The spectral properties of su(2) Hamiltonians are studied for energies near the critical classical energy ${\epsilon }_c$ for which the corresponding classical dynamics presents hyperbolic points. A general method leading to an algebraic relation for eigenvalues in the vicinity of ${\epsilon }_c$ is obtained in the thermodynamic limit, when the semiclassical parameter $n^{-1}={\left(2s\right)}^{-1}$ goes to zero (where $s$ is the total spin of the system). Two applications of this method are given and compared with numerics. Matrix elements of observables, computed between states with energy near ${\epsilon }_c$, are also computed and shown to be in agreement with the numerical results.

Based on the exact results obtained by Bethe ansatz, we demonstrate the existence of stable bound-pair (BP) wave packet in Bose-Hubbard model with arbitrary on-site interaction $U$. In large-$U$ regime, it is found that an incoming single-particle can coherently pass through a BP wave packet and leave a coherent shift in the position of it. This suggests a simple scheme for constructing a BP charge qubit to realize a quantum switch, which is capable of controlling the coherent transport of one and only one photon in a one-dimensional waveguide.

We present an approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body systems by constructing the explicit finite quantum circuits that diagonalize their dynamics. As a particularly simple instance, the full dynamics of a one-dimensional Quantum Ising model in a transverse field with four spins is shown to be reproduced using a quantum circuit of only six local gates. This opens up the possibility of experimentally producing strongly correlated states, their time evolution at zero time, and even thermal superpositions at zero temperature. Our method also allows one to uncover the exact circuits corresponding to models that exhibit topological order and to stabilizer states.

We analyze the operation of a switching-based detector that probes a qubit’s observable that does not commute with the qubit’s Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytical results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit’s energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.

We study the robustness of a fault-tolerant quantum computer subject to Gaussian non-Markovian quantum noise, and we show that scalable quantum computation is possible if the noise power spectrum satisfies an appropriate “threshold condition.” Our condition is less sensitive to very-high-frequency noise than previously derived threshold conditions for non-Markovian noise.

The effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a different model is presented, inspired by perfect quantum state transfer in qubit networks. A perturbative solution is found for the dynamics of this model which is not of a tensor-product form. In contrast to previous results, the hitting probability has a lower bound that is independent of the hypercube dimension.

In this work we report variational calculations of the two lowest vibrational states of the HD molecule within the framework that does not assume the Born-Oppenheimer (BO) approximation. The nonrelativistic energies of the states were corrected for the relativistic effects of the order of ${\alpha }^2$ (where $\alpha =\frac{1}{c}$), calculated as expectation values of the operators representing these effects with the nonrelativistic non-BO wave functions. The non-BO wave functions were expanded in terms of the one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. The $v=0\to 1$ transition energy obtained in the calculations is compared with the previous calculations, as well as with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in $\alpha$ to further improve the agreement between the theory and the experiment.

The stability of the ground state of three-unit charge $q_i=\pm 1,\pm 1\mp 1$, interacting through a statically screened Coulomb potential, has been studied as a function of the values of the constituent masses for different values of the screening parameter. General conditions are given and accurate variational calculations have been performed to determine the region where the three-body ground state is Borromean. The possible existence of Efimov states when the screening parameter is equal to the two-body critical screening parameter is discussed. The critical exponent for the energy in different regions of the stability diagram has been also calculated.

We analyze a narrow Feshbach resonance with ultracold chromium atoms colliding in $d$ wave. The resonance is made possible by dipole-dipole interactions, which couple an incoming $l=2$ collision channel with a bound molecular state with $l=0$. We find that three-body losses associated with this resonance increase with temperature, and that the loss feature width as a function of magnetic field also increases linearly with temperature. The analysis of our experimental data shows that the Feshbach coupling is small compared both to the temperature and to the density limited lifetime of the resonant bound molecular state. One consequence is that the three-body loss rate is proportional to the square of the number of atoms, and that we can directly relate the amplitude of the losses to the Feshbach coupling parameter. We compare our measurement to a calculation of the coupling between the collisional channel and the molecular bound state by dipole-dipole interactions, and find a good agreement, with no adjustable parameter. An analysis of the loss line shape is also performed, which enables to precisely measure the position of the resonance.

Closed-form analytic formulas are derived in the tunneling limit for both above-threshold detachment (ATD) of negative ions and above-threshold ionization (ATI) of neutral atoms. These formulas are shown to give precise agreement with essentially exact single-active-electron numerical results for detached or ionized electron energies corresponding to the high-energy end of the ATD and ATI plateaus (with only a small constant shift of electron energies being required in the case of ATI). These formulas for ATI and ATD rates thus provide an analytic explanation for the well-known oscillatory patterns of ATI and ATD rates as functions of electron energy and of the parameters of the laser field. They also provide an analytic explanation for the dependence of these rates on the initial orbital angular momentum of the active electron. Most significantly, these formulas provide a fully quantum justification of the well-known classical three-step scenario for strong-field ionization and detachment spectra in the high-energy region of the ATI or ATD plateau.

We present measurements of the absolute photoionization cross section of the neonlike ${\text{Si}}^{4+}$ ion over the 110–184 eV photon energy range. The measurements were performed using two independent merged-beam setups at the super-ACO and ASTRID synchrotron-radiation facilities, respectively. Signals produced in the photoionization of the $2p$ subshell of the ${\text{Si}}^{4+}$ ion both from the $2p^6{{}^{1}S}_0$ ground state and the $2p^{5}3s{{}^{3}P}_{0,2}$ metastable levels were observed. Calculations of the $2p$ photoionization cross sections were carried out using a multi-configuration Dirac-Fock code. They give results in good agreement with the measured spectra. Comparison with other available theoretical results is also presented.

We propose to create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can be qualitatively described by a simple three-level rapid adiabatic passage model.

We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the “swapping” of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\pi$ modes.

We propose a Hamiltonian of ultracold spinless atom in optical lattices including the two-body interaction of nearest neighbors, which reduces to the Bose-Hubbard model in weak-interaction limit. An atom-pair hopping term appearing in the Hamiltonian explains naturally the recent experimental observation of correlated tunneling in a double-well trap with strong atom-atom interactions and moreover leads to a dynamic process of atom-pair tunneling where strongly interacting atoms can tunnel back and forth as a fragmented pair. Finally a dynamics of oscillations induced by the atom-pair tunneling is found in the strong interaction regime, where the Bose-Hubbard model gives rise to the insulator state with fixed time-averaged value of atom-occupation number only. Quantum phase transitions between two quantum phases characterized by degenerate and nondegenerate ground states are shown to be coinciding with the Landau second-order phase-transition theory. In the system of finite atom number the degeneracy of ground states can be removed by quantum tunneling for the even number of atoms but not for the odd number.

We present an all-fiber source of frequency-entangled photon pairs by using four-wave mixing in a Sagnac fiber loop. Special care is taken to suppress the impurity of the frequency entanglement by cooling the fiber and by matching the polarization modes of the photon pairs counterpropagating in the fiber loop. Coincidence detection of signal and idler photons, which are created in pair and in different spatial modes of the fiber loop, shows the quantum interference in the form of spatial beating, while the single counts of the individual signal (idler) photons keep constant. When the production rate of photon pairs in each propagation direction of the fiber loop is about 0.065 pairs/pulse, the envelope of the quantum interference reveals a visibility of $(95\pm 2)\%$, which is close to the calculated theoretical limit 98.7%.

We investigate, both numerically and experimentally, the optical parametric generation (OPG) process in second-order nonlinear crystals driven by femtosecond pulses. We model the OPG process by solving the coupled second-order three-wave nonlinear propagation equations in the plane-wave limit, using noise fields to mimic the vacuum fluctuations. We focus on two parameters: (i) the temporal jitter between the OPG and the pump pulse; (ii) the carrier-envelope phase (CEP) relationship between the OPG and the pump pulse. Both numerical simulations and experiments support the following conclusions: (i) in the regime of low pump depletion the OPG pulse is synchronized with the pump, but its energy presents strong fluctuations; (ii) in the regime of high pump depletion, the energy of the OPG pulse stabilizes, but a temporal jitter with respect to the pump pulse is introduced; (iii) in both cases, the CEP relationship between pump and OPG pulses is completely random.

A cavity soliton laser is a device able to generate single-peak localized structures, also called cavity solitons, without the injection of an external coherent beam. We realized experimentally a cavity soliton laser by mutually coupling in face to face configuration two broad-area vertical cavity surface emitting lasers, one set to work as amplifier while the second, biased below transparency, plays the role of a saturable absorber. We explore the parameter space, showing the robustness of cavity solitons in this system, and we analyze their switching process. We also report on structures pulsing at the roundtrip time of the compound cavity defined by the two devices. Despite these structures look very similar to cavity solitons in terms of the time-averaged intensity profile, they cannot be interpreted as pulsing cavity solitons since there is no bistability associated with them.

The photoionization in a few-cycle pulse above the saturation intensity is investigated. It is found that, in the oversaturation regime, the direct electrons exhibit distinct cutoffs in the left and right directions and the fast-direct electrons around the cutoff show an asymmetry as strong as the rescattering electrons. This asymmetry depends sensitively on the carrier-envelope phase (CEP). Based on these features, we propose an efficient method for CEP measurement with direct electrons, which is 4 orders of magnitude higher than the rescattering electrons. Therefore, this method is more powerful and enables the CEP measurement on a single-shot basis.

We develop the theory of the Poynting singularities (critical points of the Poynting vector) extending the theory of dynamic systems to classify and analyze optical singularities. An optical dynamic system is described by the three first-order differential equations for the image point, with the tangent to the image point trajectory being the Poynting vector. Important feature of the Poynting singularities is the existence of the polarization-induced singularities (arise due to the specific field polarization) along with the field-induced ones (appear owing to the vanishing the fields). We analyze not only isolated critical points, but the manifolds of singularities forming lines and surfaces as well. We define the types of the singular points (vortex, saddle, sink, source, and focus) using the trace and determinant of the stability matrix. Such a criterion and the study of the dependence on parameter (bifurcations) are applied for a number of examples. We offer to study the chaotic dynamic of the image point in future.

It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path symmetry is conserved under phase shifts, the maximal phase sensitivity can be achieved at arbitrary bias phases, indicating that path-symmetric states can achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely unknown phase.