Unified Theory of Dynamically Suppressed Qubit Decoherence in Thermal Baths

We develop a unified theory of dynamically suppressed decay and decoherence by external fields in qubits coupled to arbitrary thermal baths and dephasing sources. This general theory does not invoke the rotating-wave approximation, which fails for ultrafast field-induced modulations of qubit-bath coupling. Considerations for optimizing the dynamical suppression are outlined.

Figure 1

Inset (a): Modulation scheme: a nonresonant field with Rabi frequency ${\Omega }_p$ Stark-shifts level $e$ by ${\delta }_a(t)$, whereas $V(t)$ is the near-resonant (flipping) modulation of the $e-g$ transition. Inset (b): Overlap of bath and modulation spectra (arbitrary units): solid curve: $G_0(\omega )$; dashed curve: $G_S(\omega )=[G_T(\omega )+G_T(-\omega )]/2$ for 1D phonon bath (see text), $\beta =10/{\omega }_D$; vertical bars: peaks of $F(\omega )$, located relative to ${\omega }_a=0.94{\omega }_D$; bars 1a and 1b: $\varphi =-0.15$, single peak for each choice of $\tau$; bars 2a and 2b: $\varphi =\pi$, pairs of peaks for each choice of $\tau$. Lower figure: decay rates $R=(R_e+R_g)/2$ (normalized to the unperturbed $R$) as a function of the modulation period $\tau$ (in units of $1/{\omega }_D$) for the spectra shown in inset (b): curves 1a and 1b and curves 2a and 2b correspond to the peaks of $F(\omega )$ in inset (b); dotted curves: RWA calculations of curves 1 and 2. Curve 1 is optimal.