We perform stochastic simulations of the quantum Zeno effect experiment of the type realized with trapped cooled ions. The results are carefully examined for the case where the experiment is performed on a single atomic particle. The results of the simulations for a single ion exhibit the probabilistic behavior that is required to satisfy the collapse of the wave-packet hypothesis. When a large ensemble of ions is described by the simulations, the results are the same as those produced using the density-matrix method. In this way the stochastic simulation methods provide a link between these two approaches, as they are compatible with each in the appropriate regime. The results are also discussed in terms of what may be observed experimentally given the practical limitations of performing experiments with individual ions. \textcopyright{} 1996 The American Physical Society.
We perform stochastic simulations of the quantum Zeno effect experiment of the type realized with trapped cooled ions. The results are carefully examined for the case where the experiment is performed on a single atomic particle. The results of the simulations for a single ion exhibit the probabilistic behavior that is required to satisfy the collapse of the wave-packet hypothesis. When a large ensemble of ions is described by the simulations, the results are the same as those produced using the density-matrix method. In this way the stochastic simulation methods provide a link between these two approaches, as they are compatible with each in the appropriate regime. The results are also discussed in terms of what may be observed experimentally given the practical limitations of performing experiments with individual ions. \textcopyright{} 1996 The American Physical Society.
We perform stochastic simulations of the quantum Zeno and anti-Zeno effects for a two-level system and for a decaying one. Instead of a simple projection postulate approach, a more realistic model of a detector interacting with the environment is used. The influence of the environment is taken into account using the quantum trajectory method. Simulation of the measurement for a single system exhibits probabilistic behavior showing the collapse of the wave packet. When a large ensemble is analyzed using the quantum trajectory method, the results are the same as those produced using the density matrix method. The results of numerical calculations are compared with the analytical expressions for the decay rate of the measured system, and good agreement is found. Since the analytical expressions depend on the duration of the measurement only, the agreement with the numerical calculations shows that other parameters of the model are not important.
The quantum Zeno effect (QZE) is not only interesting as a manifestation of the counterintuitive behavior of quantum mechanics, but may also have practical applications. When a spectroscopy laser is applied to target atoms or ions prepared in an initial state, the Rabi flopping of an auxiliary transition sharing one common level can be inhibited. This effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with a small excitation rate. We demonstrate this method with direct frequency comb spectroscopy using the minute power of a single mode to drive a dipole allowed transition in a single trapped ion. Resolving the individual modes of the frequency comb demonstrates that the simple instantaneous quantum collapse description of the QZE can not be applied here, as these modes need several pulses to build up.
The quantum Zeno effect is the slowing down of the rate of a quantum mechanical transition by the frequent application of measurements to the system. Following the original suggestion of an experiment to test this in trapped ions, Itano et al. performed an experiment in 1990. This was followed by several detailed theoretical treatments of the problem, making new predictions and giving a better understanding of what was happening. Also since then, suggestions for new types of experiment to test the quantum Zeno effect have been made. At Imperial College we are currently setting up an experiment to study the quantum Zeno effect on a single ion, incorporating some of these new ideas. Details of this experiment are discussed in the paper.
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.
Quantum mechanical effects which are manifested in measurements on trapped atomic ions are reviewed. Observation of these effects is facilitated by the long storage times of a fixed number of laser-cooled ions and by high detection sensitivities, primarily through the observation of scattered laser light. We discuss the observation of quantum jumps and the application of quantum jumps to measurement of atomic ion lifetimes and spectra, detection of antibunching of light, the quantum Zeno effect and quantum projection noise. Experiments which detect nonclassical features of fluorescent light from single or a few trapped ions are briefly reviewed. Finally, we discuss experiments which reveal quantum effects in the motion of trapped ions. We briefly describe possible future extensions for each of these topics.
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.