One of the intriguing phenomena of quantum electrodynamics is the emergence of the Lamb shift, which was first discovered by Lamb in 1947 1, corresponding to the energy difference between 2S 1/2 and 2P 1/2 levels of a hydrogen atom. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects.
This directly implies the interplay of virtual photon processes and explicitly signals the CLS. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located at an antinode. To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Similar to the atomic cases, RDDI comes from exchange of virtual photons of the continuous modes, and causes the so-called collective Lamb shift (CLS).
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line.
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