  It is known that the electromagnetic vacuum is responsible for the Lamb
shift, which is a crucial phenomenon in quantum electrodynamics (QED). In
circuit QED, the readout or bus resonators that are dispersively coupled can
result in a significant Lamb shift of the qubit, much larger than that in the
original broadband cases. However, previous approaches or proposals for
controlling the Lamb shift in circuit QED demand overheads in circuit designs
or non-perturbative renormalization of the system's eigenbases, which can
impose formidable limitations.In this work, we propose and demonstrate an
efficient and cost-effective method for controlling the Lamb shift of
fixed-frequency transmons. We employ the drive-induced longitudinal coupling
between the transmon and resonator. By simply using an off-resonant
monochromatic driving near the resonator frequency, we can modify the Lamb
shift by 32 to -30 MHz without facing the aforementioned challenges. Our work
establishes an efficient way of engineering the fundamental effects of the
electromagnetic vacuum and provides greater flexibility in non-parametric
frequency controls of multilevel systems. In particular, this Lamb shift
engineering scheme enables individually control of the frequency of transmons,
even without individual drive lines.
