Collisional decoherence reexamined

We re-derive the quantum master equation for the decoherence of a massive Brownian particle due to collisions with the lighter particles from a thermal environment. Our careful treatment avoids the occurrence of squares of Dirac delta functions. It leads to a decoherence rate which is smaller by a factor of 2 pi compared to previous findings. This result, which is in agreement with recent experiments, is confirmed by both a physical analysis of the problem and by a perturbative calculation in the weak coupling limit.Comment: 33 pages, 4 figure

Deconstructing Decoherence

The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit. This limit, and other simplifying assumptions, have allowed the derivation of several simple results characterizing the onset of environmentally induced superselection; but these results are increasingly often regarded as a complete phenomenological characterization of decoherence in any regime. This is not necessarily the case: The examples presented in this paper counteract this impression by violating several of the simple ``rules of thumb''. This is relevant because decoherence is now beginning to be tested experimentally, and one may anticipate that, in at least some of the proposed applications (e.g., quantum computers), only the basic principle of ``monitoring by the environment'' will survive. The phenomenology of decoherence may turn out to be significantly different.Comment: 13 two-column pages, 3 embedded figure

Quality of a Which-Way Detector

We introduce a measure Q of the "quality" of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The "quality" Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a-priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the Symmetric Quanton-Detecton System (SQDS). The SQDS can be regarded as two qubits trying to acquire which way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.Comment: 10 pages, 5 figure

On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

We consider a non relativistic quantum system consisting of $K$ heavy and $N$ light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential $\alpha V$. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming $\alpha$ sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K=1 the result is extended to arbitrary $\alpha$. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones.Comment: 38 page

Robust unravelings for resonance fluorescence

Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master equation evolution (which applies once the monitoring ceases). The ensemble of pure states arising from the maximally robust unraveling has been suggested to be the most natural way of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf 250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly driven atom requires an adaptive interferometric measurement proposed by Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant ensemble consists of just two pure states which, in the high driving limit, are close to the eigenstates of the driving Hamiltonian $\Omega\sigma_{x}/2$. This ensemble is the closest thing to a classical limit for a strongly driven atom. We also find that it is possible to reasonably approximate this ensemble using just homodyne detection, an example of a continuous Markovian unraveling. This has implications for other systems, for which it may be necessary in practice to consider only continuous Markovian unravelings.Comment: 12 pages including 5 .eps figures, plus one .jpg figur

Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States

As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as Part II of a two-part paper. The original version of quant-ph/9906125 is shortly to be replaced by a new version which is Part I of the two-part paper. This paper (Part II) also contains some material from the original version of quant-ph/990612

Environment-Induced Decoherence and the Transition From Quantum to Classical

We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection einselection in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equations we study einselection employing the general strategy of the predictability sieve. Assumptions that are usually made in the discussion of decoherence are critically reexamined along with the ``standard lore'' to which they lead. Restoration of quantum-classical correspondence in systems that are classically chaotic is discussed. The dynamical second law -it is shown- can be traced to the same phenomena that allow for the restoration of the correspondence principle in decohering chaotic systems (where it is otherwise lost on a very short time-scale). Quantum error correction is discussed as an example of an anti-decoherence strategy. Implications of decoherence and einselection for the interpretation of quantum theory are briefly pointed out.Comment: 80 pages, 7 figures included, Lectures given by both authors at the 72nd Les Houches Summer School on "Coherent Matter Waves", July-August 199

Diffusive limit for a quantum linear Boltzmann dynamics

In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the gas particle scattering is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix that evolves according to a translation-covariant Lindblad equation. The main result is a proof that the particle's position distribution converges to a Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.

A ballistic motion disrupted by quantum reflections

I study a Lindblad dynamics modeling a quantum test particle in a Dirac comb that collides with particles from a background gas. The main result is a homogenization theorem in an adiabatic limiting regime involving large initial momentum for the test particle. Over the time interval considered, the particle would exhibit essentially ballistic motion if either the singular periodic potential or the kicks from the gas were removed. However, the particle behaves diffusively when both sources of forcing are present. The conversion of the motion from ballistic to diffusive is generated by occasional quantum reflections that result when the test particle's momentum is driven through a collision near to an element of the half-spaced reciprocal lattice of the Dirac comb.Comment: 54 pages. I rewrote the introduction and simplified some of the presentatio

Decoherence, irreversibility and the selection by decoherence of quantum states with definite probabilities

The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases of decoherence are then found: (i) A ``degenerate'' case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) A general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or ``quasi projectors'') which were previously introduced in the quantum expression of classical properties. It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.Comment: 54 page