We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.

The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements.

In this paper, optical properties of coupled silica disk microresonators are investigated. The spectral response and the light intensity distribution along the coupled disks were measured. It was found that the distribution depends on the particular excited resonance, which can be attributed to the formation of normal modes of the coupled resonator system. A developed theoretical model gives quantitative agreement with the experimental observations.

The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two-level system which can be tuned in resonance with the cavity. Here, we explore the behavior of single excitations (where an excitation can be either photonic or atomic) in the linear JCH system, which describes a coupled cavity waveguide. We use direct, analytic diagonalization of the Hamiltonian to study cases where intercavity coupling is either uniform or varies parabolically along the chain. Both excitations located in a single cavity, as well as one excitation as a Gaussian pulse spread over many cavities, are investigated as initial states. We predict unusual behavior of this system in the time domain, including slower than expected propagation of the excitation and also splitting of the excitation into two distinct pulses, which travel at distinct speeds. In certain limits, we show that the JCH system mimics two Heisenberg spin chains.

We analytically investigate the influence of complex backscattering coefficients and pump current on the noise spectra of a two-mode model for semiconductor ring laser in the Langevin formulation. The system features in the bidirectional regime are naturally described in terms of the two mode-intensity sum ($I$ spectrum) and difference ($D$ spectrum). The $I$ spectrum reflects the energy exchange between the total field and the medium and behaves similarly to the relative intensity noise for single-mode semiconductor lasers. The $D$ spectrum represents the energy exchange between the two counterpropagating modes and is shaped by the noisy precursor of a Hopf bifurcation induced by the complex backscattering.

We investigate the accuracy of two mean-field theories of the trapped two-dimensional Bose gas at predicting transition region properties by comparison to nonperturbative classical field calculations. To make these comparisons we examine the density profiles and the predictions for the Berezinskii-Kosterlitz-Thouless superfluid transition temperature over a parameter range in which the degree of thermal activation in the tightly trapped direction varies considerably. These results present an important test of these mean-field theories and provide a characterization of their typical accuracy.

We generalize the discrete quantum walk on the line using a time-dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, subdiffusive, and localized.

We report wavelength measurements and energy levels for the three-times ionized cerium atom ${\text{Ce}}^{3+}$. The spectrum is that of a simple one-electron atom overlaid with a more complex three-electron spectrum originating from the excitation of an electron in the inner closed shell to the valence shell. The data provide energy levels for the inner-shell-excited configurations $5p^{5}4f5d$ and $5p^{5}4f6s$ and solve a long-standing puzzle regarding the fine structure of the $5p^{6}6d$ configuration, which is known to be anomalously large and inverted. The data show that this anomalous fine structure is the result of interaction between $5p^{6}6d$ and the inner-shell-excited configuration $5p^{5}4f5d$. The results are supported by Hartree-Fock calculations and least-squares fits of the energy parameters to the observed levels. From our observed $5p^{6}6g$ configuration, we determine the ionization energy as $297670\pm 70{\text{cm}}^{-1}$ $\left(36.906\pm 0.009\text{eV}\right)$.

The lifetime broadenings of the most intense $5s$ photolines of Cs were studied. The aim of this study was to understand the origin of the remarkable differences in the lifetime widths of different $5s^{-1}$ multiplet states. The $5s$ photoelectron spectra of the $6s\to 6p_{1/2,3/2}$ laser-excited states are presented in the binding energy region of 30–34 eV showing the main $5s$ photolines of the ground state and laser-excited states as well as the $5s5p^{6}6p$ shakeup satellites. The lifetime widths of the states were determined. The Hartree-Fock calculations were carried out to predict the $5s$ photoelectron spectrum. The lifetime broadenings of the $5s$ photolines were found to be due to the transition rates of the subsequent Coster-Kronig transitions to the $5s^{2}5p^5$ states. It was found that a straightforward single-configuration explanation cannot be given for the lifetime differences. Instead, electron correlation plays an essential role and the lifetime broadenings were found to be predicted well only when configuration interaction between the $5s^{-1}$ and $5p^{-2}5d$ configurations is taking into account.

We study a Bose Josephson junction realized with a double-well potential. We propose a strategy to observe the coherent superpositions of phase states occurring during the time evolution after a sudden rise of the barrier separating the two wells. We show that their phase content can be obtained by the full counting statistics of the spin-boson operators characterizing the junction, which could be mapped out by repeated measurements of the population imbalance after rotation of the state. This measurement can distinguish between coherent superpositions and incoherent mixtures, and can be used for a two-dimensional tomographic reconstruction of the phase content of the state.

In this report, we apply optimal control theory to design minimum energy $\pi /2$ and $\pi$ pulses for Bloch equations, in the case where transverse relaxation rate is much larger than longitudinal so the later can be neglected. Using Pontryagin’s Maximum Principle, we derive an optimal feedback law and subsequently use it to obtain analytical expressions for the energy and duration of the optimal pulses.

We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green’s function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green’s function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate the difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.

Three code constructions generating new families of good nonbinary quantum codes are presented in this paper. The first two ones are derived from Hermitian self-orthogonal non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes. The third one is derived from $q$-ary ($q\ne 2$ is a prime power) Steane’s enlargement of Calderbank-Shor-Steane codes applied to Euclidean self-orthogonal non-narrow-sense BCH codes. The quantum nonbinary BCH codes presented here have parameters better than the ones available in the literature.

Using a cold atomic gas exposed to laser pulses—a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies—we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent $\nu =1.59\pm 0.01$, which is found to be equal to the one previously computed for the Anderson model.

In a Bose superfluid, the coupling between transverse (phase) and longitudinal fluctuations leads to a divergence of the longitudinal correlation function, which is responsible for the occurrence of infrared divergences in the perturbation theory and the breakdown of the Bogoliubov approximation. We report a nonperturbative renormalization-group calculation of the one-particle Green’s function of an interacting boson system at zero temperature. We find two regimes separated by a characteristic momentum scale $k_G$ (“Ginzburg” scale). While the Bogoliubov approximation is valid at large momenta and energies, $\left|\mathbf{p}\right|,\left|\omega \right|/c⪢k_G$ (with $c$ as the velocity of the Bogoliubov sound mode), in the infrared (hydrodynamic) regime, $\left|\mathbf{p}\right|,\left|\omega \right|/c⪡k_G$, the normal and anomalous self-energies exhibit singularities reflecting the divergence of the longitudinal correlation function. In particular, we find that the anomalous self-energy agrees with the Bogoliubov result ${\Sigma }_{\text{an}}\left(\mathbf{p},\omega \right)\simeq \text{const}$ at high energies and behaves as ${\Sigma }_{\text{an}}\left(\mathbf{p},\omega \right)\sim {\left(c^2{\mathbf{p}}^2-{\omega }^2\right)}^{\left(d-3\right)/2}$ in the infrared regime (with $d$ as the space dimension), in agreement with the Nepomnyashchii identity ${\Sigma }_{\text{an}}\left(0,0\right)=0$ and the predictions of Popov’s hydrodynamic theory. We argue that the hydrodynamic limit of the one-particle Green’s function is fully determined by the knowledge of the exponent $3-d$ characterizing the divergence of the longitudinal susceptibility and the Ward identities associated to gauge and Galilean invariances. The infrared singularity of ${\Sigma }_{\text{an}}\left(\mathbf{p},\omega \right)$ leads to a continuum of excitations (coexisting with the sound mode) which shows up in the one-particle spectral function.

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-Hänchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus, the corresponding reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and reflection can be changed from positive to negative with increasing the wavelength. These negative and positive shifts can also be enhanced by transmission resonances when the frequency is far from that at the DP. All these phenomena will lead to some potential applications in the integrated optics and optical devices.

The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubit system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.

The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.

In this paper we explore the possibility of a steady-state entanglement of two two-level atoms inside a pumped cavity by taking into account cavity leakage and the spontaneous emission of photons by the atoms. We describe the system in the dressed state picture in which the coherence is built into the dressed states while transitions between the dressed states are incoherent. Our model assumes the vacuum Rabi splitting of the dressed states to be much larger than any of the decay parameters of the system which allows atom-field coherence to build up before any decay process takes over. We show that, under our model, a pumping field cannot entangle two closed two-level atoms inside the cavity in the steady-state, but a steady-state entanglement can be achieved with two open two-level atoms.

A generalized depolarizing channel acts on an $N$-dimensional quantum system to compress the “Bloch ball” in $N^2-1$ directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when $N=2^d$ (i.e., the system consists of $d$ qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.