We assess experimentally the suitability of coupled-transmission-line resonators for studies of quantum phase transitions of light. We have measured devices with low photon hopping rates $t/2\pi =0.8$ MHz to quantify disorder in individual cavity frequencies. The observed disorder is consistent with small imperfections in fabrication. We studied the dependence of the disorder on transmission-line geometry and used our results to fabricate devices with disorder less than two parts in ${10}^4$. The normal-mode spectrum of devices with a high photon hopping rate $t/2\pi =31$ MHz shows little effect of disorder, rendering resonator arrays a good backbone for the study of condensed-matter physics with photons.

We show the existence of self-similar giant rogue waves in a tapered graded-index nonlinear fiber and analytically illustrate their amplification in a rather small spatiotemporal domain by controlled manipulation of the phase. Our exact analysis takes recourse to the large manifold of available tapering profiles in conjunction with appropriate gain functions, which are allowed by the dynamical equation governing the tapered graded-index nonlinear fiber. The fact that these profiles and gain functions provide a wide class of boundary conditions makes them particularly relevant for transient rogue waves, which manifest rather rarely.

Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the preselection and the postselection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and postselections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and postselections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and postselections tend to be orthogonal.

The $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian $H=p^2+x^2{\left(ix\right)}^{\varepsilon }$ ($\varepsilon$ real) exhibits a phase transition at $\varepsilon =0$. When $\varepsilon ⩾0$, the eigenvalues are all real, positive, discrete, and grow as $\varepsilon$ increases. However, when $\varepsilon <0$ there are only a finite number of real eigenvalues. As $\varepsilon$ approaches $-1$ from above, the number of real eigenvalues decreases to 1, and this eigenvalue becomes infinite at $\varepsilon =-1$. In this paper it is shown that these qualitative spectral behaviors are generic and that they are exhibited by the eigenvalues of the general class of Hamiltonians $H^{\left(2n\right)}=p^{2n}+x^2{\left(ix\right)}^{\varepsilon }$ ($\varepsilon$ real, $n=1,2,3,...$). The complex classical behaviors of these Hamiltonians are also examined.

We consider the security of continuous-variable quantum key distribution using thermal (or noisy) Gaussian resource states. Specifically, we analyze this against collective Gaussian attacks using direct and reverse reconciliation where both protocols use either homodyne or heterodyne detection. We show that in the case of direct reconciliation with heterodyne detection, an improved robustness to channel noise is achieved when large amounts of preparation noise is added, as compared to the case when no preparation noise is added. We also consider the theoretical limit of infinite preparation noise and show a secure key can still be achieved in this limit provided the channel noise is less than the preparation noise. Finally, we consider the security of quantum key distribution at various electromagnetic wavelengths and derive an upper bound related to an entanglement-breaking eavesdropping attack and discuss the feasibility of microwave quantum key distribution.

We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore, we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases, we show that only a few local measurements are necessary to determine these lower bounds.

We observe the shift of Rydberg levels of rubidium close to a copper surface when atomic clouds are repeatedly deposited on it. We measure transition frequencies of rubidium to $S$ and $D$ Rydberg states with principal quantum numbers $n$ between 31 and 48 using the technique of electromagnetically induced transparency. The spectroscopic measurement shows a strong increase of electric fields towards the surface that evolves with the deposition of atoms. Starting with a clean surface, we measure the evolution of electrostatic fields in the range between 30 and 300 $\mu$$\mathrm{m}$ from the surface. We find that after the deposition of a few hundred atomic clouds, each containing $\sim$${10}^6$ atoms, the field of adsorbates reaches 1 V/cm for a distance of 30 $\mu$m from the surface. This evolution of the electrostatic field sets serious limitations on cavity QED experiments proposed for Rydberg atoms on atom chips.

We study the characteristics of ionization rates of an atom by an intense laser field using an extension of Keldysh theory. High-order semianalytical expressions are obtained for linear, circular, and elliptically polarized fields. We compare the features of the new rates with Keldysh analytical results as functions of frequency and electric field strength. The directionality of photoelectron emissions is compared for elliptical, circular, and linearly polarized cases. Laser polarization has significant effects on the ionization spectra and directionality of photoelectron emission.

The external coherent control over the dynamics of quantum systems has been the aim of many studies in recent years, and several theoretical frameworks have been devised for that purpose. However, several of the proposed methods have been developed to control isolated quantum systems, disregarding the decoherence effects that impinge on the ubiquitous open quantum systems that exhibit a more complex dynamics than their isolated counterparts. In this paper, we investigate the effects of dissipation and decoherence for a quantum-control procedure based on sequences of reverse optimized electromagnetic pulses. Although the method performs well for pure quantum systems, moderate decoherence and dissipation hinders its accomplishment for ordinary conditions, irrespective of the pulse sequence rate. The method can be appropriate, nonetheless, for dynamical decoupling of the quantum subsystem from the environment.

We study superconducting microtraps with rectangular shapes for cold atomic gases. We present a general argument why microtraps open if brought close to the surface of the superconductor. We show that for a given width of the strips there exists an optimal thickness under which the closest distance of the microtrap from the superconductor can be achieved. The distance can be significantly improved if the edge enhancement of the supercurrent near edges and corners is exploited. We compare the numerical calculations with results from conformal mapping and show that conformal mapping can often give useful approximate results.

We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly bound Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal long-range order for fermions we calculate analytically and numerically the pair binding energy, the energy gap, and the condensate fraction of Cooper pairs as a function of interaction strength and filling factor of atoms in the lattice at zero temperature.

We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study nonlocal effects in polar gases, as we illustrate with two parallel quasi-one-dimensional dipolar condensates. Nonlocal interactions between the condensates give rise to an excitation spectrum characterized by symmetric and antisymmetric modes, even in the absence of hopping. We show that this feature, absent in nondipolar gases, results in a critical driving frequency at which a marked transition occurs between correlated and anticorrelated Faraday patterns in the two condensates. Interestingly, at this critical frequency, the emergent Faraday pattern stems from a spontaneous symmetry-breaking mechanism.

We consider the nonlinear scattering and transmission of an atom laser or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark-soliton train from a phononlike standing wave.

We investigate the cross-phase-modulation-induced modulational instability (MI) of two co-propagating optical beams in the system of relaxing Kerr nonlinearity with the effect of higher-order dispersion (HOD) and walk-off effect. We identify and discuss the salient features of relaxation of nonlinear responses and HOD using suitable theoretical model. First, we analyzed the impact of HOD and walk-off on the MI spectrum and found both analytically and numerically that the MI exhibits alternate characteristics like the evolution of different spectral bands in addition to the conventional MI bands. The walk-off effects in the virtue of HOD not only consist of the conventional group velocity mismatch (GVM) but also the difference in third-order dispersion (TOD) of the two beams, and thereby significantly modify the dynamical behavior of the MI. We also consider the combined effect of relaxation of nonlinear response and the HOD effects, and we observe that any finite value of delay leads to the evolution of two unstable modes and thereby extends the range of unstable frequency; HOD on the other hand along with the walk-off effect brings other characteristic spectral bands. A detailed discussion about the various combinations of parameters and the relative competence of one over the other on the MI spectrum is presented. Thus the evolution of MI from cross-phase modulation in the system of relaxing Kerr nonlinearity is emphasized in detail and the influence of HOD and the walk-off effect are highlighted.

We study the transmitted intensity and correlation properties of a probe field traveling through a sample of interacting cold ${}^{87}$Rb atoms driven into the inverted $\mathsf{Y}$ configuration. Two windows of electromagnetically induced transparency are found in the transmission spectrum, which are either sensitive or immune to the input probe intensity. This means that one window is accompanied by cooperative optical nonlinearity while the other is a result of a linear optical response. Moreover, we find sufficiently suppressed two-photon correlation within the nonlinear window and greatly enhanced two-photon correlation between the linear and nonlinear windows. In the case of the degenerate window, however, it is viable to conceal the cooperative optical nonlinearity behind the linear optical response. This then allows us considerable flexibility to manipulate the propagation and evolution of a quantum light field.

We reveal the existence of polariton soliton solutions in the array of weakly coupled optical cavities, each containing an ensemble of interacting qubits. An effective, complex Ginzburg-Landau equation is derived in the continuum limit, taking into account the effects of cavity field dissipation and qubit dephasing. We have shown that an enhancement of the induced nonlinearity can be achieved by two orders of magnitude with negative interaction strength, which implies a large negative qubit-field detuning as well. Bright solitons are found to be supported under perturbations only in the upper (optical) branch of polaritons, for which the corresponding group velocity is controlled by tuning the interacting strength. With the help of perturbation theory for solitons, we also demonstrate that the group velocity of these polariton solitons is suppressed by the diffusion process.

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite projected entangled pair states. The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.

We predict the existence of a dip below unity in the second-order coherence function of a partially condensed ideal Bose gas in harmonic confinement, signaling the anticorrelation of density fluctuations in the sample. The dip in the second-order coherence function is revealed in a canonical-ensemble calculation, corresponding to a system with fixed total number of particles. In a grand-canonical ensemble description, this dip is obscured by the occupation-number fluctuation catastrophe of the ideal Bose gas. The anticorrelation is most pronounced in highly anisotropic trap geometries containing small particle numbers. We explain the fundamental physical mechanism which underlies this phenomenon, and its relevance to experiments on interacting Bose gases.

We theoretically investigate ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering (CARS) microscopy. We propose a scheme based on ground-state depopulation, which is achieved via a control laser light field incident prior to the CARS excitation light fields. This ground-state depopulation results in a reduced CARS signal generation. With an appropriate choice of spatial beam profiles, the scheme can be used to increase the spatial resolution. Based on the density matrix formalism we calculate the CARS signal generation and find a CARS signal suppression by 75$\%$ due to ground-state depletion with a single control light field and by using two control light fields the CARS signal suppression can be enhanced to 94$\%$. Additional control light fields will enhance the CARS suppression even further. In case of a single control light field we calculate resulting CARS images using a computer-generated test image including quantum and detector noise and show that the background from the limited CARS suppression can be removed by calculating difference images, yielding subdiffraction-limited resolution where the resolution achievable depends only on the intensity used.