Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases.
Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases.
Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single- and double-scattering contributions to the intensity in the weak-localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.
Abstract Evolution of a many-body system consists of permanent collisions among particles. Looking at the motion of a single particle, one can identify encounters by which a particle abruptly changes the direction of flight, these are seen as true collisions, and small-angle encounters, which in sum act as an applied force rather than randomising collisions. The scattering on impurities is used to introduce the mentioned mechanisms and, in particular, to show how they affect each other. Point impurities are assumed, i.e. impurities the potential of which is restricted to a single atomic site of the crystal lattice. In this case interaction potentials never overlap and many-body effects are due to nonlocal character of the quantum particle. To introduce elementary components of the formalism, in this chapter we first describe the interaction of an electron with a single impurity. Lippman–Schwinger equations are derived and the physics behind the collision delay, dissipativeness and optical theorems is explored.
In this thesis we investigate theoretically two distinct systems of dipole-coupled atoms. In Part I we investigate light scattering from a system of N ultracold atoms, with laser induced electric dipole interactions. We derive the equations of motion in the Heisenberg picture for the atomic operators, for an arbitrary dipole transition. Then we take the specific case of a jl = 0 → ju = 1 transition and derive the second and third-order inter-atomic correlations. We solve the resulting set of linear equations for two and three atoms exactly, with particular focus on the exact two-atom system. We find a steady-state analytic solution for the two atoms in a specific geometric configuration, and use this to derive explicit expressions for the spatial and coherence properties of the far-field scattered light intensity, valid for the full range of system parameters. A comprehensive survey of the scattering behaviour is given, with key features precisely characterised, including subradiant scattering. We examine in detail a decorrelation approximation that has potential applications for larger systems of atoms that are intractable in a full quantum treatment. We introduce the concept of an effective driving field and show that it can provide a direct and intuitive physical interpretation of key aspects of the system behaviour, including subradiant scattering. Finally, we show that this effective field interpretation, and the decorrelation approximation, is readily extended to a three atom system. In Part II of this thesis we present our investigation of the quantum many-body dynamics of a large ensemble of bosonic S = 3 chromium atoms in a three-dimensional lattice. We implement an extended Bose-Hubbard model which includes the tunnelling, onsite spinor in- teractions and dipole-dipole interactions (giving interactions between atoms on neighbouring sites). We study the dynamics of the population of the different Zeeman levels as a function of lattice depth following a sudden spin rotation, and provide comparison to experimental res- ults. We are able to identify two distinct regimes: At low lattice depths, where atoms are in the superfluid regime, we observe the spin dynamics are strongly determined by the competi- tion between particle transport, onsite interactions and external magnetic field gradients. On the contrary, at high lattice depths, transport is largely frozen out and the spin populations are mainly driven by the long range dipolar interactions and quantum fluctuations.
The Chapter 2 is devoted to the study of the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several point-like or extended time-dependent impurities (barriers) and find regimes of conductance enhancement. In Chapte 3 we study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. Concentrating on the case of a single crossing, we were able to explain recent experiments on crossed metallic and semiconducting nanotubes, which showed the presence of localized states in the region of crossing. The Chapter 4 treats the effects of disorder and interactions in a quantum Hall ferromagnet. We study the problem by projecting the original fermionic Hamiltonian into magnon states, which behave as bosons in the vicinity of the ferromagnetic ground state. The approach permits the reformulation of a strongly interacting model into a non-interacting one. The latter is a non-perturbative scheme that consists in treating the two-particle neutral excitations of the electron system as a bosonic single-particle. Indeed, the employment of bosonization facilitates the inclusion of disorder in the study of the system. It has been shown previously that disorder may drive a quantum phase transition in the Hall ferromagnet. However, such studies have been either carried out in the framework of the nonlinear sigma model, as an effective low-energy theory, or included the long-range Coulomb interaction in a quantum description only up to the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven quantum phase transition from a ferromagnetic 2DEG to a spin glass phase by taking into account interactions between electrons up to the random phase approximation level in a fully quantum description. In the Chapter 5 we derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, Zeeman field. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously, and show that the system can develop a coupled spin-charge-density wave order. This ordering is absent in studies of the Hubbard model that treat spin and charge density separately.
We explore the inelastic electron-scattering cross section off a metallic quantum dot close to the Stoner instability. We focus on the regime of strong Coulomb blockade in which the scattering cross section is dominated by the cotunneling processes. For large enough exchange interaction, the quantum dot acquires a finite total spin in the ground state. In this so-called mesoscopic Stoner instability regime, we find that at low enough temperatures, the inelastic scattering cross section (including the contribution due to an elastic electron spin flip) for an electron with an energy close to the chemical potential is different from the case of a magnetic impurity with the same spin. This difference stems from (i) the presence of low-lying many-body states of a quantum dot and (ii) the correlations of the tunneling amplitudes. Our results provide a possible explanation for the absence of the dephasing rate saturation at low temperatures in a recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012)] in which the existence of local spin droplets in disordered electron liquid has been unraveled.
A central goal in the study of modern condensed matter physics is the characterization of the dynamical properties of quantum systems. Many decades of effort towards this goal, studying a diverse range of (near-equilibrium) quantum matter, from Fermi liquids, to quantum two-level systems, to interacting spin models, and more, has revealed a remarkable pervasiveness of the simple dynamical description of these complex systems in terms of quasi-particles that carry spin, charge, and heat, and that are generally able to equilibrate systems. \n\nThis thesis is an examination of some exceptions to this rule. Specifically, we study a number of instances of quantum matter where equilibration phenomena happens at rather long time scales, or does not occur at all. Particular emphasis is laid on the role of dimensionality, disorder, and dissipation in engendering such novel dynamical behavior.\n\nFirst, we consider non-equilibrium dynamics in one-dimensional quasi-condensates. Low dimensionality inhibits scattering in these systems, and low-energy excitations are long-lived phase fluctuations that exhibit an enriched conformal symmetry. Utilizing this symmetry, we generalize sudden quenches typically used to study non-equilibrium dynamics to quenches along general relativistic and conformal trajectories. Gases never truly equilibrate after such a quench; instead, they evolve into a `prethermal' state with thermal-looking correlations and a chiral asymmetry. \n\nWe then study the problem of the dynamical transition driven by disorder, from an ergodic to a non-ergodic phase, in one-dimensional quantum spin chains. In particular, in XXZ chains with on-site disorder, we find a unique intermediate phase straddling the boundary of the dynamical phase transition, wherein rare-region effects lead to long-time tails in equilibration and vanishing DC conduction before the onset of non-ergodicity. We propose generalizations of such `Griffiths' behavior to arbitrary dimensions. We also study the dynamics of random-bond Heisenberg chains by developing a strong-disorder renormalization group protocol for these systems. We discuss how magnetic noise from such disordered systems contains signatures of their anomalous dynamical properties. \n\nNext, we re-examine the phenomenological theory of two-level systems in amorphous materials in the light of new experimental evidence that these states have large electric/magnetic dipole moments. We propose and justify an interpretation of the model as one of tunneling electrons slowed down by a large phonon drag and discuss the dynamical consequences of such polaronic effects. \n\nFinally, we discuss how magnetic noise measurements can be used to non-invasively access the anomalous properties of systems such as those discussed above. In particular, we examine how scattering properties of isolated magnetic impurities and non-local transport in a variety of two-dimensional materials can be probed experimentally using NV centers as noise magnetometers.