We introduce an experimentally accessible method to measure a unique degree of nonclassicality, based on the quantum superposition principle, for arbitrary quantum states. We formulate witnesses and test a given state for any particular value of this measure. The construction of optimal tests is presented as well as the general numerical implementation. We apply this approach on examples such as squeezed states, and we show how to formulate conditions to certify a particular degree of nonclassicality for single- and multimode radiation fields.

We solve the Maxwell-Dirac equations to study the dynamics of a spatially localized charged particle in one spatial dimension. While the coupling of the Maxwell equations to the Dirac equation predicts correctly the attractive or repulsive interaction between different particles, it also reveals an unphysical interaction of a single electron or positron with itself leading to an enhanced spatial spreading of the wave packet. Using a comparison with a relativistic ensemble of mutually interacting classical quasiparticles, we suggest that this quantum mechanical self-repulsion can be understood in terms of relativistic classical mechanics. We show that due to the simple form of the Coulomb law in one spatial dimension it is possible to find analytical expressions of the time-dependent spatial width for the interacting classical ensemble. A better understanding of the dynamical impact of this unavoidable self-repulsion effect is relevant for recent studies of the field-induced pair creation process from the vacuum.

We consider the problem of unambiguous (error-free) discrimination of $N$ linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive an upper bound on the optimal average probability of success using a result on optimal local conversion between two bipartite pure states. We prove that for any $N\ge 2$ an optimal measurement in general saturates our bound. In the exceptional cases we show that the bound is tight, but not always optimal.

We propose a repeat-until-success protocol to improve the performance of probabilistic quantum repeaters. Conventionally, these rely on passive static linear-optics elements and photodetectors to perform Bell-state measurements (BSMs) with a maximum success rate of 50%. This is a strong impediment for entanglement swapping between distant quantum memories. Every time a BSM fails, entanglement needs to be redistributed between the corresponding memories in the repeater link. The key ingredients of our scheme are repeatable BSMs. Under ideal conditions, these turn probabilistic quantum repeaters into deterministic ones. Under realistic conditions, our protocol too might fail. However, using additional threshold detectors now allows us to improve the entanglement generation rate by almost orders of magnitude, at a nominal distance of 1000 km, compared to schemes that rely on conventional BSMs. This improvement is sufficient to make the performance of our scheme comparable to the expected performance of some deterministic quantum repeaters.

We investigate how the genuine multipartite entanglement is distributed among the components of superposed states. Analytical lower and upper bounds for the usual multipartite negativity and the genuine multipartite entanglement negativity are derived. These bounds are shown to be tight by detailed examples.

Inelastic transitions in slow ion-atom collisions are described using an adiabatic representation of the collision system, where the transition probabilities are determined by the branch points of the potential energy curves in the complex plane of internuclear separation $R$. As an example, the ${\mathrm{HeH}}^{2+}$ system is treated, in which the evolution of the branch points related to hidden, avoided, and $L_3$ crossings in the dynamical adiabatic basis of three-body Coulomb problem as functions of parameter $\omega =\rho v$ ($\rho$ is the impact parameter and $v$ the impact velocity) is studied. Rearrangement of hidden couplings due to the passage of $L_3$ branch points with the increase of $\omega$ is discussed.

We present a theoretical study of bremsstrahlung produced by high-energy electrons scattered by heavy atomic targets. Considering coincident observation of the emitted photons and the scattered electrons, we pay special attention to the polarization degree and direction of the outgoing light. To investigate these properties of atomic bremsstrahlung, we apply the density matrix approach and solutions of the Dirac equation. Detailed calculations are performed for initial electron energies ranging from 100 to 500 keV and different fixed electron scattering angles. The results of these calculations are compared with predictions obtained under the assumption that the scattered electrons remain unobserved. This comparison reveals that both the degree and the direction of linear polarization of bremsstrahlung are very sensitive to the direction of the scattered electron.

We study the transverse-electron-momentum distribution (TEMD) of the wave packets launched in a pump-probe sequential double ionization from the valence shell of a noble gas atom. Our calculations, based on an accurate numerical solution of the time-dependent Schrödinger equation (TDSE), reproduce a characteristic cusp of the TEMD which is attributed to the Coulomb singularity. The evolution of the TEMD with the time delay between the pump and probe pulses is shown to be similar to the prediction of the standard tunneling formula (TF), as was observed experimentally for argon by Fechner et al. [Phys. Rev. Lett. 112, 213001 (2014)]. However, TDSE calculations show a clear deviation from the TF and predict a much more complicated structure which cannot be reproduced by the target orbital momentum profile filtered by the tunneling Gaussian. The accuracy of the TF can be improved if the target momentum profile is calculated with the Coulomb waves instead of the plane waves.

We report the all-optical production of Bose-Einstein condensates (BEC) of ${}^{39}\mathrm{K}$ atoms. We directly load $3\times {10}^7$ atoms in a large volume optical dipole trap from gray molasses on the D1 transition. We then apply a small magnetic quadrupole field to polarize the sample before transferring the atoms in a tightly confining optical trap. Evaporative cooling is finally performed close to a Feshbach resonance to enhance the scattering length. Our setup allows one to cross the BEC threshold with $3\times {10}^5$ atoms every 7 s. As an illustration of the interest of the tunability of the interactions we study the expansion of Bose-Einstein condensates in the one-dimensional to three-dimensional crossover.

The interference of waves evenly separated in frequency generates a periodic signal, whose intensity fluctuations depend on the phases of the individual waves. A fundamental question in telecommunications and acoustics is the minimization of the peak-to-average-power ratio (PAR): for a given spectrum, how to arrange the phases of the individual frequency components to ensure minimal intensity fluctuations of the resulting signal? For a flat spectrum a near-optimal solution is brought by the so-called Newman phases, commonly used in acoustic and radio waves. Here we transpose this property into the optical domain and prove the possibility to suppress the intensity fluctuations resulting from intermodal beating of a broadband comb of optical frequencies, whose phases are set according to a generalization of the Newman phases. We demonstrate experimentally a broadband laser, whose intensity contrast (defined as the standard deviation-to-mean ratio) is reduced down to 0.54 as compared to 1 when the phases are set randomly.

We have theoretically and experimentally studied the spectroscopic properties of dressed levels in a strong monochromatic field, and propose a model of cascade splitting of two atomic energy levels. In this model two related dressed levels can be split into four levels, and transitions connecting four new levels will constitute spectroscopic structures. Two types of proof-in-principle experiments are performed to verify the model. One experiment measures the probe absorption spectra of a degenerate two-level atomic system with two strong monochromatic coupling fields. The system consists of $5^2{S}_{1/2},F=2$ and $5^2{P}_{3/2},F^{\prime }=3$ states of ${}^{87}\mathrm{Rb}$ atoms in a magneto-optical trap (MOT) as well as the cooling beams and an additional coupling field. New spectral features are observed and proven to be due to the transitions of new levels generated by splitting of the dressed levels. The other experiment measures the pump-probe spectra in a degenerate two-level atomic system with one strong monochromatic coupling field. The system consists of $5^2{S}_{1/2},F=2$ and $5^2{P}_{3/2},F^{\prime }=3$ states of the ${}^{87}\mathrm{Rb}$ atom in a magneto-optical trap and one coupling field. We have observed spectral features that obviously differ from the prediction that comes from the two-level dressed-atom approach. They cannot be explained by existing theories. The model of cascade splitting of two atomic energy levels is employed to explain the observations in these two types of experiments.

We present an analysis of the $N$-boson spectrum computed using a soft two-body potential, the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length $a$ close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground state of the system with one less particle. It is governed by a unique universal function $\Delta \left(\xi \right)$, already known in the case of three bosons. In the three-particle system the angle $\xi$, determined by the ratio of the two- and three-body binding energies $E_3/E_2={tan}^2\xi$, characterizes the discrete scale invariance of the system. Extending the definition of the angle to the $N$-body system as $E_N/E_2={tan}^2\xi$, we study the $N$-boson spectrum in terms of this variable. The analysis of the results, obtained for up to $N=16$ bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of $N$ is observed at fixed values of $a$. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length $a$ and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

The physics of spin-exchange collisions have fueled several discoveries in fundamental physics and numerous applications in medical imaging and nuclear magnetic resonance. We report on the experimental observation and theoretical justification of spin-noise exchange, the transfer of spin noise from one atomic species to another. The signature of spin-noise exchange is an increase of the total spin-noise power at low magnetic fields, on the order of 1 mG, where the two-species spin-noise resonances overlap. The underlying physical mechanism is the two-species spin-noise correlation induced by spin-exchange collisions.

The Crank-Nicolson (C-N) method combined with a $B$-spline basis set can be used in both time-dependent and time-independent calculations of the photoionization cross sections of atoms and molecules. For time-independent systems, the imaginary-time propagation (ITP) method can usually only converge an arbitrary initial state to the ground state directly. Contrary to existing methods, it is found that the C-N method can converge an arbitrary initial state directly to not only the ground state but also excited and continuum states by controlling the time-step size. It is very useful if one is interested in only part of the spectral information since the computation is relatively cheap. The C-N method can also be directly applied in time-dependent calculations. During the time evolution, the spectral information, such as energy and momentum, can be retrieved by projecting the wave function on the eigenstates obtained using the ITP method. Both time-dependent and time-independent calculations agree very well with previous results. This method can also be extended to two-electron systems directly.

We study a system comprising of a double quantum well embedded in a micropillar optical cavity, where strong coupling between a direct exciton, an indirect exciton, and a cavity photon is achieved. We show that the resulting hybrid quasiparticles—dipolaritons—can induce strong photon correlations and lead to antibunched behavior of the cavity output field. The origin of the observed single-photon emission is attributed to unconventional photon blockade. We find that the second-order equal-time correlation function $g^{\left(2\right)}\left(0\right)$ can be tuned over a large range by using an electric field applied to the structure, or by changing the frequency of the pump. This allows for on-the-flight control of cavity output properties and is important for the future generation of tunable single-photon-emission sources.

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay faster than any power of the distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous buildup of collective coherence in the system.

We study the photon statistics of symmetric and antisymmetric modes in a photonic molecule consisting of two linearly coupled nonlinear cavity modes. Our calculations show that strong photon antibunching of both symmetric and antisymmetric modes can be obtained even when the nonlinearity in the photonic molecule is weak. The strong antibunching effect results from the destructive interference between different paths for two-photon excitation. Moreover, we find that the optimal frequency detunings for strong photon antibunching in the symmetric and antisymmetric modes are linearly dependent on the coupling strength between the cavity modes in the photonic molecule. This implies that the photonic molecules can be used to generate tunable single-photon sources by tuning the values of the coupling strength between the cavity modes with weak nonlinearity.

Given a many-body system, we define a quantity, the codification volume of an operator algebra, which measures the size of the subfactor of the full Hilbert space with which a given algebra is correlated. We explicitly calculate it for some limit cases, including vacuum states of local Hamiltonians and random states taken from the Haar ensemble. We argue that this volume should grow irreversibly in a thermalization process, and we illustrate it numerically on a nonintegrable quantum spin chain.

We discuss the time continuous path integration in the coherent-state basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and nonperturbative approximations already known in the quantum-field-theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.

We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement-swapping operations and solve numerically for up to three intermediate entanglement-swapping operations. Our model yields two-photon interference visibilities postselected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through the parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.