We propose an experiment to observe the quantum Zeno effect in atomic Bragg scattering. The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a decohering measurement process. This effect is usually studied theoretically in an idealized two-level system, though this system has been difficult to realize in practice. The coherent population exchange between the forward and Bragg beams provides an ideal two-level system, though as there is no practical scheme for continuously monitoring the motion of an atom we include decoherence by adding noise to the laser. Using the method of stochastic Hamiltonians we show that the noise suppresses tunneling in the two-state system and, in the large noise limit, the system can freeze in its initial state.
We propose an experiment to observe the quantum Zeno effect in atomic Bragg scattering. The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a decohering measurement process. This effect is usually studied theoretically in an idealized two-level system, though this system has been difficult to realize in practice. The coherent population exchange between the forward and Bragg beams provides an ideal two-level system, though as there is no practical scheme for continuously monitoring the motion of an atom we include decoherence by adding noise to the laser. Using the method of stochastic Hamiltonians we show that the noise suppresses tunneling in the two-state system and, in the large noise limit, the system can freeze in its initial state.
The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a measurement process. The authors of one recent experiment study, W. M. Itano et al., [Phys. Rev. A 41, 2295 (1990)] claimed a demonstration of the quantum Zeno effect. This was done by performing discontinuous atomic-level measurements on a coherently evolving two-level atomic stystem. The measurement was implemented using a pulsed laser strong enough to saturate the two-level atomic system. In this paper, we examine the simpler case where the measurement laser is continuously on and does not saturate the two-level atomic system. In contrast to previous treatments, we show certain parameter regimes wherein an effective state reduction does occur. We ascertain the experimental parameter regimes under which a measurement can be said to have been performed. We show that, in some regimes, fully efficient photon detection does not give good information about the atomic-level populations and hence no measurement has been performed. Throughout, we emphasize that the design of an atomic level-measurement device requires more than the analysis of a mechanism for photon detection or of coherence loss. We gain insight into the operation of a particular measurement process by following the selective evolution of various systems using the quantum-trajectories approach.
We present a scheme for experimentally observing the quantum Zeno effect using the quantum-nondemolition measurement recently proposed by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. The Zeno effect refers to the freezing of the (unitary) free dynamics of a system by rapid measurements. We generalize the Zeno effect to be any change in the survival probability of an initial state induced by very rapid measurements, when such measurements are the dominant source of fluctuations in the system. We derive a master equation for the evolution of a cavity mode when the photon number is monitored by this method. This equation describes a phase-diffusion process. We propose that this measurement scheme be used to monitor the exchange of a single photon between the cavity and a single Rydberg atom. We show that for very rapid monitoring the free oscillation of the atomic inversion is disrupted and the atom can be trapped close to the initial excited state. This is the quantum Zeno effect.
Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.
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.
Measurements performed on a system will alter the dynamics of that system, and in the strong-measurement limit, can theoretically freeze the free evolution completely. This is the quantum Zeno effect. We utilize quantum-nondemolition photon-counting techniques to realize the Zeno effect on the evolution of either a two-level Jaynes-Cummings atom interacting with a resonant cavity mode, or on two electromagnetic modes configured as a multilevel parametric frequency converter. These systems interact with another electromagnetic cavity mode via a quadratic coupling system based on four-wave mixing and constructed so as to be a nondemolition measurement of the photon number. This mode is then coupled to the environment through the cavity mirrors. This measurement is shown to be a measurement of system populations, which generates the desired Zeno effect and in the strong-measurement limit will freeze the free dynamics of the system.
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.