A continuous measurement of energy that is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy (unsharp), continuous monitoring gives a readout $E(t)$ from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes, in the absence of measurement, Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: (i) the Zeno regime, where the measurement results in a freezing of the transitions between the levels, and (ii) the Rabi regime, where the transitions are maintained. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time-dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.A continuous measurement of energy that is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy (unsharp), continuous monitoring gives a readout $E(t)$ from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes, in the absence of measurement, Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: (i) the Zeno regime, where the measurement results in a freezing of the transitions between the levels, and (ii) the Rabi regime, where the transitions are maintained. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time-dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.

arXiv:quant-ph/9703049Physical Review AJul 1, 199726 citations

Realization scheme for continuous fuzzy measurement of energy and the monitoring of a quantum transition

Audretsch, J., Mensky, M. B.

The continuous fuzzy measurement of energy of a single two-level system driven by a resonant external field is studied. An analysis is given in the framework of the phenomenological restricted path integral approach (RPI) (which reduces effectively to a Schrodinger equation with a complex Hamiltonian) as well as with reference to the microphysical details of a class of concrete physical realizations. Within the RPI approach it is demonstrated that for appropriately adjusted fuzziness, information about the evolution of the state of the system can be read off from the measurement readout E(t). It is shown furthermore how a measurement of this type may be realized by a series of weak and short interactions of the two-level system with a quantum mechanical meter system. After each interaction a macroscopic measuring apparatus causes the meter to transit into one of two states. The result is used to generate the energy readout E(t). In this way a complete agreement with the RPI approach is demonstrated which thus obtains an operational interpretation.The continuous fuzzy measurement of energy of a single two-level system driven by a resonant external field is studied. An analysis is given in the framework of the phenomenological restricted path integral approach (RPI) (which reduces effectively to a Schrodinger equation with a complex Hamiltonian) as well as with reference to the microphysical details of a class of concrete physical realizations. Within the RPI approach it is demonstrated that for appropriately adjusted fuzziness, information about the evolution of the state of the system can be read off from the measurement readout E(t). It is shown furthermore how a measurement of this type may be realized by a series of weak and short interactions of the two-level system with a quantum mechanical meter system. After each interaction a macroscopic measuring apparatus causes the meter to transit into one of two states. The result is used to generate the energy readout E(t). In this way a complete agreement with the RPI approach is demonstrated which thus obtains an operational interpretation.

arXiv:quant-ph/9808062Aug 28, 19987 citations

E(t)

from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes, in the absence of measurement, Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: (i) the Zeno regime, where the measurement results in a freezing of the transitions between the levels, and (ii) the Rabi regime, where the transitions are maintained. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time-dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.