Pulsed coherent drive in the Jaynes-Cummings model

The Jaynes-Cummings system is one of the most fundamental models of how light and matter interact. When driving the system with a coherent state (e.g., laser light), it is often assumed that whether the light couples through the cavity or atom plays an important role in determining the dynamics of the system and its emitted field. Here, we prove that the dynamics are identical in either case except for the offset of a trivial coherent state. In particular, our formalism allows for both steady state and the treatment of any arbitrary multimode coherent state driving the system. Finally, the offset coherent state can be interferometrically canceled by appropriately homodyning the emitted light, which is especially important for nanocavity quantum electrodynamics where driving the atom is much more difficult than driving the cavity.

Figure 1

Schematic of a Jaynes-Cummings system, containing a two-level quantum system coherently interacting with a cavity mode. The cavity couples to the reservoir $b$, while the two-level atom couples to reservoir $c$.

Figure 2

Energy-level structure of a Jaynes-Cummings system when the atom and cavity have the same natural oscillation frequency. Blue arrows denote allowed transitions from the reservoir-cavity coupling, while red arrows denote allowed transitions from the reservoir-atom coupling.

Figure 3

Schematic of the Jaynes-Cummings system with the reservoir $b$ homodyned with field $e$ using a beamsplitter.

Figure 4

Schematic of a drop filter that automatically generates the appropriate coherent state to compensate the coherent field that builds up in the Jaynes-Cummings system. The first beamsplitter divides the incident pulse and sends it to the JC system and the bare cavity, while the second beamsplitter homodynes the signals together. The response out of the homodyne channel of the drop filter $e_{\text{out}}$ is the same as if the JC system were instead driven through the atom by the input coherent field convolved with the impulse response of the cavity.