The quantum Zeno effect is known as the inhibition of a system's reversible dynamics by frequent measurements. Aharonov and Vardi [Phys. Rev. D 21, 2235 (1980)] proposed a scheme intimately related to the quantum Zeno effect. They showed that, by performing a dense sequence of measurements along a presumed path, the system is found to follow this---arbitrarily chosen---trajectory. The proof was based on the von Neumann projection hypothesis. In this paper we investigate whether this effect still holds if we model a realistic measurement process instead of the artificial instantaneous von Neumann collapse. We test the orientation of the Bloch vector of a two-level system using a third level and resonance fluorescence as the measuring apparatus. Therefore we are able to use a dynamical collapse governed by the three-level master equations. We show that a sequence of orientation measurements designed to monitor a particular trajectory indeed induces a dynamics exactly along this trajectory.
The quantum Zeno effect is known as the inhibition of a system's reversible dynamics by frequent measurements. Aharonov and Vardi [Phys. Rev. D 21, 2235 (1980)] proposed a scheme intimately related to the quantum Zeno effect. They showed that, by performing a dense sequence of measurements along a presumed path, the system is found to follow this---arbitrarily chosen---trajectory. The proof was based on the von Neumann projection hypothesis. In this paper we investigate whether this effect still holds if we model a realistic measurement process instead of the artificial instantaneous von Neumann collapse. We test the orientation of the Bloch vector of a two-level system using a third level and resonance fluorescence as the measuring apparatus. Therefore we are able to use a dynamical collapse governed by the three-level master equations. We show that a sequence of orientation measurements designed to monitor a particular trajectory indeed induces a dynamics exactly along this trajectory.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.
The change of dynamics in a quantum system under frequent or continuous observation, known as the quantum Zeno effect, is generally derived from the projection or reduction of the wave-packet hypothesis that is the central postulate in the theory of quantum measurements. The only experiment in which the Zeno effect has yet been clearly demonstrated, though, allows no conclusion on the necessity or validity of the projection postulate. This is shown by calculating, in detail, the outcome of the experiment on the basis of the standard three-level Bloch equations. These equations follow from the quantum theory of irreversible processes with no additional assumptions necessary, such as which part of the system serves as measuring apparatus or how efficient the measurement would be.
In this paper we study the quantum Zeno effect in real space due to a position measurement. The motion of a particle is decelerated or comes to a complete stop when its position is observed. Instead of using the von Neumann collapse hypothesis, we treat a real measurement process. The measurement consists of coupling a two-level atom in a double-well potential to a resonant laser beam. Subsequent resonance fluorescence can be used to determine the atom's position within the double well, provided the laser wavelength is short enough to ensure a resolvable scattering pattern of the fluorescence photons. Treating this process in the framework of dissipative quantum mechanics, we derive a master equation which describes the measurement process in all relevant details. Solving the master equation analytically as well as numerically we study the conditions for the decay of the nondiagonal elements. This leads directly to the inhibition of the center-of-mass motion, i.e., to a quantum Zeno effect. Because we treat the measurement process in detail we are able to investigate the conditions for a complete measurement. In particular, we study the role of the intensity and the wavelength of the probing laser field.
A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ``collapse of the wave function'' is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann's projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.
This is a theoretical thesis in the area of quantum measurement theory. Due to the extensive breadth of this field we choose to narrow our focus to examine a particular problem - the quantum Zeno effect (defined below). Quantum measurement theory is introduced in Chap. 1, using the terminology of effects and operations. This approach allows an operational definition of such terms as a state vector, an ensemble, and a measurement device (for instance), and a consideration of interactions between quantum systems and inaccurate measurement devices. We further introduce the quantum trajectories approach to consider the evolution of an individual quantum system subject to measurement. The quantum Zeno effect is introduced in Chap. 2. Any quantum treatment of a measurement interaction must consider the measurement backaction onto the measured system and this backaction will disrupt the free evolution of the system. The quantum Zeno effect occurs in the strong measurement limit where the measurement backaction totally freezes the evolution of the system, thus rendering the measurement useless. The effect is introduced via projective measurements of two level systems subject to measurement of level populations. At this stage we are able to discuss the main questions addressed by this thesis, and present its structure in Chap. 2. We then develop a new measurement model for the interaction between a system and a measurement device in Chap. 3. Our motivation in doing this is to better model the usual laboratory meter, and in our approach the meter dynamics are such that it relaxes towards an appropriate readout of the system parameter of interest. The irreducible quantum noise of the meter introduces fluctuations that drive the stochastic dynamical collapse of the system wavefunction. In our model, the measured system dynamics (if treated selectively) are described by a stochastic, nonlinear Schroedinger equation. A double well system subject to position measurement provides a natural first application for this model. This is done in Chap. 4 where we monitor the coherent tunnelling of a particle from one well to the other. The advantage afforded by considering this system is that it displays differing regimes where the measurement observable (position) is approximated as possessing either, respectively, a continuous or a discrete eigenvalue structure. Thus, we use this one model to explore the quantum Zeno effect in both measurement regimes. The above treatment is of a theoretical measurement model. In Chap. 5 we turn to consider a recent experimental test of the quantum Zeno effect which examined the dynamics of a two level atom subject to pulsed measurements of atomic level populations. We treat a slightly modified experiment in a fully continuous measurement regime. By first unravelling the optical Bloch equations, and second, using the quantum trajectories approach we demonstrate the existence of certain measurement regimes where there is a quantum Zeno effect, and other regimes where no measurement of the atomic populations is being effected at all. Through these results we demonstrate the importance of making a full analysis of the system-detector interaction before any conclusions can be made. In the remainder of the thesis we propose further possible tests of the quantum Zeno effect. In Chap. 6 the evolution of a Rydberg atom exchanging one photon with a single cavity mode subject to measurement is examined. The measurement is made by monitoring the photon number occupancy of the cavity mode using a beam of Rydberg atoms configured so as to perform phase sensitive detection. In the limit of frequent monitoring we show that the free oscillation of the atomic inversion is disrupted, and the atom is trapped close to its initial state. This is the quantum Zeno effect. In Chap. 7 we realize the Zeno effect on two possible systems. We consider first, a two level Jaynes-Cumming atom interacting with a cavity mode, and second, two electromagnetic modes configured as a multi-level parametric frequency converter. These systems interact with another cavity mode via a quadratic coupling system based on four wave mixing, and constructed to be a quantum nondemolition measurement of the photon number. This mode is damped to the environment thus effecting a measurement of the system populations. Again we show that this interaction, can manifest the quantum Zeno effect. Our explicit modelling of the system-detector interaction enables us to show how the effect depends on the resolution time of the detector. Finally, we consider a proposed measurement of the square of the quadrature phase of an electromagnetic mode in Chap. 8. Here, a three mode interaction mediated by a second order nonlinear susceptibility is considered. One mode, the pump, is prepared in a feedback generated photon number state to give insight into the role of pump noise. The other two modes are treated as an angular momentum system, and we show that photon counting on the two mode rotation system effects the above mentioned measurement. In addition, this measurement provides a direct measure of the second order squeezing of the signal. With that we finish our investigation of the quantum Zeno effect using the techniques of quantum measurement theory. However, in the epilogue [Chap. 9] we note that no thesis in quantum measurement theory would be complete without some consideration of the ``meaning attributed to the theory. In the epilogue we take a novel historical approach and examine the method by which metaphysical theories are formed to draw conclusions regarding quantum metaphysics.