Decoherence by quantum telegraph noise: A numerical evaluation

We investigate the time evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time evolution of the coherence that are strikingly different from the usual case of a harmonic-oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.

Figure 1

(Color online) (a) Schematic picture of the bistable fluctuator: A localized level tunnel coupled to an electron reservoir. (b) Time evolution of the visibility $\left|D\left(t\right)\right|$ for classical telegraph noise (top to bottom: $v/\gamma =0.2,0.6,1.0,1.4,1.8,2.2,2.6,3.0$).

Figure 2

(Color online) Time evolution of the visibility $\left|D\left(t\right)\right|$ for different couplings $v$, for quantum telegraph noise acting on a qubit at low temperatures $\left(T/\gamma =0.01\right)$. The dashed lines show the Gaussian approximation. From top to bottom: $v/\gamma =0.2,0.6,1.0,1.4,1.8,2.2,2.6,3.0$ (with ${\epsilon }_0=0$).

Figure 3

(Color online) Density plot of $e^{+iv/2t}D\left(t\right)$, which is real valued, as a function of time (horizontal) and coupling (vertical). (a)–(d) $T/\gamma =1.0,0.3,0.2,0.01$ (with ${\epsilon }_0=0$). The bold green/light gray lines indicate the contours of vanishing coherence $D\left(t\right)=0$. The dashed line indicates the critical coupling strength $v_c^q/\gamma \approx 1.1,1.9,2.2,2.7$ [from (a)–(d)].

Figure 4

(Color online) Critical coupling strength $v_c^q\left(T\right)$ as a function of temperature (with ${\epsilon }_0=0,\gamma =1$). The strong-coupling regime is located above the dashed line. At high temperatures, one has $v_c^q\left(T\right)\to 1$ according to the classical limit.

Figure 5

(Color online) Time evolution of the spin-echo signal $\left|D_{\text{echo}}\left(t\right)\right|$ (solid line) after applying a $\pi$ pulse at $t^{\prime }=t/2$, in comparison with the visibility $\left|D\left(t\right)\right|$ for free evolution (dashed line), (a)–(d): $T/\gamma =1.0,0.5,0.25,0.01$ $\left(v/\gamma =3.0,{\epsilon }_0=0\right)$.