Quantum dynamics in single-spin measurement

We study the quantum dynamics of a model for the single-spin measurement in magnetic-resonance force microscopy. We consider an oscillating driven cantilever coupled with the magnetic moment of the sample. Then, the cantilever is damped through an external bath and its readout is provided by a radiation field. Conditions for reliable measurements will be discussed.

Figure 1

Phase distribution for an initial state of the spin $\left(\mid g⟩-\mid e⟩\right)∕\sqrt{2}$ (in the nonrotated frame) at times $\tau =0$ (dotted line), $\tau =8\times {10}^4$ (dashed and solid line). The dashed line refers to $\chi =0$ while the solid line to $\chi =0.5$. The values of other parameters are $\gamma ={10}^{-4}$, $\kappa ∕\gamma =0.08$, $\alpha =4i$, $\beta =3$, and $N={10}^2$ (a), $N={10}^4$ (b).

Figure 2

Phase distribution for an initial state of the spin $\mid e⟩$ (in the nonrotated frame) at times $\tau =0$ (dotted line), $\tau =8\times {10}^4$ (dashed and solid line). The dashed line refers to $\chi =0$ while the solid line to $\chi =0.5$. The values of other parameters are $\gamma ={10}^{-4}$, $\kappa ∕\gamma =0.08$, $\alpha =4i$, $\beta =3$, and $N={10}^2$ (a), $N={10}^4$ (b).

Figure 3

Phase distribution for an initial state of the spin $\mid e⟩$ (in the nonrotated frame) for different values of $\kappa$ at time $\tau =8\times {10}^4$. It is $\kappa ∕\gamma =0.04$ dotted line, $\kappa ∕\gamma =0.08$ solid line, and $\kappa ∕\gamma =0.12$ dashed line. The values of other parameters are $\gamma ={10}^{-4}$, $\chi =0.5$, $\alpha =4i$, $\beta =3$, $N={10}^2$.