A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We characterize the maximum noncontextual and quantum values of these inequalities, and provide evidence supporting the conjecture that the maximum quantum violation of these inequalities is exactly singled out by the exclusivity principle.

A linear one-dimensional Schrödinger equation, defined by means of a non-Hermitian Hamiltonian characterized by position-dependent masses, was proposed lately. Herein we present an exact classical field theory for this equation, showing the need for an extra field $\Phi (x,t)$, in addition to the usual one, $\Psi (x,t)$, similar to what was done recently in the analysis of a class of nonlinear quantum equations. These generalizations of the Schrödinger equation depend on an index $q$, in such a way that the standard case is recovered in the limit $q\to 1$. Particularly, the field $\Phi (x,t)$ becomes ${\Psi }^{*}(x,t)$ only when $q\to 1$ and satisfies a similar Schrödinger equation for the Hermitian conjugate of the Hamiltonian operator. In terms of these two fields one may define a probability density following a standard continuity equation, leading to the preservation of probability in Cartesian space. Simple applications are performed by solving the equations for the two fields.

In connection with the recently proposed Lamb-shift experiments at Paul Scherrer Institute in ${\mu }^4{\mathrm{He}}^{+}$ and ${\mu }^3{\mathrm{He}}^{+}$ by using the laser-spectroscopy method, the pressure shift and width of the $2p$-$2s$ spectral lines in muonic-helium ions were studied in the present paper within the fully quantum-mechanical close-coupling approach. The calculations of the $S$ matrix as well as of the energy-dependent shift and width were made for collisional energies $E={10}^{-5}–1$ eV. The shift and width averaged over energy were obtained for target temperatures up to 350 K. It is shown that the fine-structure effect does not exceed a few percent. The isotopic effect is very small and can be neglected for the shift at $T\ge 150$ K, contrary to the width, for which the isotopic effect becomes much more pronounced at $T\ge 150$ K. At density $N=2.4145\times {10}^{18}$ atom/cm${}^3$ corresponding to the target pressure 100 mbar ($T=300$ K) the predicted values of the shifts are equal to 35 (50) MHz for ${\mu }^3{\mathrm{He}}^{+}$ and 33 (35) MHz for ${\mu }^4{\mathrm{He}}^{+}$ respectively for upper (lower) values of the $2p$-$2s$ energy-level separation. At the same conditions the values of the widths are equal to 2.4 (13.6) MHz for ${\mu }^3{\mathrm{He}}^{+}$ and 2.0 (3.0) MHz for ${\mu }^4{\mathrm{He}}^{+}$.

In this study, we apply the monitoring master equation describing decoherence of internal states to an optically active molecule prepared in a coherent superposition of nondegenerate internal states interacting with thermal photons at low temperatures. We use vibrational Raman scattering theory up to the first chiral-sensitive contribution, i.e., the mixed electric-magnetic interaction, to obtain scattering amplitudes in terms of molecular polarizability tensors. The resulting density matrix is used to obtain elastic decoherence rates.

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim, we use the hyperspherical adiabatic expansion and we extract the $S$ matrix through the integral relations recently derived. The results are compared to the universal form, $\alpha \approx 67.1{\sin }^2[s_0\ln \left({\kappa }_{*}a\right)+\gamma ]$, for different values of $a$ and selected values of the three-body parameter ${\kappa }_{*}$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed [A. Kievsky and M. Gattobigio, Phys. Rev. A 87, 052719 (2013)]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length.

Total electron-scattering cross sections of pyrimidine, the basic component for the nucleic bases cytosine and thymine, were measured for electron energies from 5 eV to 1 keV using the linear transmission method. The measured results were compared to semiempirical data obtained by means of the additivity rule and to experimental data for benzene since it has a similar ring structure and the same number of valence electrons as pyrimidine. Furthermore, integral elastic and inelastic electron-scattering cross sections of pyrimidine were calculated by applying the spherical complex optical potential model. The sum of both cross sections agrees reasonably well with the experimental total electron-scattering cross sections of pyrimidine in the energy range from 20 eV to 1 keV. The experimental data are, however, significantly lower than the theoretical cross sections when including the contribution of rotational excitations to the electron scattering.

We calculate resonant absorption line shapes in helium atoms subject to the combination of an attosecond pulse of XUV radiation and a delayed, few-cycle infrared (IR) laser pulse. We are in particular interested in how the resonant features evolve with the delay between the fields and with increasing IR intensity. We first compare the single-atom absorption calculated by a nonperturbative solution of the time-dependent Schrödinger equation (TDSE) to a simple model in which the resonant absorption is modified only by a laser-imposed phase (LIP) that originates in the instantaneous ac Stark shift of the resonant state. We find that the LIP model can explain many features of the resonant absorption, including the direction of the resonance energy shift and the onset of dispersive line shapes with increasing IR intensity. We also find, however, that the LIP model predicts the energy shifts and the line shapes only qualitatively when the resonant states are strongly IR coupled to nearby states. We then use a coupled solution of the Maxwell wave equation and the TDSE to examine how the line shapes are modified by propagation effects at helium densities such that the resonant absorption is strong. We find that when the resonant absorption saturates, their line shapes are strongly modified due to reshaping of the attosecond pulse time profile during propagation. This in turn alters the ultrafast absorption and emission dynamics.

We develop a general theoretical framework for the analytical description of the interaction of a model diatomic molecular system with an intense, arbitrarily polarized monochromatic laser field. The model molecule comprises an electron in the field of two zero-range potentials separated by the internuclear distance. This model has an exact analytical solution within the theoretical framework of the quasistationary quasienergy (Floquet) approach. In addition to the development of this general framework, we also present a detailed analysis of the weak-field limit, within which we obtain both the frequency-dependent polarizability and the angle-resolved photodetachment cross section for the model system. These fundamental properties are analyzed for both homonuclear and heteronuclear molecular systems in a linearly polarized laser field, for both ground and excited electronic states, and for arbitrary orientation of the molecular axis relative to the polarization vector of the laser field. The analytical expressions for the polarizability and angle-resolved photoelectron spectra exhibit characteristic double-slit interference patterns, allowing one to study their dependence on the parameters of the problem beyond the level of the Born approximation.

Recent experiments on fermions in synthetic gauge fields result in systems with a spin-orbit coupling along one spatial axis, a detuning field, and a Zeeman field. We show theoretically that the presence of all three results in interesting and unusual phenomena in a system of interacting fermions (interactions described by a scattering length). For two fermions, bound states appear only over a certain range of the center-of-mass momenta. The deepest bound state appears at a nonzero center-of-mass momentum. For center-of-mass momenta without a bound state, the gauge field induces a resonance-like feature in the scattering continuum resulting in a large scattering phase shift. In the case of many particles, we demonstrate that the system, in a parameter range, shows flow-enhanced pairing, i.e., a Fulde-Farrell-Larkin-Ovchnnikov superfluid state made of robust pairs with a finite center-of-mass momentum. Yet another regime of parameters offers the opportunity to study strongly interacting normal states of spin-orbit-coupled fermionic systems utilizing the resonance-like feature induced by the synthetic gauge field.

We study the collective modes of the confined unitary Fermi gas under anisotropic harmonic confinement as a function of the number of atoms. We use the equations of extended superfluid hydrodynamics, which take into account a dispersive von Weizsäcker-like term [C. F. von Weizsäcker, Z. Phys. 96, 431 (1935)] in the equation of state. We also discuss the inclusion of a backflow term in the extended superfluid Lagrangian and the effects of this anomalous term on sound waves and the Beliaev damping of phonons [S. T. Beliaev, Sov. Phys. JETP 7, 299 (1958)].

In this work we introduce a model for quantum-state transfer between tripod atoms over a dark fiber. Two tripod atoms are confined in separate cavities linked by an optical fiber. The cavities and the fiber sustain two optical modes of opposite circular polarization. For each atom, the two ground states encode the quantum state to be transferred and are coupled to a common excited state by the cavity modes of opposite polarization. The remaining transition for each atom is used to control the transfer process. We demonstrate that by using laser pulses the dynamics of the system can be confined within a degenerate dark state subspace, with the different dark states interacting via nonadiabatic couplings. We solve analytically the dynamics in the dark state subspace, and determine the conditions on the pulse shape for the implementation of the quantum transfer. We identify a possible pulse shape which satisfies the required conditions, and demonstrate the quantum-state transfer via numerical simulations.

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks: a blazed axicon, a binary axicon, and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.

We propose a scheme for preparing a set of bases constituted by equidistant states of a quantum system in prime dimension starting with a single entangled system-ancilla state. The required quantum correlations between the involved systems as a function of the separability constant are analyzed. A comparative analysis of errors in tomographic reconstruction process using bases of different separation is given in the frame of the Fisher information approach.

We present a theoretical and experimental study aimed at characterizing statistical regimes in a random laser. Both the theoretical simulations and the experimental results show the possibility of three regions of fluctuations increasing the pumping energy. An initial Gaussian regime is followed by Lévy statistics, and Gaussian statistics is recovered again for high pump pulse energy. These different statistical regimes are possible in a weakly diffusive active medium, while the region of Lévy statistics disappears when the medium is strongly diffusive presenting always a Gaussian regime with smooth emission spectrum. Experiments and theory agree in identification of the key parameters determining the statistical regimes of the random laser.

Fine-structure splitting of the exciton energy levels in a quantum dot introduces an energy difference between the two biexciton decay paths. This energy difference greatly reduces the entanglement of the photon pairs generated via biexciton recombination. Here, we propose a feasible method to eliminate the “which-path” information by using a fast frequency down-conversion technique, which substantially improves the entanglement of the photon pairs. Moreover, the wavelengths of both of the entangled photons can be transferred to the telecommunication band, which makes this method further appropriate for quantum communication.

We theoretically investigate protocols based on optimal control theory (OCT) for manipulating Bose-Einstein condensates in magnetic microtraps, using the framework of the Gross-Pitaevskii equation. In our approach we explicitly account for filter functions that distort the computed optimal control, a situation inherent to many experimental OCT implementations. We apply our scheme to the shakeup process of a condensate from the ground to the first excited state, following a recent experimental and theoretical study, and demonstrate that the fidelity of OCT protocols is not significantly deteriorated by typical filters.

Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, but the lack of complete positivity of a quantum evolution (called the “negativity”) can be used as a measure of the system-bath coupling and correlation. The negativity can be computed from the Choi representation of a channel, is always defined and bounded, and contains some information about environmentally induced noise in a quantum system.

The understanding of the dynamics of a two-level quantum system with relaxation is one of the fundamental questions of quantum mechanics. We describe geometrically the structure of this system by introducing different vector fields, which give insight into the global dynamics of the system. The vector fields are organized through two basic geometric objects, the magic plane and the steady-state ellipsoid. We show how these latter help analyzing the time-optimal control of two-level dissipative quantum systems.

Exceptional points (EPs) corresponding to resonance coalescence (i.e., complex energy degeneracy and identical wave functions) occur in many areas of non-Hermitian physics and, in particular, in laser-induced molecular dynamics for specific choices of two control parameters. We have previously shown [Atabek, et al., Phys. Rev. Lett. 106, 173002 (2011)] how these control parameters, namely, the wavelength and the intensity of the external field, have to be tuned to take advantage of EPs for selective vibrational transfers within a reduced one-dimensional model describing a diatomic molecule with frozen rotation. Moreover, the possibility offered by such transfers to adiabatically transport all the vibrational population to the ground $v=0$ level has been presented as a realistic vibrational cooling strategy with an entropy flow toward the field-induced dissociative channel. The purpose of the present article is twofold: (i) Extend the model to a full three-dimensional quantum description of the rotating molecule and discuss the existence, determination, and role of EPs involving rovibrational resonances; (ii) examine the possibility for a further challenging step in obtaining ultracold molecules through combined vibrational and rotational laser control dynamics, aiming at total purification for reaching the ground ($v=J=0$) rovibrational level. The illustrative example is the ${\mathrm{Na}}_2$ molecule for which translationally cold species have experimentally been obtained.

We study fermion pairing in a population-imbalanced mixture of ${}^6$Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation, and the equation for the Helmholtz free energy, we determine the gap, chemical potentials, and pair-momentum as functions of polarization. These parameters define the stability regions for a Fulde-Ferrell-Larkin-Ovchinnikov phase, a phase separation region where Bardeen-Cooper-Schrieffer and normal phases coexist, a Sarma phase when the pair-momentum vanishes, and the transition to the normal phase when the gap disappears. The collective-mode energies are then calculated using a Bethe-Salpeter approach in the generalized random-phase approximation assuming that the system is well described by the single-band Hubbard model. An interesting result is that this fermionic gas has a superfluid phase revealed by rotonlike minima in the asymmetric collective-mode energy spectrum.