We theoretically study an extension of the Dicke model, where the single-particle Hamiltonian has three energy levels in Lambda configuration (i.e., the excited state is coupled to two nondegenerate ground states via two independent quantized light fields). The corresponding many-body Hamiltonian can be diagonalized in the thermodynamic limit with the help of a generalized Holstein-Primakoff transformation. Analyzing the ground-state energy and the excitation energies, we identify one normal and two superradiant phases, separated by phase transitions of both first and second oder. A phase with both superradiant states coexisting is not stable. In addition, in the limit of two degenerate ground states a dark state emerges, which seems to be analogous to the dark state appearing in the well-known stimulated Raman adiabatic passage scheme.

We consider the interaction of a femtosecond light pulse with a one-dimensional photonic crystal with relaxing cubic nonlinearity in the regime of self-trapping. By use of numerical simulations, it is shown that, under certain conditions, the spectra of reflected and transmitted light possess the properties of narrowband (quasimonochromatic) or wideband (continuumlike) radiation. It is remarkable that these spectral features appear due to a significant frequency shift and occur inside a photonic band gap of the structure under investigation.

The nonlinearity of a conditional photon-counting measurement can be used to “de-Gaussify” a Gaussian state of light. Here we present and experimentally demonstrate a technique for photon-number resolution using only homodyne detection. We then apply this technique to inform a conditional measurement, unambiguously reconstructing the statistics of the non-Gaussian one- and two-photon-subtracted squeezed vacuum states. Although our photon-number measurement relies on ensemble averages and cannot be used to prepare non-Gaussian states of light, its high efficiency, photon-number-resolving capabilities, and compatibility with the telecommunications band make it suitable for quantum-information tasks relying on the outcomes of mean values.

We study the collision of two spin-polarized Fermi clouds in a harmonic trap using a simulation of the Boltzmann equation. As observed in recent experiments, we find three distinct regimes of behavior. For weak interactions the clouds pass through each other. If interactions are increased they approach each other exponentially and for strong interactions they bounce off each other several times. We thereby demonstrate that all these phenomena can be reproduced using a semiclassical collisional approach and that these changes in behavior are associated with an increasing collision rate. We then show that the oscillation of the clouds in the bounce regime is an example of an unusual case in quantum gases: a nonlinear coupling between collective modes, namely, the spin dipole mode and the axial breathing mode, which is enforced by collisions. We also determine the frequency of the bounce as a function of the final temperature of the equilibrated system.

In this paper we consider the problem of tracking the state of a quantum system via a continuous weak measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency.

A finite-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states, even for ergodic systems. However, as shown recently by us [Phys. Rev. Lett. 106, 020406 (2011)], it is possible to construct adaptive monitorings which restrict the system to jumping between a finite number of states. That is, it is possible to track the system using a finite state machine as the apparatus. In this paper we consider the question of the stability of these monitoring schemes. Restricting to cyclic jumps for a qubit, we give a strong analytical argument that these schemes are always stable and supporting analytical and numerical evidence for the example of resonance fluorescence. This example also enables us to explore a range of behaviors in the evolution of individual trajectories, for several different monitoring schemes.

We analyze the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects. This consists of coherently expanding the wave function of a ground-state-cooled mechanical resonator, performing a squared position measurement that acts as a double slit, and observing interference after further evolution. The analysis is performed in a general framework and takes into account only unavoidable sources of decoherence: blackbody radiation and scattering of environmental particles. We also discuss the limitations imposed by the experimental implementation of this protocol using cavity quantum optomechanics with levitating dielectric nanospheres.

We consider the entanglement between two internal states of a single atom and two photon number states describing either the vacuum or a single photon and thus containing, on average, less than one photon. We show that this intriguing entanglement can be characterized through substantial violations of a Bell inequality by performing homodyne detections on the optical mode. We present the experimental challenges that need to be overcome to pave the way toward a loophole-free Bell test.

In this paper, we systematically study property testing of unitary operators. We first introduce a distance measure that reflects the average difference between unitary operators. Then we show that, with respect to this distance measure, the orthogonal group, quantum juntas (i.e., unitary operators that only nontrivially act on a few qubits of the system), and the Clifford group can be all efficiently tested. In fact, their testing algorithms have query complexities independent of the system's size and have only one-sided error. Then we give an algorithm that tests any finite subset of the unitary group, and demonstrate an application of this algorithm to the permutation group. This algorithm also has one-sided error and polynomial query complexity, but it is unknown whether it can be efficiently implemented in general.

We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such a quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As an application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as $X$ states and the mixture of two aligned states.

Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses such as those introduced by a realistic quantum communication channel, e.g., by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situation reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement can survive for all partial losses. Different loss scenarios are examined, and we derive criteria to test the robustness of entangled states. These criteria are necessary and sufficient for Gaussian states. Our study provides a framework to investigate the robustness of continuous-variable entanglement in more complex multipartite systems.

We have observed a density-dependent frequency shift of more than 4 MHz in a cold ${}^{85}$Rb Rydberg gas trapped in a magneto-optical trap. A one-dimensional linearly aligned four-body model is proposed to explain the experimental data, and the calculation matches the experimental data. The calculation also shows that if the energy detuning between the two coupled states, the $nsnsns(n+1)s$ and $nsnsnpnp$ states in this case, is small, the lowest level of the $nsnsnpnp$ manifold has the maximum mixing probability, causing a frequency shift instead of line broadening. The results reported may be used for few-body blockade, Rydberg single-atom imaging, studying few-body to many-body transitions and interactions, and few-body ionization as well as quantum metrology.

We present a nonperturbative theory to describe multielectronic processes occurring in the course of collisions between an ion and a molecule. The approach is based on the expansion of the electronic scattering wave function onto asymptotic mono- or multicenter states with proper translational conditions and includes both static and dynamical electronic correlations. Therefore, it has a wide application range around intermediate impact velocities $v\approx v_e$, where $v_e$ is the averaged electron velocity in the initial state. As a first application, we report results on single- and double-electron capture processes in He${}^{2+}$-H${}_2$ collisions for impact energies ranging from 0.01 to 25 keV/u. Special emphasis on the prediction of cross sections for double-electron capture into doubly excited states of helium is addressed.

We investigate the angular correlations between the photons emitted in the dielectronic recombination (DR) of initially hydrogenlike heavy ions. The theoretical analysis is performed based on a density-matrix approach and Dirac's relativistic theory. Special emphasis has been placed upon the effects of the higher-order, nondipole terms in the expansion of the electron-photon interaction. To illustrate these effects, we present and discuss detailed calculations for $K$-$LL$ DR of initially hydrogenlike xenon, gold, and uranium. These computations show that the angular correlations are significantly affected by interference between the leading electric-dipole ($E1$) and the magnetic-quadrupole ($M2$) transitions.

Recently, $p$-wave cold collisions were shown to dominate the density-dependent shift of the clock transition frequency in a ${}^{171}$Yb optical lattice clock. Here we demonstrate that by operating such a system at the proper excitation fraction, the cold-collision shift is canceled below the $5\times {10}^{-18}$ fractional frequency level. We report inelastic two-body loss rates for ${}^3{P}_0$-${}^3{P}_0$ and ${}^1{S}_0$-${}^3{P}_0$ scattering. We also measure interaction shifts in an unpolarized atomic sample. Collision measurements for this spin-1/2 ${}^{171}$Yb system are relevant for high-performance optical clocks as well as strongly interacting systems for quantum information and quantum simulation applications.

We employed the Schwinger multichannel method to compute elastic integral, differential, and momentum transfer cross sections for low-energy electron collisions with Si$Y$${}_4$ ($Y$ $=$ Cl, Br, I) molecules. The calculations were carried out in the static-exchange and static-exchange plus polarization approximations for energies up to 10 eV. The elastic integral cross section for SiCl${}_4$ and SiBr${}_4$, computed in the static-exchange plus polarization approximation, shows two shape resonances belonging to the $T_2$ and $E$ symmetries of the $T_d$ group, and for SiI${}_4$ shows one shape resonance belonging to the $E$ symmetry of the $T_d$ group. The present results agree well in shape with experimental total cross sections. The positions of the resonances observed in the calculated integral cross sections are also in agreement with the experimental positions. We have found the presence of a virtual state for SiCl${}_4$ and a Ramsauer-Townsend minimum for SiI${}_4$ at 0.5 eV. The present results show that the proper inclusion of polarization effects is crucial in order to correctly describe the resonance spectra of these molecules and also to identify a Ramsauer-Townsend minimum for SiI${}_4$ and a virtual state for SiCl${}_4$.

We study the lifetime of the excited state of an atom or molecule near a plane surface with a given random surface roughness. In particular, we discuss the impact of the scattering of surface modes within the rough surface. Our study is completed by considering the lateral correlation length of the decay rate and the variance discussing its relation to the $C_0$ correlation.

Ultracold Rydberg atoms in a static electric field can exchange energy via the dipole-dipole interaction. The Stark effect shifts the energy levels of the atoms which tunes the energy exchange into resonance at specific values of the electric field (Förster resonances). We excite rubidium atoms to Rydberg states by focusing either a 480 nm beam from a tunable dye laser or a pair of diode lasers into a magneto-optical trap. The trap lies at the center of a configuration of electrodes. We scan the electric field by controlling the voltage on the electrodes while measuring the fraction of atoms that interact. Dipole-dipole interaction spectra are presented for initially excited rubidium $nd$ states for $n=31$ to 46 and for four different pairs of initially excited rubidium $ns$ states. We also present the dipole-dipole interaction spectra for individual rubidium 32$d$ $(j,m_j)$ fine structure levels that have been selectively excited. The data are compared to calculated spectra.

A practical way of writing long sequences of entangled atomic qubits using coherent control with classical light sources is proposed. The method utilizes one-photon vs two-photon interference as a means of controlling the directionality of the motion of valence electrons during molecular dissociation processes. We show that, by dissociating in an optical lattice a one-dimensional array of ultracold diatomic molecules (e.g., ${\mathrm{Na}}_2\to \mathrm{Na}+{\mathrm{Na}}^{*}$), using a combination of photoabsorption of two mutually perpendicularly polarized beams at center frequency $\omega$ and a coherent Raman transition at frequencies ${\omega }_1$ and ${\omega }_2={\omega }_1-\omega$, one can craft entangled states composed of arbitrary superpositions of sequences of atomic states, such as $|f\rangle |f\rangle |b\rangle +\cdots +|b\rangle |b\rangle |f\rangle +\cdots ,$ where $|f\rangle$ designates a dissociation process in which the ground-state Na atom goes in the forward direction and the excited-state Na${}^{*}$ goes in the backward direction, while $|b\rangle$ designates the reverse process, namely, Na going in the backward direction and Na${}^{*}$ going in the forward direction. The method, which on the basis of past work is expected to be robust against decoherence, would enable the encoding of very long sequences of entangled qubits.

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.