Multiple perfectly transmitting states of a discrete level at strong coupling

We analyze the transport properties of a discrete level between two reservoirs with a band structure. We focus on the case where the level is strongly coupled to the reservoirs, the coupling parameter is typically of the order of the energy scales of the band structures. In the absence of interactions, this system has an exact solution and the nonlinear Lamb shift can be derived. As expected, the Lamb shift has the effect of pushing the perfectly transmitting state (the reservoir state that flows through the discrete level without reflection) out of resonance with the discrete level, and can possibly turn it into a bound state. However, we show that additional pairs of perfectly transmitting states may appear due to the nonlinear Lamb shift when the coupling exceeds a critical value. The transmission function of the discrete level then resembles that of a multi-level system. Even in situations where the energy of the discrete level is outside the reservoirs' band, a perfectly transmitting state can be created inside the band if the coupling is strong enough. We propose observing the bosonic version of this physics in microwave cavities, and the fermionic version in the conductance of a quantum dot coupled to 1D or 2D reservoirs.