Measurement of Energy Eigenstates by a Slow Detector

We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a slow detector. Such a detector is sensitive only to slowly changing variables, e.g., energy, while its backaction can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.

Figure 1

Simulation of the oscillator occupation number dynamics, described by Eq. (7). The parameters of simulation are ${\Gamma }_{\mathrm{up}}=1$, ${\Gamma }_{\mathrm{dn}}=1.2$.

Figure 2

Four-point correlation function containing the information about fast switching between the number states. The parameters of simulation are ${\Gamma }_{\mathrm{up}}=1$, ${\Gamma }_{\mathrm{dn}}=1.2$.

Figure 3

Scheme for SET displacement detector. The position of the oscillator modulates capacitance $C_g(x)$, thus modifying the current between the left and the right leads.