We consider a driven 2-level system with one level showing spontaneous decay to an otherwise uncoupled third level. Rabi transitions to the unstable level are strongly damped. This simple configuration can be used to demonstrate and to explore the quantum Zeno effect leading to a freezing of the system to the initial level. A comparison with repeated projection measurements is given. A treatment within a phenomenological theory of continuous measurements is sketched. The system visualizes the important role of null measurements (negative result measurements) and may serve as a good example for a truly continuous measurement. 1 1
We consider a driven 2-level system with one level showing spontaneous decay to an otherwise uncoupled third level. Rabi transitions to the unstable level are strongly damped. This simple configuration can be used to demonstrate and to explore the quantum Zeno effect leading to a freezing of the system to the initial level. A comparison with repeated projection measurements is given. A treatment within a phenomenological theory of continuous measurements is sketched. The system visualizes the important role of null measurements (negative result measurements) and may serve as a good example for a truly continuous measurement. 1 1
A metastable atomic level can be rendered unstable in a controllable way by coupling it to a decaying state. In this work we carry out a full dynamical analysis of the Zeno effect in this kind of unstable systems, comparing it to the inhibition of purely coherent Rabi oscillations. Simple and experimentally feasible measuring strategies involving three atomic levels are considered. It is shown that this induced decay is actually an example of a partial Zeno effect so that the observed evolution results from the competition of two Zeno effects. We also show that a three-level scheme can display both coherent, incoherent, and anti-Zeno effects.
Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.
Frequent Measurements on an unstable particle located at observable initial state freeze the particle on this state, known as quantum Zeno effect [1-14]. Measurements on an observable subspace further open the prelude of quantum Zeno dynamics [15-17]. These phenomena affect the results of quantum measurement that has been widely used in quantum information and quantum computation [18-21]. However, this common argument is insufficient when the initial state is coupled with a continuum reservoir. In such an irreversible system, intrinsic decay property destroys the frozen behavior. Although it has been proven that the decay rate of the initial state will be affected by measurements [7], the knowledge of detailed mechanisms for this measurement-dependent decay is still limited. In this work, we found based on three-subsystem perturbation theory that the indirect correlation between a continuum reservoir and a measurement apparatus through the interaction with a quantum system causes a Rabi-like inter-modulation among these subsystems. The indirect correlation effect from this combination drives the system into quantum Zeno and reactivation regions, which are dependent upon the Rabi strength, pulse duty, and its repetition rate. We also found that the dynamical changes of decay rate are quite different in continuous and pulsed measurements, and, thus, significantly affect the dynamics of the system.
A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where N goes to infinity and we obtain that the non-decay probability law is a pure exponential, therefore recovering the classical behavior.
It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.
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.