We present a systematic investigation of attractive binary mixtures in the presence of both spin- and mass-imbalance in one-dimensional setups described by the Hubbard model. After discussing typical cold atomic experimental realizations and the relation between microscopic and effective parameters, we study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures such as density profiles, momentum distributions, and correlation functions by means of density-matrix-renormalization-group and quantum Monte Carlo simulations. In particular, we focus on the stability of Fulde-Ferrell-Larkin-Ovchinnikov, dimer, and trimer fluids in inhomogeneous situations, as typically realized in cold gas experiments due to the harmonic confinement. We finally consider possible experimental signatures of these phases both in the presence of a finite polarization and of a finite temperature.

Coherent-population-trapping transients induced by an ac magnetic field are investigated theoretically for a realistic three-level $\Lambda$ system in the $D_1$ line of ${}^{87}$Rb. The contributions to the transient probe absorption from the various subsystems that compose the realistic atomic system are examined and the absorption of each $\Lambda$ subsystem is compared to that of a simple $\Lambda$ system. The population redistribution due to optical pumping is shown to be the dominant cause of the difference between the contributions of the various subsystems to the oscillatory character of the probe absorption. We also discuss the series of transients that reappear every half-cycle time of a modulated magnetic field when the system is in two-photon resonance, and we study the transient behavior as a function of the probe detuning. The effect of a buffer gas on the amplitude and shape of the transients is considered.

We determine antiferromagnetic (AF) signatures in the half-filled Hubbard model at strong coupling on a cubic lattice and in lower dimensions. Upon cooling, the transition from the charge-excitation regime to the AF Heisenberg regime is signaled by a universal minimum of the double occupancy at entropy $s\equiv S/\left(N{k}_{\text{B}}\right)=s^{*}\approx \ln \left(2\right)$ per particle and a linear increase of the next-nearest-neighbor (NNN) spin correlation function for $s<s^{*}$. This crossover, driven by a gain in kinetic exchange energy, appears as the essential AF physics relevant for current cold-atom experiments. The onset of long-range AF order (at low $s$ on cubic lattices) is hardly visible in nearest-neighbor spin correlations versus $s$, but could be detected in spin correlations at or beyond NNN distances.

We consider a $p$-polarized surface electromagnetic wave (a classical surface polariton) at the interface between the vacuum and a metal or left-handed medium. We show that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which, together with a superluminal orbital energy flow, form the total Poynting vector. This spin energy flow generates a well-defined (but not quantized) spin angular momentum of surface polaritons which is orthogonal to the propagation direction. The spin of evanescent waves arises from the imaginary longitudinal component of the electric field which makes the polarization effectively elliptical in the propagation plane. We also examine the connection between the spin and chirality of evanescent modes.

It is shown that a nonclassicality witness, whose expectation value can be measured for all quantum states, can be constructed from every nonclassicality filter. This finding leads to a set of universal witnesses, parameterized by only three real numbers, for the detection of nonclassicality of any quantum state of a harmonic oscillator. An explicit operator expression is given for such a universal witness. The application of the witnesses is demonstrated for a nontrivial example, and its experimental measurement is briefly considered.

Based on a set of “quasicomplete bases,” using the large-scale multiconfiguration Dirac-Fock (MCDF) method, we calculate the forbidden electric quadrupole ($E2$) and magnetic dipole ($M1$) transition rates of the transitions ${}^2{D}_{5/2,3/2}^o\to {}^4{S}_{3/2}^o$ of the O ii ground state considering the quantum electrodynamics (QED) corrections. Our calculations demonstrate that the Breit interactions are most important among all the QED corrections. The calculated $E2$ and $M1$ transition rates converge in a systematical and uniform manner with the extending orbital basis and the calculation uncertainty of 2.5$\%$ is achieved by considering the valence- and core-excitation correlations totally. With the converged transition rates, a value of the intensity ratio between the two transitions in high-electron-density limit in planetary nebulas is given, that is, $r\left(\infty \right)=0.363\pm 0.009$, which is within the overlap of the different observations and with the least uncertainty up to now. In addition, the $E2$ and $M1$ transition rates of two transitions ${}^2{P}_{3/2,1/2}^o\to {}^4{S}_{3/2}^o$ of O ii ground state and the ratio between the two transition rates in high-electron-density limit are calculated and compared with the previous results.

We recently presented a constructive solution to the $N$-representability problem of the two-electron reduced density matrix (2-RDM)—a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic $N$-electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. (to be published)]. In this paper we provide additional details and derive further $N$-representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the $(2,q)$-positivity conditions, where the $q$ indicates their derivation from the non-negativity of $q$-body operators. In addition to the known T1 and T2 conditions, we derive another class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is, conditions which arise from lifting lower $(2,q)$-positivity conditions to higher $(2,q+1)$-positivity conditions, and (ii) pure conditions, that is, conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure $(2,q)$-positivity conditions for $q>3$ require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the derived $N$-representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation.

We experimentally investigated dissociative double ionization of CO${}_2$ induced by intense femtosecond laser pulses. Three-dimensional momenta were precisely measured for correlated fragmental ions CO${}^{+}$ and O${}^{+}$. The dissociation dynamics of CO${}_2$${}^{2+}$ was theoretically simulated by using a Coulomb potential approximation. The ultrashort dissociation time (∼400 fs) can well explain the observed anisotropic angular distribution of fragmental ions relative to the laser polarization.

By combining experiments and numerical simulations, we investigate the redistribution of quasimomentum in a gas of atoms trapped in an optical lattice when the lattice depth is rapidly reduced. We find that interactions lead to significant momentum redistribution on millisecond time scales, thereby invalidating previous assumptions regarding adiabaticity. Our results indicate band mapping is an inaccurate probe of the equilibrium quasimomentum distributions of interacting bosons in the single-band regime.

We investigate the properties of an $N$-site tight-binding lattice with periodic boundary conditions (PBCs) in the presence of a pair of gain and loss impurities $\pm i\gamma$ and two tunneling amplitudes, $t_0$ and $t_b$, that are constant along the two paths that connect them. We show that the parity and time-reversal ($\mathcal{P}\mathcal{T}$)-symmetric phase of the lattice with PBCs are robust, insensitive to the distance between the impurities, and that the critical impurity strength for $\mathcal{P}\mathcal{T}$-symmetry breaking is given by ${\gamma }_{\mathrm{PT}}=|t_0-t_b|$. We study the time-evolution of a typical wave packet, initially localized on a single site, across the $\mathcal{P}\mathcal{T}$-symmetric phase boundary. We find that it acquires nonzero chirality for $\gamma \ne 0$, and the associated momentum reaches a universal maximum value at the threshold, $\gamma ={\gamma }_{\mathrm{PT}}$, irrespective of the initial location of the wave packet and the lattice parameters. Our results imply that $\mathcal{P}\mathcal{T}$-symmetry breaking on a lattice with PBCs has consequences that have no counterpart in open chains.

The inhomogeneous Singwi, Tosi, Land, and Sjolander (ISTLS) correlation energy functional of Dobson, Wang, and Gould [Phys. Rev. B 66, 081108(R) (2002)] has proved to be successful at predicting correlation energies in semihomogeneous systems, showing promise as a robust “next step” fifth-rung functional by using dynamic correlation to go beyond the limitations of the direct random-phase approximation (dRPA), but with similar numerical scaling with system size. In this work we test the functional on spherically symmetric, neutral, and charged atomic systems and find it gives excellent results (within 2mHa/$e^{-}$ except Be) for the absolute correlation energies of the neutral atoms tested, and good results for the ions (within 4mHa/$e^{-}$ except B${}^{+}$). In all cases it performs better than the dRPA. When combined with the previous successes, these new results point to the ISTLS functional being potentially suitable for high-accuracy, benchmark DFT correlation energy calculations in a wide range of systems.

In a previous work [Phys. Rev. A 85, 022502 (2012)] we calculated, with the use of the Gaussian expansion method for few-body systems, the energy levels and spatial structures of the ${}^4$He trimer and tetramer ground and excited states using the LM2M2 potential, which has a very strong short-range repulsion. In this work, we calculate the same quantities using the currently most accurate ${}^4$He-${}^4$He potential [Przybytek et al., Phys. Rev. Lett. 104, 183003 (2010)] that includes the adiabatic, relativistic, QED, and residual retardation corrections. Contributions of the corrections to the tetramer ground-(excited-) state energy $-573.90(-132.70)$ mK are respectively $-4.13(-1.52)$ mK, $+9.37(+3.48)$ mK, $-1.20(-0.46)$ mK, and $+0.16(+0.07)$ mK. Further including other realistic ${}^4$He potentials, we calculated the binding energies of the trimer and tetramer ground and excited states, $B_3^{\left(0\right)},B_3^{\left(1\right)},B_4^{\left(0\right)}$, and $B_4^{\left(1\right)}$, respectively. We found that the four kinds of the binding energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for ${}^4$He atoms (namely, six types of the generalized Tjon lines are observed). The dimerlike-pair model for ${}^4$He clusters, proposed in the previous work, predicts a simple interaction-independent relation $\frac{B_4^{\left(1\right)}}{B_2}=\frac{B_3^{\left(0\right)}}{B_2}+\frac{2}{3}$, which precisely explains the correlation between the tetramer excited-state energy and the trimer ground-state energy, with $B_2$ being the dimer binding energy.

We consider the Auger decay of atomic inner-shell vacancies in the field of a positive charge, as it occurs in multiply ionized molecules and clusters in strong x-ray laser pulses. First-principles numerical calculations of the decay rate as a function of the ion-charge distance are presented for a series of Auger transitions. The dependence of the rate on the distance is analyzed qualitatively within the Wentzel theory. Our results show that Auger rates can be modified significantly at ion-charge distances of the order of chemical bond lengths. The origin of the predicted effect is traced back to the distortion of the valence orbitals by the field of the positive charge.

The adiabatic theory of ionization of atoms by intense few-cycle laser pulses, whose development was initiated recently [Tolstikhin et al., Phys. Rev. A 81, 033415 (2010)], is applied to the study of high-order harmonic generation (HHG). The same one-dimensional zero-range-potential model is considered. The asymptotic formula for the HHG spectrum in this model is obtained in the leading-order adiabatic approximation. This asymptotics is uniform in terms of the photon energy in the cutoff region. It is shown that the factorization formula for the HHG spectrum, first proposed by Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of numerical solution of the time-dependent Schrödinger equation, results from the adiabatic theory, and the structure of the rescattering photoelectron wave-packet factor is clarified. The theory is illustrated by calculations.

Here we report on the realization of a Michelson-Sagnac interferometer whose purpose is the precise characterization of the motion of, i.e., membranes showing significant light transmission. Our interferometer has a readout noise spectral density (imprecision) of $3\times {10}^{-16}\mathrm{m}/\sqrt{\mathrm{Hz}}$ at frequencies around the fundamental resonance of a SiN${}_{\mathrm{x}}$ membrane at about 100 kHz, without using optical cavities. The readout noise demonstrated is more than 16 dB below the peak value of the membrane's standard quantum limit (SQL). This margin is significantly bigger than those of previous works with nanowires [Teufel et al.,   Nature Nano. 4, 820 (2009); Anetsberger et al., Nature Phys. 5, 909 (2009)]. We discuss the meaning of the SQL for force measurements and its relation to the readout performance and emphasize that neither our nor previous experiments achieved a total noise spectral density as low as the SQL due to thermal noise.

We report on an experimental implementation of a tunable source of mixed two-photon entangled states. In contrast to previous implementations there is no correlation between the phase shift and spectral property of photons which would in principle allow local spectral filtration. The source provides genuinely mixed states that mimic various statistics of polarization-dispersion fluctuations. We believe that our source may be useful for testing robustness of quantum-information protocols against this specific form of noise. We demonstrate this function on a simple case of filtration by means of a balanced beam splitter.

We show that a statistical theory of nanoparticle sensing emerges for the detection systems using a whispering-gallery-mode resonator in the large particle-influx regime. The statistical theory predicts that the number of particles adsorbed onto the resonator is accurately determined by the spectral shift of the center of the transmission spectrum and is independent of the intrinsic dissipations of the particles as well as the angular positions of the particles.

We investigate quantum correlations in the ground state of noninteracting Fermi gases of $N$ particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose we compute one-particle correlations, particle fluctuations, and bipartite entanglement entropies of extended space regions, and study their large-$N$ scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining $S_{\mathrm{HS}}\approx c_l{N}^{(d-1)/d}\ln N$ analogously to homogenous systems, with $c_l=1/6,1/\left(6\sqrt{2}\right),1/\left(6\sqrt{6}\right)$ in one, two, and three dimensions, respectively. We show that the asymptotic large-$N$ relation $S_A\approx {\pi }^2{V}_A/3$, between the von Neumann entanglement entropy $S_A$ and particle variance $V_A$ of an extended space region $A$, holds for any subsystem $A$ and in any dimension, analogously to homogeneous noninteracting Fermi gases.

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e., the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.