We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.
We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.
We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displays the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong-disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.
In this thesis, we investigate the coherent scattering of light propagating in a random medium.We are interested in phenomena like the super-and subradiance and Anderson localization that are related to waves interferences and spatial disorder.However, the fundamental difference between subradiance and Anderson localization still needs to be clarified.This thesis gives new elements for the understanding of these phenomena and we present a new method to observe Anderson localization.A mean-field model that does not contain disorder is developed, and we show that super-and subradiance do not require disorder whereas Anderson localization does.In this theoretical work, the coupling between the light and many atoms is reduced to a coupling matrix between the atoms by tracing over the degrees of freedom of the light, which results in a linear problem for the atomic dipoles.The study of the eigenvalues and eigenmodes of this matrix then allows to determine the super-and subradiant modes, and to probe the Anderson localization phase transition with a scaling analysis.Furthermore, the link to the experiment is realized by showing that the intensity fluctuations present an increase at the localization transition.The system is studied in the steady-state regime when the medium is continuously charged by a laser until reaches a stationary regime, and the decay dynamics, when the laser is switched off, so the cloud releases the energy stored.Finally, we present a preliminary work that shows that the diagonal disorder might be a good strategy to reach Anderson localization.
We present a field-theory description of ultracold bosonic atoms in the presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e., superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
Theories of gravity in which the metric is fundamentally classical predict stochastic fluctuations in the gravitational field. In this article, we study the stochastic Klein-Gordon equation as a starting point to understand the phenomenology of linearised classical-quantum hybrid gravity. In particular, we describe how to compute the non-equilibrium two point function of the scalar field, showing explicitly the role of the initial state in regulating divergences. To do so, we use a "mod-squared-retarded" pole-prescription and find that the covariance in the field is non-zero only outside the lightcone, scales inversely with the spatial distance of the spacetime points and grows linearly in time. The energy has a contact divergence similar to that found in the quantum case. We conclude by discussing possible implications of anomalous diffusion for hybrid theories of gravity, especially looking at the energy density in the predicted gravitational waves background, which can be inferred from the scalar covariances.