We derive a general linear-response many-body theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented Bose-Einstein condensates (BECs). To obtain the linear-response equations we linearize the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method, which provides a self-consistent description of many-boson systems in terms of orbitals and a state vector (configurations), and is in principle numerically exact. The derived linear-response many-body theory, which we term LR-MCTDHB, is applicable to systems with interaction potentials of general form. For the special case of a $\delta$ interaction potential we show explicitly that the response matrix has a very appealing bilinear form, composed of separate blocks of submatrices originating from contributions of the orbitals, the state vector (configurations), and off-diagonal mixing terms. We further give expressions for the response weights and density response. We introduce the notion of the type of excitations, useful in the study of the physical properties of the equations. From the numerical implementation of the LR-MCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubov–de Gennes (BdG) equations. The derived theory is first applied to study BECs in a one-dimensional harmonic potential. The LR-MCTDHB method contains the BdG excitations and, also, predicts a plethora of additional many-body excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow one-dimensional double-well potential. We find with LR-MCTDHB low-lying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LR-MCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.

We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving nonperturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate $T_c$ and a vanishing diatom condensate $T^{☆}$. The second-order phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature $T_c$ exhibits a quantum phase transition, where $T_c$ goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than $T_c$ and less than $T_0$, the critical temperature of the noninteracting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of ab initio Monte Carlo simulations.

Propagation of polarized vortex light beams in a rotationally symmetric graded-index optical waveguide is investigated by solving analytically the three-component field Maxwell's equations. An operator approach to calculate the average values describing the propagating beams is developed. Polarization-dependent transmission associated with spin-orbit interaction for left- and right-handed circularly polarized Gauss-Laguerre light beams is shown.

We investigate the nonlinear propagation of femtosecond laser filaments created at central wavelengths between 0.8 and 8 $\mu$m in a pressurized argon gas. Attention is paid to spectral broadenings and self-compression of mid-infrared pulses. It is shown that the longer the central wavelength is, the more efficient the pulse compression is. Three key mechanisms entering the spectral dynamics, i.e., low-order-harmonic generation, four-wave mixing, and self-steepening, are discussed.

We propose a scheme that exploits the combined effects of nonlinear dynamics and dissipation to generate macroscopic quantum superpositions in massive optomechanical oscillators. The effective degenerate three-wave mixing interaction between the mechanical and optical cavity modes that results from quadratic optomechanical coupling, together with the cavity dissipation, can result in the existence of dark macroscopic superpositions. We show analytically and confirm numerically that various quantum superpositions can be achieved deterministically, depending on the initial state of the mechanics. The effects of mechanical damping are also studied in detail and quantified by the negativity of the Wigner function. The present scheme can be realized in various optomechanical systems with current technology.

A study is made of frequency-comb generation described by the driven and damped nonlinear Schrödinger equation on a finite interval. It is shown that frequency-comb generation can be interpreted as a modulational instability of the continuous-wave pump mode, and a linear stability analysis, taking into account the cavity boundary conditions, is performed. Further, a truncated three-wave model is derived, which allows one to gain additional insight into the dynamical behavior of the comb generation. This formalism describes the pump mode and the most unstable sideband and is found to connect the coupled mode theory with the conventional theory of modulational instability. An in-depth analysis is done of the nonlinear three-wave model. It is demonstrated that stable frequency-comb states can be interpreted as attractive fixed points of a dynamical system. The possibility of soft and hard excitation states in both the normal and the anomalous dispersion regime is discussed. Investigations are made of bistable comb states and the dependence of the final state on the way the comb has been generated. The analytical predictions are verified by means of direct comparison with numerical simulations of the full equation and the agreement is discussed.

We have measured the ratios of doubly to singly charged molecular parent ions of azulene and phenanthrene, which are isomers of naphthalene and anthracene, respectively. The photon-energy dependences of the ratio curves have been analyzed and compared to each other from threshold to the carbon $K$ edge. Qualitatively, the ratio curves for azulene and naphthalene as well as phenanthrene and anthracene are very similar, but we have found a distinct quantitative difference in both cases for the two isomers.

Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarization states of single photons has been widely used as these states form a natural closed two-state qubit. However, photons are able to encode much more—in principle, infinite—information via the continuous spatiotemporal degrees of freedom. Here we consider the information capacity of an optical quantum channel, such as an optical fiber, where a spectrally encoded single photon is the means of communication. We use the Holevo bound to calculate an upper bound on the channel capacity, and relate this to the spectral encoding basis and the spectral properties of the channel. Further, we derive analytic bounds on the capacity of such channels, and, in the case of a symmetric two-state encoding, calculate the exact capacity of the corresponding channel.

A programmable architecture called “quantum FPGA (field-programmable gate array)” (QFPGA) is presented for quantum computing, which is a hybrid model combining the advantages of the qubus system and the measurement-based quantum computation. There are two kinds of buses in QFPGA, the local bus and the global bus, which generate the cluster states and general multiqubit rotations around the $z$ axis, respectively. QFPGA consists of quantum logic blocks (QLBs) and quantum routing channels (QRCs). The QLB is used to generate a small quantum logic while the QRC is used to combine them properly for larger logic realization. Considering the error accumulating on the qubus, the small logic is the general two-qubit quantum gate. However, for the application such as $n$-qubit quantum Fourier transform, one QLB can be reconfigured for four-qubit quantum Fourier transform. Although this is an implementation-independent architecture, we still make a rough analysis of its performance based on the qubus system. In a word, QFPGA provides a general architecture to integrate different quantum computing models for efficient quantum logic construction.

We report a nuclear magnetic resonance experiment, which simulates the quantum transverse Ising spin system in a triangular configuration, and further demonstrate that multipartite quantum correlations can be used to distinguish between the frustrated and the nonfrustrated regimes in the ground state of this system. Adiabatic state preparation methods are used to prepare the ground states of the spin system. We employ two different multipartite quantum correlation measures to analyze the experimental ground state of the system in both the frustrated and the nonfrustrated regimes. As expected from theoretical predictions, the experimental data confirm that the nonfrustrated regime shows higher multipartite quantum correlations compared to the frustrated one.

Fourier transform records of $A{}^1{\Sigma }_u^{+}-b{}^3{\Pi }_u\to X{}^1{\Sigma }_g^{+}$ and $\left(2\right){}^1{\Pi }_g\to A{}^1{\Sigma }_u^{+}-b{}^3{\Pi }_u$ laser-induced fluorescence in hot rubidium vapor have identified more than 4500 rovibronic term values in the spin-orbit-coupled $A{}^1{\Sigma }_u^{+}$ and $b{}^3{\Pi }_u$ states of Rb${}_2$. We report a 4×4 coupled-channel deperturbation analysis of some 6100 term energies in ${}^{85}$Rb${}_2$ and ${}^{85}$Rb${}^{87}$Rb, including term values taken from papers by Salami et al. [Phys. Rev. A 80, 022515 (2009)], Amiot et al. [Phys. Rev. Lett. 83, 2316 (1999)], and Amiot [J. Chem. Phys. 93, 8591 (1990)]. Spin-orbit and spin-rotation interactions between $A{}^1{\Sigma }_u^{+}$ and $b{}^3{\Pi }_{u(\Omega =0,1,2)}$ are taken into account explicitly, fitting to analytical potential curves of the interacting $A{}^1{\Sigma }_u^{+}$ and $b{}^3{\Pi }_{0u}$ states and to $r$-dependent diagonal and off-diagonal spin-orbit-coupling functions. The resulting mass-invariant fitting parameters reproduce 96% of all available experimental term values of the $A-b$ complex for all Rb${}_2$ isotopologs (covering 93% of the $A{}^1{\Sigma }_u^{+}$ potential energy well) with a standard deviation of 0.005 cm${}^{-1}$, matching experimental uncertainties estimated to be $\le$$0.01$ cm${}^{-1}$.

We have measured and calculated fully differential cross sections for target ionization in 16-MeV O${}^{7+}$+He and 24-MeV O${}^{8+}$+Li collisions. As in previous studies, in the case of the He target we observe a pronounced forward shift in the angular distribution of the electrons relative to the direction of the momentum transfer q at small $q$ ($q$ < 1 a.u.). An unexpected result is that we also find a strong forward shift at large $q$ ($q$ > 2 a.u.), while at intermediate $q$ this shift becomes very weak or even turns into a backward shift. For the Li target, in contrast, the forward shift monotonically increases with increasing $q$. These observations are qualitatively reproduced by our calculations. The comparison to theory suggests that at large $q$ the forward shift is due to the postcollision interaction between the outgoing projectile and the ejected electron, but at small $q$ it is mostly due to an interplay between the projectile-target core interaction and the electron-target core interaction.

In this work, a broadband 1071 nm crossed optical dipole trap was loaded simultaneously from a two-atomic-species K-Rb magneto-optical trap. The number of atoms loaded into the dipole trap, for both species, was characterized as a function of different laser parameters and loading procedures. The best observed loading procedure for K is explained by the ac Stark shift of the hyperfine states involved in the $D_2$ transition. For the optimum conditions, the dipole trap has about $3\times {10}^6$ ${}^{39}$K atoms at an atomic density of $7\times {10}^{12}$ cm${}^{-3}$ and $2\times {10}^6$ Rb atoms at an atomic density of $5\times {10}^{12}$ cm${}^{-3}$, with temperatures of 22 and 10 $\mu$K, respectively. Finally, by studying the time evolution of both species trapped in the crossed optical dipole trap, we have observed a nonexponential decay associated with heteronuclear two-body losses. Such losses may be due to KRb photoassociation by the broadband 1071 nm laser.

The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which are responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibrium of a magneto-optical trap, allowing us to describe the crossover between the two limiting cases: temperature-dominated and multiple-scattering-dominated traps. The normal collective modes of the system are also computed.

We obtain optical instabilities in all-optical bistable systems arising from competing cooperative pathways at low input light levels. In particular, for three-level atomic systems in the $\Lambda$ and V configuration interacting with two independent cavity modes, we identify the necessary conditions related to the incoherent pathways required to obtain instabilities. The instabilities arise when atomic states involved in the bistable transition are leaky and have substantial population, where the incoherent processes directly hinder the cooperative preparation of the atomic ensemble.

The main features of the light scattering from a Bose-Einstein condensate are analyzed. In particular, we show that the intensity of superradiant scattering critically depends on the recoil frequency shift and that, in turn, determines the time scale of the scattered pulse.

We study the finite-temperature dynamical structure factor $S(k,\omega )$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\omega )$ has a width $\propto$${\left|k\right|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.

The quantum measurement problem still finds no consensus. Nonlocal interferometry provides an unprecedented experimental probe by entangling two photons in the “measurement state” (MS). The experiments show that each photon measures the other; the resulting entanglement decoheres both photons; decoherence collapses both photons to unpredictable but definite outcomes; and the two-photon MS continues evolving coherently. Thus, when a two-part system is in the MS, the outcomes actually observed at both subsystems are definite. Although standard quantum physics postulates definite outcomes, two-photon interferometry verifies them to be not only consistent with, but also actually a prediction of, the other principles. Nonlocality is the key to understanding this. As a consequence of nonlocality, the states we actually observe are the local states. These actually observed local states collapse, whereas the global MS, which can be “observed” only after the fact by collecting coincidence data from both subsystems, continues its unitary evolution. This conclusion implies a refined understanding of the eigenstate principle: Following a measurement, the actually observed local state instantly jumps into the observed eigenstate. We also discuss and rebut objections to this.

We analyze two classes of Einstein-Podolsky-Rosen (EPR)-steering inequalities, the violation of which can be used to demonstrate EPR-steering with an entangled two-qubit Werner state: linear inequalities and quadratic inequalities. We discuss how post-selection of results (by appeal to the fair sampling assumption) can compromise the rigor of these inequalities in experimental tests of EPR-steering. By considering the worst-case scenarios in which detector inefficiency or other loss could be exploited within a local hidden-state model, we derive inequalities that enable rigorous but loss-tolerant demonstrations of EPR-steering. The linear inequalities, and special cases of the quadratic inequalities, have been used in recent experiments. Our results indicate that regardless of the number of settings used, quadratic inequalities are never better, and often worse, than linear inequalities.

We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded, perspective from which to understand the elements of the traditional approach. We first show that in principle all measurable probabilities and correlations can be expressed entirely in terms of quantum instruments without the need for conventional quantum states or observables. We then show how these states and observables reappear as derived quantities by conditioning joint detection probabilities on the first or last measurement in a sequence as a preparation or a postselection. Both predictive and retrodictive versions of states and observables appear in this manner, as well as more exotic bidirectional and interdictive states and observables that cannot be easily expressed using the traditional approach. We also revisit the conceptual meaning of the Heisenberg and Schrödinger pictures of time evolution as applied to the various derived quantities, illustrate how detector loss can be included naturally, and discuss how the instrumental approach fully generalizes the time-symmetric two-vector approach of Aharonov et al. to any realistic laboratory situation.