Academic literature on the topic 'Open quantum systems: Redfield equation'

Markovian master equations are a ubiquitous tool in the study of open quantum systems, but deriving them from first principles involves a series of compromises. On the one hand, the Redfield equation is valid for fast environments (whose correlation function decays much faster than the system relaxation time) regardless of the relative strength of the coupling to the system Hamiltonian, but is notoriously non-completely-positive. On the other hand, the Davies equation preserves complete positivity but is valid only in the ultra-weak coupling limit and for systems with a finite level spacing, which makes it incompatible with arbitrarily fast time-dependent driving. Here we show that a recently derived Markovian coarse-grained master equation (CGME), already known to be completely positive, has a much expanded range of applicability compared to the Davies equation, and moreover, is locally generated and can be generalized to accommodate arbitrarily fast driving. This generalization, which we refer to as the time-dependent CGME, is thus suitable for the analysis of fast operations in gate-model quantum computing, such as quantum error correction and dynamical decoupling. Our derivation proceeds directly from the Redfield equation and allows us to place rigorous error bounds on all three equations: Redfield, Davies, and coarse-grained. Our main result is thus a completely positive Markovian master equation that is a controlled approximation to the true evolution for any time-dependence of the system Hamiltonian, and works for systems with arbitrarily small level spacing. We illustrate this with an analysis showing that dynamical decoupling can extend coherence times even in a strictly Markovian setting.

Master equations are a vital tool to model heat flow through nanoscale thermodynamic systems. Most practical devices are made up of interacting sub-system, and are often modelled using either local master equations (LMEs) or global master equations (GMEs). While the limiting cases in which either the LME or the GME breaks down are well understood, there exists a 'grey area' in which both equations capture steady-state heat currents reliably, but predict very different transient heat flows. In such cases, which one should we trust? Here, we show that, when it comes to dynamics, the local approach can be more reliable than the global one for weakly interacting open quantum systems. This is due to the fact that the secular approximation, which underpins the GME, can destroy key dynamical features. To illustrate this, we consider a minimal transport setup and show that its LME displays exceptional points (EPs). These singularities have been observed in a superconducting-circuit realisation of the model \cite{partanen2019exceptional}. However, in stark contrast to experimental evidence, no EPs appear within the global approach. We then show that the EPs are a feature built into the Redfield equation, which is more accurate than the LME and the GME. Finally, we show that the local approach emerges as the weak-interaction limit of the Redfield equation, and that it entirely avoids the secular approximation.

We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system–environment coupling strength and, thus, the strength of the dissipation.

The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasiprobability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a timedependent linear partial differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time dependence of expectation values, Wigner function and Weyl operator, are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.

The dissipation generated during a quasistatic thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Here, we show how to generalize this approach to open quantum systems by finding the thermodynamic metric associated to a given Lindblad master equation. The obtained metric can be understood as a perturbation over the background geometry of equilibrium Gibbs states, which is induced by the Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on two paradigmatic examples: an Ising chain and a two-level system interacting with a bosonic bath with different spectral densities.

Motivated by the continuous advancements in the miniaturization of devices down to reveal the quantum nature of matter, in this thesis we investigate the way a quantum system is affected by the presence of a thermal environment and propose methodologies to exploit this kind of sensitivity for quantum technologies. Since treating exactly the dynamics of the full system-environment compound is generally problematic for the diverging number of degrees of freedom involved in the calculation, effective master equations for the reduced system density matrix were developed in literature during the last century. Among them, the Redfield approach is an equation obtained under weakcoupling (or Born) and Markovian assumptions. Despite offering effective descriptions in a plethora of situations, it was criticized for not preserving the positivity (and hence the complete positivity) of the system density matrix. The latter property is in general a fundamental feature for assigning a probabilistic interpretation to the theory. We hence begin by facing the problem of the non-positivity character of the Redfield equation, curing it of the strict amount that is necessary via coarse-grain averaging performed on the Redfield equation in the interaction picture. In the analysis a central role is played by the coarse grain timescale. Once set it equal to a critical threshold value, the resulting equation (CP-Redfield) enables conserving the predictive power of the Redfield approach and preserving positivity at the same time. About it, we report both practical estimation and self-consistent methods to evaluate the critical timescale. Our strategy also allows to continuously map the Redfield equation into the secular master equation (diverging coarse-grain time interval) by appropriately tuning the coarse grain time, the latter being the equation usually adopted in the literature for ensuring thermodynamic consistency by enforcing a rotating-wave approximation. Starting from a minimal example concerning the dipole coupling between a qubit and a bosonic bath, we then apply this methodology to dissipative multipartite systems, for which the local vs global debate is of current interest. The local master equation is instead the equation that is obtained by assigning to each subsystem its proper thermal dissipator, preserving the local character of the microscopic interactions, while the global approach is the Redfield equation in the secular limit. In this context, we studied an asymmetric energy transfer model constituted by harmonic oscillators which, being exactly solvable, provides the appropriate benchmark for testing the efficiency of the different master equations.. Beyond finding useful the application of the CP-Redfield equation, we point out a sensible convex-mixture of the local and global solutions based on the timescale separation of the two strategies. The local approach is then applied in the context of quantum batteries, a field that was previously analyzed under closed (i.e. Hamiltonian) settings. We hence provide one of the first attempts of schematizing an open quantum battery, where, recalling in part the aforementioned asymmetric model, the charging process originates from external sources (coherent and/or noisy) and is mediated by a proper quantum charger. By studying different implementations, particular attention was devoted to find possible interplay between coherent and incoherent energy supply mechanisms in producing stored energy and ergotropy, the latter being defined in literature as the maximum extractable work. As a central result, increasing temperature is not always detrimental for the stored ergotropy. Going beyond the particular instance of bosonic bath, the sensitivity of a quantum system to its surrounding environment is finally exploited in the context of statistical tagging, where one aims to guess the quantum statistics (fermionic or bosonic) of a thermal bath of interest, introducing in this way a novel research line in the field of quantum metrology. We propose an indirect measurement protocol in which a quantum probe is let to interact with the unknown bath and relies on the consideration that, despite the final probe equilibrium configuration is not necessarily influenced by the bath nature, the latter generally leaves residual imprintings in the probe state before thermalization, i.e. out-of-equilibrium. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we treated the cases of qubit and harmonic oscillator probes, finding that, generally, the presence of coherences in the input state of the probe is beneficial for the discrimination capability and noticing a bosonic advantage in reducing to zero the error probability.

Questo lavoro di tesi nasce con lo scopo di fornire una inquadratura generale del campo di studi relativo ad i sistemi quantistici aperti. Esattamente come avviene nel caso della termodinamica, questo tipo di approfondimento vuole tenere conto delle interazioni che un qualunque sistema quantistico può sviluppare con l'ambiente esterno. La prima parte del lavoro intende introdurre il lettore all'argomento; in queste prime sezioni si trattano anche alcuni argomenti più concettuali di rilevanza prettamente fisica, come ad esempio il fenomeno dell'entanglement o del quantum eraser. La seconda parte presenta un approccio geometrico, allo scopo di chiarire come vengono a modificarsi in questo nuovo contesto le strutture geometriche entro cui si sviluppa il sistema quantistico interagente, intendendo con ciò sia le orbite unitarie, sia gli spazi formati dagli stati puri e dagli stati misti. Infine, la parte finale della tesi sviluppa questi argomenti in due circostanze applicative, relative all'insieme delle matrici densità rispettivamente di dimensione due e tre. Nello specifico, queste due trattazioni analizzano specialmente le problematiche relative all'evoluzione temporale aperta , ossia quel tipo di evoluzione osservabile esclusivamente in caso di interazione del sistema quantistico con un ambiente esterno, e che per questo si discosta dalle usuali evoluzioni unitarie descrivendo invece una traiettoria che permette il passaggio dall'una all'altra di queste orbite.

We investigate the some of the many subtleties in taking a microscopic approach to modelling the decoherence of an Open Quantum System. We use the RF-SQUID, which will be referred to as a simply a SQUID throughout this paper, as a non-linear example and consider different levels of approximation, with varied coupling, to show the potential consequences that may arise when characterising devices such as superconducting qubits in this manner. We first consider a SQUID inductively coupled to an Ohmic bath and derive a Lindblad master equation, to first and second order in the Baker-Campbell-Hausdorff expansion of the correlation-time-dependent flux operator. We then consider a SQUID both inductively and capacitively coupled to an Ohmic bath and derive a Lindblad master equation to better understand the effect of parasitic capacitance whilst shedding more light on the additions, cancellations and renormalisations that are attributed to a microscopic approach.

This thesis addresses the problem of a form of anomalous decoherence that sheds light into the spectroscopy of blinking quantum dots. The system studied is a two-state system, interacting with an external environment that has the effect of establishing an interaction between the two states, via a coherence generating coupling, called inphasing. The collisions with the environment produce also decoherence, named dephasing. Decoherence is interpreted as the entanglement of the coherent superposition of these two states with the environment. The joint action of inphasing and dephasing generates a Markov master equation statistically equivalent to a random walker jumping from one state to the other. This model can be used to describe intermittent fluorescence, as a sequence of "light on" and "light off" states. The experiments on blinking quantum dots indicate that the sojourn times are distributed with an inverse power law. Thus, a proposal to turn the model for Poisson fluorescence intermittency into a model for non-Poisson fluorescence intermittency is made. The collision-like interaction of the two-state system with the environment is assumed to takes place at random times rather than at regular times. The time distance between one collision and the next is given by a distribution, called the subordination distribution. If the subordination distribution is exponential, a sequence of collisions yielding no persistence is turned into a sequence of "light on" and "light off" states with significant persistence. If the subordination function is an inverse power law the sequel of "light on" and "light off" states becomes equivalent to the experimental sequences. Different conditions are considered, ranging from predominant inphasing to predominant dephasing. When dephasing is predominant the sequel of "light on" and "light off" states in the time asymptotic limit becomes an inverse power law. If the predominant dephasing involves a time scale much larger than the minimum time scale accessible to the experimental observation, thereby generating persistence, the resulting distribution becomes a Mittag-Leffler function. If dephasing is predominant, in addition to the inverse power law distribution of "light off" and "light on" time duration, a strong correlation between "light on" and "light off" state is predicted.

Some physical systems exhibit topological properties in the form of topological invariants— features of the system that remain constant unless the system undergoessignificant changes i.e. changes that require closing the energy gap of the Hamiltonian.This work studies one example of a system with topological properties — a Kitaevchain. Here, this model is studied when it is coupled to an environment. We studythe effect of the coupling on the topology of the system and attempt to find signaturesof topological phases in the dynamics of the system. By using the Lindblad equationdefined in the formalism of third quantization, we study the time evolution of thesystem numerically by using the Euler method. We find that the dynamics of theentanglement spectrum of half of the chain is different in the topological and trivialphases: if the system undergoes a quench from trivial to topological phase, the entanglementspectrum exhibits crossings as the system evolves in time. We also studythe topological phases when disorder is added to the system. We test the stabilityof the topological phases of the system against disorder and find that the topologicalphases are not affected by a weak disorder. Moreover, by studying the statistics of theminimum entanglement spectrum gap, we find that, in general, a stronger disordermakes the crossings less likely to appear in the topological phase and more likely toappear in the trivial phase.<br>Det finns fysiska system som visar topologiska egenskaper i form av topologiska invarianter,som ändras inte så länge systemet genomgår ändringar som inte stängerHamiltonianens energigap. I det här arbetet undersöker vi ett exempel av ett systemmed topologiska egenskaper — en Kitaev kedja. Denna modell är studerat närden är kopplad till en omgivning. Vi undersöker kopplingens påverkan på systemetstopologi och vi försöker hitta tecken på topologiska faser i systemets dynamik. Vianvänder Lindblads ekvation definierat i tredje kvantiserings formalism för att studerasystemets tidsutveckling numeriskt, genom att använda Eulers metod. Vi upptäckeratt det finns skillnader i tidsutveckling av kvantsammanflätningsspektrumav häften av kedjan som beror på systems topologiska fas. Om systemet genomgåren kvantsläckning från den triviala till den topologiska fasen, kommer det finnas korsningari kvantsammanflätningensspektrum som uppstår under dess tidsutveckling.Dessutom studerar vi de topologiska faserna när det finns oordning i systemet. Viundersöker topologiska fasernas stabilitet mot oordning och upptäcker att en svagoordning påverkar inte de topologika faserna. Dessutom, genom att studera den minstakvantsammanflätningsspektrumsgap upptäcker vi att en starkare oordning ledertill kvantsammanflätningsspektrumskorsningar att vara mindre sannolika i den topologiskafasen och mer sannolika i den triviala fasen.

On etudie la contrôlabilité des systèmes quantiques dans deux contextes différents: le cadre standard fermé, dans lequel un système quantique est considéré comme isolé et le problème de contrôle est formulé sur l'équation de Schrödinger; le cadre ouvert qui décrit un système quantique en interaction avec un plus grand, dont seuls les paramètres qualitatifs sont connus, au moyen de l'équation de Lindblad sur les états.Dans le contexte des systèmes fermés on se focalise sur la classe intéressante des systèmes spin-boson, qui décrivent l'interaction entre un système quantique à deux niveaux et un nombre fini de modes distingués d'un champ bosonique. On considère deux exemples prototypiques, le modèle de Rabi et le modèle de Jaynes-Cummings qui sont encore très populaires dans plusieurs domaines de la physique quantique. Notamment, dans le contexte de la Cavity Quantum Electro Dynamics (C-QED), ils fournissent une description précise de la dynamique d'un atome à deux niveaux dans une cavité micro-onde en résonance, comme dans les expériences récentes de S. Haroche. Nous étudions les propriétés de contrôlabilité de ces modèles avec deux types différents d'opérateurs de contrôle agissant sur la partie bosonique, correspondant respectivement – dans l'application à la C-QED – à un champ électrique et magnétique externe. On passe en revue quelques résultats récents et prouvons la contrôlabilité approximative du modèle de Jaynes-Cummings avec ces contrôles. Ce résultat est basé sur une analyse spectrale exploitant les non-résonances du spectre. En ce qui concerne la relation entre l'Hamiltonien de Rabi et Jaynes-Cummings nous traitons dans un cadre rigoureux l'approximation appelée d'onde tournante. On formule le problème comme une limite adiabatique dans lequel la fréquence de detuning et le paramètre de force d'interaction tombent à zero, ce cas est connu sous le nom de régime de weak-coupling. On prouve que, sous certaines hypothèses sur le rapport entre le detuning et le couplage, la dynamique de Jaynes-Cumming et Rabi montrent le même comportement, plus précisément les opérateurs d'évolution qu'ils génèrent sont proches à la norme.Dans le cadre des systèmes quantiques ouverts nous étudions la contrôlabilité de l'équation de Lindblad. Nous considérons un contrôle agissant adiabatiquement sur la partie interne du système, que nous voyons comme un degré de liberté qui peut être utilisé pour contraster l'action de l'environnement. L'action adiabatique du contrôle est choisie pour produire une transition robuste. On prouve, dans le cas prototype d'un système à deux niveaux, que le système approche un ensemble de points d'équilibre déterminés par l'environnement, plus précisément les paramètres qui spécifient l'opérateur de Lindblad. Sur cet ensemble, le système peut être piloté adiabatiquement en choisissant un contrôle approprié. L'analyse est fondée sur l'application de méthodes de perturbation géométrique singulière<br>We investigate the controllability of quantum systems in two differentsettings: the standard 'closed' setting, in which a quantum system is seen as isolated, the control problem is formulated on the Schroedinger equation; the open setting that describes a quantum system in interaction with a larger one, of which just qualitative parameters are known, by means of the Lindblad equation on states.In the context of closed systems we focus our attention to an interesting class ofmodels, namely the spin-boson models. The latter describe the interaction between a 2-level quantum system and finitely many distinguished modes of a bosonic field. We discuss two prototypical examples, the Rabi model and the Jaynes-Cummings model, which despite their age are still very popular in several fields of quantum physics. Notably, in the context of cavity Quantum Electro Dynamics (C-QED) they provide an approximate yet accurate description of the dynamics of a 2-level atom in a resonant microwave cavity, as in recent experiments of S. Haroche. We investigate the controllability properties of these models, analyzing two different types of control operators acting on the bosonic part, corresponding -in the application to cavity QED- to an external electric and magnetic field, respectively. We review some recent results and prove the approximate controllability of the Jaynes-Cummings model with these controls. This result is based on a spectral analysis exploiting the non-resonances of the spectrum. As far as the relation between the Rabi andthe Jaynes-Cummings Hamiltonians concerns, we treat the so called rotating waveapproximation in a rigorous framework. We formulate the problem as an adiabaticlimit in which the detuning frequency and the interaction strength parameter goes to zero, known as the weak-coupling regime. We prove that, under certain hypothesis on the ratio between the detuning and the coupling, the Jaynes-Cumming and the Rabi dynamics exhibit the same behaviour, more precisely the evolution operators they generate are close in norm.In the framework of open quantum systems we investigate the controllability ofthe Lindblad equation. We consider a control acting adiabatically on the internal part of the system, which we see as a degree of freedom that can be used to contrast the action of the environment. The adiabatic action of the control is chosen to produce a robust transition. We prove, in the prototype case of a two-level system, that the system approach a set of equilibrium points determined by the environment, i.e. the parameters that specify the Lindblad operator. On that set the system can be adiabatically steered choosing a suitable control. The analysis is based on the application of geometrical singular perturbation methods

Cette thèse s'intéresse à la modélisation mathématique et à la simulation numérique du transport électronique dans des dispositifs semiconducteurs nanométriques. Différents modèles de transport, destinés à la description des diverses régions d'un transistor MOSFET, sont introduits et analysés. Une attention particulière est portée sur la modélisation des effets quantiques ayant lieu dans ces dispositifs (système auto-consistant de Schrödinger/Poisson avec des conditions aux bords ouvertes)<br>The present PhD thesis is concerned with the mathematical modelling and the numerical simulation of the electron transport in nanoscale semiconductor devices. Different transport models are introduced and analyzed, aimed to describe the various regions of a MOSFET transistor. We focus our attention particularly on the modelling of quantum effects taking place in such devices (self-consistent Schrödinger-Poisson system with open boundary conditions)

In the theory of open quantum systems, a quantum Markovian master equation, the Lindblad equation, reveals the most general form for the generators of a quantum dynamical semigroup. In this thesis, we present the derivation of the Lindblad equation and several examples of Lindblad equations with their analytic and numerical solutions. The graphs of the numerical solutions illuminate the dynamics and the stabilization as time increases. The corresponding von Neumann entropies are also presented as graphs. Moreover, to illustrate the difference between the dynamics of open and isolated systems, we prove two theorems about the conditions for stabilization of the solutions of the von Neumann equation which describes the dynamics of the density matrix of open quantum systems. It shows that the von Neumann equation is not satisfied for modelling dynamics in the cognitive contextin general. Instead, we use the Lindblad equation to model the mental dynamics of the players in the game of the 2-player prisoner’s dilemma to explain the irrational behaviors of the players. The stabilizing solution will lead the mental dynamics to an equilibrium state, which is regarded as the termination of the comparison process for a decision maker. The resulting pure strategy is selected probabilistically by performing a quantum measurement. We also discuss two important concepts, quantum decoherence and quantum Darwinism. Finally, we mention a classical Neural Network Master Equation introduced by Cowan and plan our further works on an analogous version for the quantum neural network by using the Lindblad equation.

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.

The theory of open systems is used in quantum optics in two distinct ways: to model sources of light such as lasers and parametric oscillators, and to describe the response of irradiated cavities and atoms. Sometimes the two applications are used in combination; first, statistical properties of the field radiated by a source are calculated, and these are then used in a separate calculation to determine the response of a system that is irradiated by the source. But the usefulness of this approach is quite hunted. It is essentially limited to coherent sources and certain broadband sources such as broadband squeezed or chaotic light. There exists no general theory for cascaded open systems - a theory that gives the response of system B to radiation emitted by system A when there exists an open-systems treatment for A and B separately. In this paper I develop such a theory using the quantum trajectory formulation of open systems. The source A and irradiated system B are described by a single stochastic wave-function. Generally the wavefunction describes an entangled state of the A and B subsystems. In the quantum trajectory formalism the wavefunction undergoes a coherent evolution governed by a nonunitary Schrödinger equation, interrupted at random times by wavefunction collapses. I derive the nonunitary Schrödinger equation and the form of the collapses. I illustrate the theory with some simple examples and discuss potential applications to problems involving the interaction of atoms with nonclassical light.

In the quantum trajectory approach an open quantum system is represented by a stochastic pure-state wave function. The mixed-state density operator that satisfies the usual master equation is recovered from the quantum trajectories by performing either an ensemble average or, for stationary systems, an average over time. This unraveling of the master equation dynamics into pure-state trajectories provides new insight into the decay of quantum coherence in systems that are open to the environment. Under some conditions macroscopic superposition states are preserved as macroscopic superposition states along individual trajectories, but are reduced to mixtures by the trajectory average. Under other conditions one of the states in a macroscopic superposition becomes dominant (in amplitude) over the other along each quantum trajectory. We discuss the mechanisms that produce these dynamics and assess the implications for the observation of Schrodinger cat states in optics experiments. We present results for some specific examples of macroscopic superposition states generated by a cavity QED system. The system involves a small collection of atoms in an optical cavity driven by a coherent laser field. Under strong-coupling conditions this system produces a variety of Schrodinger cat states whose precise form depends on the number of atoms, the method of excitation (through a cavity mirror or from the side), the initial state of the atoms, and the position of the atoms in the cavity.