Effect of Poisson noise on adiabatic quantum control

We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014)] that this type of noise may improve rather than destroy adiabaticity.

Figure 1

Phase-changing scheme. Fidelity $F\left(t\right)$ versus time $t$. (a) $J=0$ (blue dashed line), $J=0.01$ (black dotted line), $J=0.1$ (green dot-dashed line), $J=1$ (red solid line), with $D{\mathrm{\Omega }}_0={10}^{-4}$ in all cases. (b) $J=0$; $D=0$ (blue dashed line), $D{\mathrm{\Omega }}_0=0.01$ (black dotted line), $D{\mathrm{\Omega }}_0=0.05$ (green dot-dashed line), $D{\mathrm{\Omega }}_0=0.1$ (red solid line). $\mathrm{\Omega }=0.4{\mathrm{\Omega }}_0$ and $T{\mathrm{\Omega }}_0=20$.

Figure 2

RAP scheme in a two-level system with $H_0=H_1$. (a) Fidelity $F\left(T\right)$ against noise strength $D$ for ${\delta }_0=3.5{\mathrm{\Omega }}_0$ (blue lower lines) and ${\delta }_0=1{\mathrm{\Omega }}_0$ (green upper lines) for the numerically exact solution (solid lines), small-noise approximation (36) (dotted lines), naive strong-noise approximation (dashed lines), and strong-noise approximation (B5) (dot-dashed lines); $T{\mathrm{\Omega }}_0=20$. (b) Fidelity $F\left(T\right)$ against both noise strength $D$ and total time $T$; ${\delta }_0=1{\mathrm{\Omega }}_0$.

Figure 3

RAP scheme in a two-level system with $H_0\ne H_1$. ${\delta }_0=3.5{\mathrm{\Omega }}_0$ (black upper lines), ${\delta }_0=1{\mathrm{\Omega }}_0$ (green middle lines), and ${\delta }_0=0.5{\mathrm{\Omega }}_0$ (blue lower lines) for the numerically exact solution (solid lines) and small-noise approximation (36) (dotted lines). (a) Fidelity $F\left(T\right)$ against noise strength $D$ for frequency error. (b) Fidelity $F\left(T\right)$ against noise strength $D$ for both timing and frequency error with $c=1$.

Figure 4

STIRAP pulse sequence with $T{\mathrm{\Omega }}_0=1$ and $\tau {\mathrm{\Omega }}_0=0.1$ for ${\mathrm{\Omega }}_{12}$ (blue dashed line) and ${\mathrm{\Omega }}_{23}$ (red solid line).

Figure 5

STIRAP population transfer in a three-level system with $H_0=H_1$, $\tau {\mathrm{\Omega }}_0=0.1$ for the numerically exact solution (solid lines), small-noise approximation (36) (dotted lines), and strong noise approximation (B5) (dashed lines). (a) Fidelity $F$ versus frequency $\nu$ for $\sigma {\mathrm{\Omega }}_0=2$ and $T{\mathrm{\Omega }}_0=100,200,300$ (blue lower lines, black middle lines, and green upper lines, respectively). (b) Fidelity $F$ versus frequency $\nu$ for $T{\mathrm{\Omega }}_0=200$ and $\sigma {\mathrm{\Omega }}_0=1,2,3$ (blue rightmost lines, black middle lines, and green leftmost lines, respectively).

Figure 6

STIRAP population transfer in a three-level system. (a) Fidelity $F$ versus noise parameter $\nu$ and final time $T$ for $H_1=H_0$; $\sigma {\mathrm{\Omega }}_0=2$. (b) Fidelity $F$ versus noise parameter $\nu$ and distribution width $\sigma$ for $H_1=H_0$; $T{\mathrm{\Omega }}_0=200$. (c) Fidelity $F$ versus noise parameter $\nu$ and final time $T$ for the case of phase fluctuations; $\sigma {\mathrm{\Omega }}_0=2$. $\tau {\mathrm{\Omega }}_0=0.1$ in all cases