In the framework of the trap-size scaling theory, we study the scaling properties of the Bose-Hubbard model in two dimensions in the presence of a trapping potential at finite temperature. In particular, we provide results for the particle density and the density-density correlator at the Mott transitions and within the superfluid phase. For the former quantity, numerical outcomes are also extensively compared to local density approximation predictions.

Bose-Hubbard Hamiltonian of cold two-component Bose gas of spinor chromium atoms is studied. Dipolar interactions of magnetic moments while tuned resonantly by an ultralow magnetic field can lead to a transfer of atoms from the ground to excited Wannier states with a nonvanishing angular orbital momentum. Hence we propose the way of creating $P_x+i{P}_y$ orbital superfluid. The spin introduces an additional degree of control and leads to a variety of different stable phases of the system. The Mott insulator of atoms in a superposition of the ground and vortex Wannier states as well as a superposition of the Mott insulator with orbital superfluid are predicted.

We study a mechanism to create a vorton or three-dimensional skyrmion in phase-separated two-component BECs with the order parameters ${\Psi }_1$ and ${\Psi }_2$ of the two condensates. We consider a pair of a domain wall (brane) and an antidomain wall (antibrane) stretched by vortices (strings), where the ${\Psi }_2$ component with a vortex winding is sandwiched by two domains of the ${\Psi }_1$ component. The vortons appear when the domain wall pair annihilates. Experimentally, this can be realized by preparing the phase separation in the order ${\Psi }_1$, ${\Psi }_2$, and ${\Psi }_1$ components, where the nodal plane of a dark soliton in ${\Psi }_1$ component is filled with the ${\Psi }_2$ component with vorticity. By selectively removing the filling ${\Psi }_2$ component gradually with a resonant laser beam, the collision of the brane and antibrane can be made, creating vortons.

We present a moment expansion for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincaré sphere and provide a scheme for polarization tomography without resorting to full-state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.

Many papers in the 1970s and 1980s state that inner shells cause considerable difficulties in resonance studies with the direct complex-coordinate method, especially for high-$Z$ systems. However, our studies show that after rotating the Hamiltonian into complex space, inner-shell orbitals for atoms are not highly oscillatory. Because of an overall exponential decay, they do not cause grave difficulties in resonance studies. The results depend greatly on the choice of basis set. To demonstrate this, the doubly excited 2$s^2$ ${}^{1}S$ states of He and He-like Ne (Ne${}^{8+}$) are examined with a complex-scaled multireference configuration-interaction method.

We present a procedure for confirming the generation of long strings of photons in an entangled (cluster) state that does not rely on complete state tomography and that works even at low collection efficiencies. The scheme has the added advantage of being passive: it does not require switching of optical elements to perform measurements in different bases, for instance.

The recently realized Bose-Einstein condensate of dysprosium will become a spin-8 spinor condensate at low magnetic fields. In such a high-spin condensate, many phases with different symmetries can exist. Among them the most interesting ones are those with non-Abelian point group symmetry. In this Rapid Communication we discuss the variety of symmetry phases in a spin-8 condensate resulting from numerical solutions of the Hamiltonian. We show that these symmetries can be determined uniquely from the measurements of density population on each spin component in an ultralow magnetic field, together with the measurements of the collective modes in the zero-field limit. This method can also be applied to Bose-Einstein condensates of other magnetic atoms, such as Cr and Er.

It is well known that ultranarrow electromagnetically induced transparency (EIT) resonances can be observed in atomic gases at room temperature. We report here the experimental observation of another type of ultranarrow resonance, as narrow as the EIT ones, in a $\Lambda$ system selected by light polarization in metastable ${}^4$He at room temperature. It is shown to be due to coherent population oscillations in an open two-level system (TLS). For perpendicular linearly polarized coupling and probe beams, this system can be considered as two coupled open TLSs, in which the ground-state populations exhibit antiphase oscillations. We also predict theoretically that in the case of two parallel polarizations, the system would behave like a closed TLS, and the narrow resonance associated with these oscillations would disappear.

We analyze the backaction of homodyne detection and photodetection on superconducting qubits in circuit quantum electrodynamics. Although both measurement schemes give rise to backaction in the form of stochastic phase rotations, which leads to dephasing, we show that this can be perfectly undone provided that the measurement signal is fully accounted for. This result improves on an earlier one [Phys. Rev. A 82, 012329 (2010)], showing that the method suggested can be made to realize a perfect two-qubit parity measurement. We propose a benchmarking experiment on a single qubit to demonstrate the method using homodyne detection. By analyzing the limited measurement efficiency of the detector and bandwidth of the amplifier, we show that the parameter values necessary to see the effect are within the limits of existing technology.

We theoretically explore the external electric field control of a species of ultralong-range molecules that emerge from the interaction of a ground-state polar molecule with a Rydberg atom. The external field mixes the Rydberg electronic states and, therefore, strongly alters the electric field seen by the polar diatomic molecule due to the Rydberg electron. As a consequence, the adiabatic potential energy curves responsible for the molecular binding can be tuned in such a way that an intersection with neighboring curves occurs. The latter leads to admixture of $s$-wave character in the Rydberg wave function and will substantially facilitate the experimental preparation and realization of this particular class of Rydberg molecule species.

Polarizabilities and Verdet constants are calculated using a relativistic particle-hole configuration-interaction (CI) method. Particle-hole CI is saturated by including quasicontinuum states built by enclosing an atom in a cavity. Agreement with experiment is achieved, and the method is more accurate than, for example, the Hartree-Fock method. The accuracy of the particle-hole CI method is limited by the omission of configurations with double excitations. Perturbation theory can be applied to account for these excitations, and we expect in the future to further improve the accuracy. The method can be also applied to the calculations of polarizabilities of excited states and can be generalized to other open-shell atoms.

Nonrelativistic energies for the low-lying states of lithium are calculated using the variational method in Hylleraas coordinates. Variational eigenvalues for the infinite nuclear mass case with up to 34 020 terms are $-7.478060323910147\left(1\right)$ a.u. for $1s^{2}2s{}^{2}S$, $-7.35409842144437\left(1\right)$ a.u. for $1s^{2}3s{}^{2}S$, $-7.31853084599891\left(1\right)$ a.u. for $1s^{2}4s{}^{2}S$, $-7.41015653265241\left(4\right)$ a.u. for $1s^{2}2p{}^{2}P$, and $-7.335523543524688\left(3\right)$ a.u. for $1s^{2}3d{}^{2}D$. The selection of the minimum set of angular momentum configurations is discussed, with the $2P$ and $3D$ states as examples to demonstrate the impact of various configurations on the variational energies. It is shown by numerical example that the second spin function (i.e., coupled to form a triplet intermediate state) has no significant effect on either the variational energies or the spin-dependent Fermi contact term. Results of greatly improved accuracy for the Fermi contact term are presented for all the states considered.

Proton collisions with water molecules are analyzed at impact energies ranging from 20 keV to several MeV to distinguish fragmentation patterns in collisions involving capture and ionization. Solutions of the time-dependent Schrödinger equation restricted to an independent-electron model are complemented with a fragmentation model for water molecules. Recent measurements can be explained when electron processes up to triple electron removal are taken into account.

The valence orbitals of the iodine molecule (I${}_2$) have been studied using the high-resolution electron-momentum spectroscopy at impact energies of 1200 and 600 eV. Experimental momentum distributions of outer valence orbitals were compared with the nonrelativistic, scalar relativistic, and spin-orbital relativistic calculations, as well as the relativistic pseudopotential calculation. The experimental cross-section ratios of $8J_g^{3/2}$ to $17J_g^{1/2}$, $8J_u^{3/2}$ to $16J_u^{1/2}$, and the electron-momentum profiles of orbital $16J_g^{1/2}$ clearly manifested the relativistic effects. In the inner valence region, the symmetry-adapted-cluster configuration-interaction theory was used to interpret the ionization spectrum and the electron-momentum distributions.

We study the interplay of squeezing and phase randomization near the hyperbolic instability of a two-site Bose-Hubbard model in the Josephson interaction regime. We obtain results for the quantum Zeno suppression of squeezing far beyond the previously found short time behavior. More importantly, we contrast the expected outcome with the case where randomization is induced by erratic driving with the same fluctuations as the quantum noise source, finding significant differences. These are related to the distribution of the squeezing factor, which has log-normal characteristics: hence its average is significantly different from its median due to the occurrence of rare events.

We use the Bogoliubov–de Gennes formalism and study the ground-state phases of trapped spin-orbit-coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba-type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e., $\uparrow$ and $\downarrow$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular Bose-Einstein-condensate limit, which can be achieved by increasing either the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in the $x$ and $y$ directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral $p$-wave superfluids and superconductors.

A scheme is discussed that allows for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe laser setup, which both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, the amplitude of which is proportional to the condensate fraction of the quantum gas. The setup can be extended to measure the first-order correlation function of a quantum gas. The dynamics discussed here makes use of the entanglement between atoms and photons, which is established by the scattering process in order to access detailed information on the quantum state of matter.

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second-order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal; however, the entropy changes as a function of the rotation or synthetic magnetic-field strength.

The Husimi distribution is proposed for a phase-space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp signatures of the quantum phase transition. The analysis is done using two frameworks: a numerical treatment and an analytical variational approximation. Additionally, we propose a characterization of the Dicke model quantum phase transition by means of the zeros of the Husimi distribution in the variational approach.