Freezing light with cold atoms

The impact of disorder and localisation in electronic conduction was introduced more than half a century ago by Philip Anderson. In a much broader context of disorder-mediated wave dynamics it remains an important research area, and surprises abound. Meanwhile, research in ultracold atomic physics has led to phenomenally detailed elucidation of properties, including changes in phase, of quantum degenerate Bosonic and Fermionic gases. For example, beautiful experiments have recently demonstrated, in quasi one-dimensional systems, Anderson localisation of matter waves. In this brief essay, we describe and discuss research on wave localisation in the context of ultracold atomic physics, with a particular emphasis on light localisation in ultracold and high-density atomic gases. Essential ideas are reviewed, along with the current experimental status of the field, and promising avenues for future research are discussed.     

Out of equilibrium Anderson model: Conductance and Kondo temperature

We calculate the conductance through a quantum dot weakly coupled to metallic contacts by means of the Keldysh out of equilibrium formalism. We model the quantum dot with the SU(2) Anderson model and consider the limit of infinite Coulomb repulsion. The interacting system is solved with the numerical diagrammatic Non-Crossing Approximation (NCA) and the conductance is obtained as a function of temperature and gate voltage from differential conductance (dI/dV) curves. We discuss the results in comparison with those from the linear response approach which can be performed directly in equilibrium conditions. Comparison shows that out of equilibrium results are in good agreement with the ones from linear response supporting reliability of the method employed. The last discussion becomes relevant when dealing with general transport models through interacting regions. We also analyze the evolution of conductance vs gate voltage with temperature. While at high temperatures the conductance is peaked, when the Fermi energy coincides with the localized level it presents a plateau at low temperatures as a consequence of the Kondo effect. We discuss different ways to determine Kondo's temperature.     

Wave function multifractality and dephasing at metal–insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.     

Exponential gain in quantum computing of quantum chaos and localization

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization, and Anderson transition can be modeled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

Thermoelectric properties of correlated double quantum dot system in Coulomb blockade regime

We theoretically study thermoelectric properties of a coupled double quantum dot (DQD) system coupled to normal leads using two impurity Anderson model with intra- as well as interdot Coulomb interactions. A generic formulation, which was earlier developed to study electronic properties (zero bias maximum of differential conductance and interesting partial swapping in Fano phenomena) of DQD system within Coulomb blockade regime for a non-magnetic case, is extended to investigate thermoelectric properties i.e. electrical conductance, thermoelectric power and thermal conductance of the same system, as a function of temperature by varying interdot Coulomb interaction and interdot tunneling. Interdot Coulomb interaction is found to trigger some novel features like crossover in thermoelectric power with temperature in all the configurations (series, parallel and T-shape) and a small peak in thermal conductance toward low temperatures, T≈Γ/10, in series and T-shape configurations, which is found to be missing in case of symmetric parallel configuration. The origin of these novel features is attributed to the interplay of renormalization of energy levels caused by the interdot Coulomb interaction which is interpreted in terms of local density of states and the asymmetry effects related to dot-lead couplings/interference effects.     

Pressure induced valence transitions in the Anderson lattice model

We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E_f, and U.     

Quantum computation with programmable connections between gates

A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e.g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the quantum switch, which can be programmed to switch the order of two channels with a single use of each one.     

Robust entanglement transfer through a disordered qubit ladder

We study an entanglement transfer protocol in a two-leg ladder spin-1/2 chain in the presence of disorder. In the scenario where the on-site energies and intrachain couplings are correlated, following approximately constant proportions along the chain, we set up a scheme for high-fidelity state transfer via a particular subspace wherein effective fluctuations in the parameters ultimately depend on the degree of such correlations, rather on the disorder featured by each leg individually, accounted by a box distribution of strength W. Moreover, we find that the leakage of information out of that subspace is suppressed upon increasing W and thus the transfer fidelity, evaluated through the entanglement concurrence at the other end of the ladder, also builds up with W.     

Quantifying interference in multipartite quantum systems

The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle interference patterns produced by general two- and three-qubit systems. From this we establish on phenomenological grounds a new type of quantum correlation for these systems, which we name quantum interference, deriving some quantifiers that are given explicitly in terms of the density matrix elements of the complete system. By using these quantifiers, we show that, contrary to our expectations, entanglement is not a required property for a composite quantum system to manifest multiparticle interference.     

Quantum Impurity Models with Coupled Cluster Method

We investigate the ground-state properties of the Anderson single impurity model （finite Coulomb impurity repulsion） with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green＇s function results for the non-interacting model and with Brillouin-Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Towards hybrid circuit quantum electrodynamics with quantum dots

Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Thermoelectric transport properties through a T-shaped single quantum dot

We study the thermopower, thermal conductance, electric conductance and the thermoelectric figure of merit for a gate-defined T-shaped single quantum dot (QD). The QD is solved in the limit of strong Coulombian repulsion U→∞, inside the dot, and the quantum wire is modeled on a tight-binding linear chain. We employ the X-boson approach for the Anderson impurity model to describe the localized level within the quantum dot. Our results are in qualitative agreement with recent experimental reports and other theoretical researches for the case of a quantum dot embedded into a conduction channel, employing analogies between the two systems. The results for the thermopower sign as a function of the gate voltage (associated with the quantum dot energy) are in agreement with a recent experimental result obtained for a suspended quantum dot. The thermoelectric figure of merit times temperature results indicates that, at low temperatures and in the crossover between the intermediate valence and Kondo regimes, the system might have practical applicability in the development of thermoelectric devices.     

Quantum communication through chains with diluted disorder

We investigate a single-qubit state transfer protocol along a channel featuring diagonal diluted disorder. In the regime where the source and destination sites are weakly coupled to the channel, we report the possibility of transmitting quantum states with high fidelity as well as establishing end-to-end entanglement in that sort of configuration. We further discuss how the performance of the protocol depends upon the availability of extended states within the disordered channel.