Photon routing in cavity QED: Beyond the fundamental limit of photon blockade

The most simple and seemingly straightforward application of the photon blockade effect, in which the transport of one photon prevents the transport of others, would be to separate two incoming indistinguishable photons to different output ports. We show that time-energy uncertainty relations inherently prevent this ideal situation when the blockade is implemented by a two-level system. The fundamental nature of this limit is revealed in the fact that photon blockade in the strong coupling regime of cavity QED, resulting from the nonlinearity of the Jaynes-Cummings energy level structure, exhibits efficiency and temporal behavior identical to those of photon blockade in the bad cavity regime, where the underlying nonlinearity is that of the atom itself. We demonstrate that this limit can be exceeded, yet not avoided, by exploiting time-energy entanglement between the incident photons. Finally, we show how this limit can be circumvented completely by using a three-level atom coupled to a single-sided cavity, enabling an ideal and robust photon routing mechanism.

Figure 1

Schematic depiction of a microtoroid setup. Note that $b_{\mathrm{in}}$ (not shown here) is vacuum.

Figure 2

A schematic of the photon router model. The input pulse is modeled by introducing a feeder cavity which leaks into the system with rate $2{\kappa }_s$.

Figure 3

Two-photon detection probabilities as a function of the pulse width ${\kappa }_s^{-1}$.

Figure 4

Marginal probability density functions of the various reflection and transmission events, as a function of the interval between the photon detection times $\tau$, for (a) long pulses (${\kappa }_s=0.05{\gamma }_c$), (b) short pulses (${\kappa }_s=5{\gamma }_c$), and (c) intermediate pulses (${\kappa }_s=1.5{\gamma }_c$). The different curves correspond to events of double reflection (RR), double transmission (TT), a transmission followed by a reflection (TR), and a reflection followed by a transmission (RT). Note that RR is practically zero in (b).

Figure 5

Simulated results for the two-photon detection probabilities as a function of the pulse width for square pulses (dashed curves), Gaussian pulses (dash-dotted curves), and exponential pulses (solid curves). For square and Gaussian pulses the pulse width ${\kappa }_s^{-1}$ is defined by their half width at half maximum. The parameters are $g/2\pi =$ 70 MHz, ${\kappa }_{\mathrm{ex}}/2\pi =500$ MHz, without losses (${\kappa }_i=\gamma =0$). We note that the simulated results for exponential pulses are practically identical to the analytically calculated results presented in Fig. 3.

Figure 6

The feeder cavity is driven by a three-level atom emitting two photons at once.

Figure 7

The routing efficiency $C^{\mathrm{tr}}$ as a function of the pulse length ${\kappa }_s^{-1}$ and the ratio ${\kappa }_s/{\gamma }_s$.

Figure 8

Cascading of a single-sided cavity QED system and a photon router. Due to the quarter-wave plate (QWP), the pulse is reflected by the polarizing beam splitter (PBS) after interaction with the single-sided cavity. The trajectory of the two-photon pulse is shown by the dashed line.

Figure 9

Probability of detecting two photons at times $t^{\prime }$ and $t^{\prime \prime }$ for an exponential pulse (${\gamma }_{c1}=5{\kappa }_s$) after passage through a single-sided cavity QED system.

Figure 10

Routing efficiency as a function of the cavity-enhanced decay rates during the first and second passages through the system.

Figure 11

Schematic depiction of a three-level atom in the $\Lambda$ configuration inside a single-sided cavity. The trajectory of the pulse is shown by the dashed line.

Figure 12

Routing efficiency $C^{\mathrm{tr}}$ as a function of the cavity-enhanced decay rates ${\gamma }_{cH}$ and ${\gamma }_{cV}$.