Photon-number-dependent effective Lamb shift

Single-junction quantum-circuit refrigerator

“…We suggest that these branches correspond to the multi-photon transitions in the resonator, similar to those found in Ref. 36. If the voltage is eV 0 ≈ ∆− hω r n, where n is a positive integer, then tunneling processes with absorption of n and more photons from the resonator are allowed.…”

Assessment of weak-coupling approximations on a driven two-level system under dissipation

“…We simulate the qubit dynamics for a broad range of effective qubit dissipation rates γ, comprising values of 2π × 2.5 MHz (0.05% of ω q ) up to 2π × 500 MHz (10% of ω q ). Such tunability has been demonstrated in similar physical setups in recent protocols for engineered environments [78][79][80][81][82][83]. For simplicity of comparison between Lindblad and SLED in the present model, we assume that the intrinsic dephasing and decay rates of the qubit are low compared to Ω d and γ, such that they have a negligible effect on the qubit dynamics.…”

“…In this paper, we focus on the case where a single qubit is weakly driven by nearly resonant transverse fields and the interaction with a cold Ohmic bath produces effective dissipation rates that reach up to 10% of the bare qubit angular frequency. Experimentally, this scenario has been motivated by the recent progress in the implementation of tunable and engineered environments, for example, in circuit quantum electrodynamics (cQED) [78][79][80][81][82][83][84][85][86][87][88]. Note that another numerically exact and non-perturbative method has been proposed to capture more general initial system-bath states, including correlated ones [89].…”

Recent Developments in Quantum‐Circuit Refrigeration

“…An alternative operation principle is provided in Viitanen et al. (2021) [ 51 ] by a radio‐frequency drive to a supporting mode in the system, such as a higher mode of a CPW resonator. The QCR is then activated by multiphoton‐tunneling processes which absorb photons from both the supporting rf mode and the primary mode which we intend to control with the QCR.…”

“…[19]. We obtain [ 51 ] $$\begin{align} &\gamma _{\mathrm{T}, \mathrm{p}}{\left(V_\mathrm{QCR}, \bar{n}_{\mathrm{s}}\right)} = 2\underbrace{\pi \alpha _{\mathrm{p}}^{2} \frac{Z_{\mathrm{p}}}{R_{\mathrm{T}}}}_{\text{primary mode}} \underbrace{\sum _{k, l} P_{k}{\left(\bar{n}_{\mathrm{s}}\right)}{\left|M_{k l}^{(\mathrm{s})}\right|}^{2}}_{\text{supporting rf mode}} \nonumber\\ &\quad\times\underbrace{\sum _{\ell _{\mathrm{p}}, \tau =\pm 1} \ell _{\mathrm{p}} F{\left(\tau eV_\mathrm{QCR}/2+\ell _{\mathrm{p}} \hbar \omega _{\mathrm{p}}+\ell _{\mathrm{s}} \hbar \omega _{\mathrm{s}}-E_{\mathrm{N}}\right)}}_{\text{tunnel junctions}} \end{align}$$where α p takes into account the capacitances of the resonator modes, Z p is the characteristic impedance of the primary mode, R T is the tunneling resistance, $$P_k$$ is the occupation probability of the k th Fock state of the supporting mode given a mean supporting‐mode occupation $$\bar{n}_\mathrm{s}$$, …”