (6) without the pump terms on the particle number manifold. Parameters: $E_1=0\mathrm{meV}$, $E_1=0.12\mathrm{meV}$, $E_2=0\mathrm{meV}$, $\alpha =0.012\mathrm{meV}$, $\Gamma =0.1\mathrm{meV}$. The transitions caused by optical pumping and decay are shown by the solid and dashed arrows, respectively.

Figure 3

(a) Variation of $g_{2,11}(0)$ with $E_2$ and $E_3$ for $E_1=0$, $F=0.1\mathrm{meV}$. (b) The optimum energy levels. (c) $g_{2,11}$ for the optimum parameters. Other parameters: $\Gamma =0.1\mathrm{meV}$, $\alpha =0.012\mathrm{meV}$. (d) Comparison of the $g_{2,11}(0)$ available from the single mode polariton blockade (with pump resonant with the bare mode energy), the two coupled mode case (from Fig. 1) and the three parametrically coupled modes. $g_{2,11}(0)$ is plotted as a function of the average occupation number of the signal mode. Dashed curves show the effect of dephasing.