The nature of the Lamb shift in weakly-anharmonic atoms: from normal mode splitting to quantum fluctuations

Understand

When a two level system (TLS) is coupled to an electromagnetic resonator, its transition frequency changes in response to the quantum vacuum fluctuations of the electromagnetic field, a phenomenon known as the Lamb shift.

• Remarkably, by replacing the TLS by a harmonic oscillator, normal mode splitting leads to a quantitatively similar shift, without taking quantum fluctuations into account.
• In a weakly-anharmonic system, lying in between the harmonic oscillator and a TLS, the origins of such shifts can be unclear.
• An example of this is the dispersive shift of a transmon qubit in circuit quantum electrodynamics (QED).