We study spin-1/2 fermions, interacting via a two-body contact potential, in a one-dimensional harmonic trap. Applying exact diagonalization, we investigate their behavior at finite interaction strength and discuss the role of the ground-state degeneracy which occurs for sufficiently strong repulsive interaction. Even low temperature or a completely depolarizing channel may then dramatically influence the system's behavior. We calculate level occupation numbers as signatures of thermalization, and we discuss the mechanisms to break the degeneracy.

For the dynamics of Bose-Einstein condensates (BECs), differences between mean-field (Gross-Pitaevskii) physics and $N$-particle quantum physics often disappear if the BEC becomes larger and larger. In particular, the time scale for which both dynamics agree should thus become larger if the particle number increases. For BECs in a double-well potential, we find both examples for which this is the case and examples for which differences remain even for huge BECs on experimentally realistic short time scales. By using a combination of numerical and analytical methods, we show that the differences remain visible on the level of expectation values even beyond the largest possible numbers realized experimentally for BECs with ultracold atoms.

Current theoretical treatments of mode splitting and scattering loss resulting from subwavelength scatterers attached to the surface of high-quality-factor whispering-gallery-mode microresonators are not satisfactory. Different models proposed for distinct scatterer regimes cannot be reconciled. In addition, many experimental results are difficult to understand within the existing theoretical framework. Here, we develop a unified approach that applies to an arbitrary number of scatterers. Comparison with the existing theoretical models reveals their applicable conditions and limits. Moreover, many new understandings on the mode splitting and scattering loss are achieved, which are supported by numerical and experimental evidence.

The propagation of a spatially inhomogeneous few-cycle laser field, linked to surface plasmon polaritons, through an ensemble of quantum wells is investigated under two conditions. It is found that the transmitted spectra sensitively depend on the spatial inhomogeneity due to the nonlinear propagation effects. Under the small-frequency mismatch condition, the transmitted spectral distribution is continuous for the spatially homogeneous case. However, when spatial inhomogeneity is introduced, the distribution is discrete instead, with clearly even- and odd-order harmonic peaks coexisting, which is related to the strong-field reshaping effect and the inversion symmetry breaking due to the introduction of the spatially inhomogeneous field. As for the large-frequency mismatch condition, only odd-order harmonics exist, no matter how strong the spatial inhomogeneity is. Under both conditions, the propagation effect can obviously enhance the intensity of higher spectral components.

We demonstrate detection of a weak alternate-current magnetic field by application of the spin-echo technique to $F=2$ Bose-Einstein condensates. A magnetic field sensitivity of 12 pT$/\sqrt{\mathrm{Hz}}$ is attained for an atom number of $5\times {10}^3$ at a spatial resolution of 100 $\mu$m${}^2$. Our observations indicate magnetic field fluctuations synchronous with the power supply line frequency. We show that this noise is greatly suppressed by application of a reverse phase magnetic field. Our technique is useful in order to create a stable magnetic field environment, which is an important requirement for atomic experiments which require a weak bias magnetic field.

We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single nondegenerate two-level system. We analyze how the binary degree of freedom perturbs the free evolution of the wave packet producing decoherence, which is quantified by the Loschmidt echo. This magnitude measures the reversibility of a perturbed quantum evolution. In particular, we use it here to study the relative “fragility” of coherent superpositions (cat states) with respect to incoherent ones. This fragility or sensitivity turns out to increase exponentially with the energy separation of the two components of the superposition.

Transmission of quantum states is a central task in quantum information science. Remote state preparation (RSP) has the same goal as teleportation, i.e., transferring quantum information without sending physically the information carrier, but in RSP the sender knows the state which is to be transmitted. We present experimental demonstrations of RSP for two and three locations. In our experimental scheme Alice (the preparer) and her three partners share four and six photon polarization entangled singlets. This allows us to perform RSP of two or three copies of a single-qubit state, a two-qubit Bell state, and a three-qubit $W$, or $\overline{W}$ state. A possibility to prepare two-qubit nonmaximally entangled and GHZ states is also discussed. The ability to remotely prepare an entangled states by local projections at Alice is a distinguishing feature of our scheme.

We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform ($d+1$) mutually unbiased measurements in a classically simulated prepare-and-measure scheme and on a pair of entangled photons for dimensions ranging from $d=2$ to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver, and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon. However, we find that the benefit of increasing the dimension is limited by practical implementation considerations, which in our case results in deleterious effects observed beyond a dimension of $d=4$.

We construct optimal time-local control pulses based on a multipartite entanglement measure as target functional. The underlying control Hamiltonians are derived in a purely algebraic fashion, and the resulting pulses drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mechanism, and which bears entanglement that is robust against decoherence. Moreover, it is shown that the control scheme is insensitive to experimental imperfections in first order.

An important method for search engine result ranking works by finding the principal eigenvector of the “Google matrix.” Recently, a quantum algorithm for generating this eigenvector as a quantum state was presented, with evidence of an exponential speedup of this process for some scale-free networks. Here we show that the run time depends on features of the graphs other than the degree distribution, and can be altered sufficiently to rule out a general exponential speedup. According to our simulations, for a sample of graphs with degree distributions that are scale-free, with parameters thought to closely resemble the Web, the proposed algorithm for eigenvector preparation does not appear to run exponentially faster than the classical case.

We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat $\pi$ pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols.

We study the surface modes of a homogenous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that supports spectral singularities. Because the latter have a divergent quality factor, we call them the singular gallery modes. We show that they can be excited using arbitrarily small amounts of gain, and as a result, the system lacks a lasing threshold, effectively. This shows that we can realize spectral singularities in the surface modes of extremely small spherical samples with modest amounts of gain. We also examine the possibility of exciting singular gallery modes with different wavelengths using the same amount of gain. This corresponds to the situation where the system undergoes simultaneous lasing at different wavelengths.

We analyze the dynamics of a superconducting qubit and the phenomenon of multiorder Rabi oscillations in the presence of a time-modulated external field. Such a field is also presented as a bichromatic field consisting of two spectral components, which are symmetrically detuned from the qubit resonance frequency. This approach leads to obtaining qualitative quantum effects beyond those for the case of monochromatic excitation of qubits. We calculate Floquet states and quasienergies of the composite system “superconducting qubit plus time-modulated field” for various resonant regimes. We analyze the dependence of quasienergies from the amplitude of an external field, demonstrating the zeros of difference between quasienergies. We show that, as a rule, populations of qubit states exhibit aperiodic oscillations, but we demonstrate the specific important regimes in which dynamics of populations becomes periodically regular.

We report a detailed investigation on the properties of intensity correlation spectra for laser beams interacting with cold atoms under the condition of electromagnetically induced transparency (EIT). We describe the transition of their intensity fluctuations from correlation to anticorrelation as the mean intensity of the fields increases. Such a transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anticorrelation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magneto-optical traps, one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in $\Lambda$ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.

We theoretically study the dynamical behavior of semiconductor ring lasers coupled by a single bus waveguide, both when weakly coupled and when strongly coupled. We provide a detailed analysis of the multistable landscape in the coupled system, analyze the stability of all solutions, and relate the internal dynamics in the individual lasers to the field effectively measured at the output of the waveguide. We show that coupling phases close to $\pi /2$ generally promote instabilities. Finally, our analysis enables us to discuss the advantages and disadvantages for optical memory operation of coupled semiconductor ring lasers versus solitary ones.

The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons $\overline{n}\lesssim 1$. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.

The amplification of high-order-harmonics (HOH) seed pulses in a swept-gain XUV laser is investigated through numerical simulations of the full set of Bloch and two-dimensional paraxial propagation equations with our code colax. The needed atomic data are taken from a hydrodynamics and collisional-radiative simulation in the case of a Ni-like Ag plasma created from the interaction of an infrared laser with a solid target and pumped in the transient regime. We show that the interplay of strong population inversion and diffraction or refraction due to the short transverse dimensions and steep density gradient of the active plasma can lead to the amplification of an intense, ultrashort, quasi-“$\pi$” pulse triggered by the incoming seed. By properly tuning the system geometry and HOH pulse parameters, we show that an $\simeq$10 fs, $8\times {10}^{12}$ W/cm${}^2$ amplified pulse can be achieved in a 3-mm-long Ni-like Ag plasma, with a factor of $\gtrsim$10 intensity contrast with respect to the longer-lasting wake radiation and amplified spontaneous emission.

I compute the index of refraction, the light-velocity slowing factor, and the group-velocity dispersion in a medium of glass doped with silver spherical nanoshells coated with CuCl in the spectral region separating the real parts of the semiconductor-dressed excitonic daughters’ eigenfrequencies. Slowing of light by more than three orders of magnitude is observed.

Closed-form analytical expressions for the electric and magnetic (EM) field components of a high-order Bessel vortex beam of fractional type α (HOBVB-Fα) are derived based on the axial polarization of the vector potentials [denoted by ($z,-z$)]. The fields’ components correspond to the most generalized case of quasi-standing-waves that reduce to perfect (i.e., equiamplitude) standing waves or progressive waves with appropriate choice of the quasi-standing-wave coefficient $0\le {\rm Y}\le 1$. The beam components are exact solutions of the vector wave equation (Helmholtz equation) and Maxwell's equations. Moreover, computations of the EM components and comparison with the results obtained from a transverse polarization scheme [denoted by (x,−y)] illustrate the analysis. In addition, the time-averaged angular momentum density and flux are evaluated with particular emphasis on the axial and transverse polarization states of the vector potentials. It is found that the quasi-standing-wave effect does not influence the spatial distributions of the EM components in the transverse polarization scheme (x,−y); however, it affects the transverse EM field components in the axial polarization (z,−z). Moreover, both the linear and angular momenta density fluxes are shown to reverse sign for a particular value of the half-cone angle β. These phenomena anticipate the production of a “tractor” beam where particulate matter may be pulled back toward the source, and a spinning reversal effect in which particulate matter may rotate with opposite handedness to a HOBVB-Fα. The results are particularly useful in applications involving optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque.

In this Rapid Communication we study the transient dynamics of a Bose superfluid subsequent to an interaction quench. Essential for equilibration is a source of dissipation which we include following the approach of Caldeira and Leggett. Here we solve the equations of motion exactly by integrating out an environmental bath. We thereby derive precisely the time dependent density correlation functions with the appropriate analytic and asymptotic properties. The resulting structure factor exhibits the expected damping and thereby differs from that of strict Bogoliubov theory. These damped sound modes, which reflect the physics beyond mean-field approaches, are characterized and the structure factors are found to compare favorably with experiment.