We theoretically and numerically study spin turbulence (ST) with small spin magnitude in spin-1 spinor Bose-Einstein condensates by using the spin-1 spinor Gross-Pitaevskii (GP) equations. This kind of ST is realized in two cases: (i) with antiferromagnetic interaction and (ii) with ferromagnetic interaction under a static magnetic field. The ST with small spin magnitude can exhibit two characteristic power laws in the spectrum of the spin-dependent interaction energy: $-1$ and $-7/3$ power laws in the low- and high-wave-number regions, respectively. These power laws are derived from a Kolmogorov-type dimensional scaling analysis for the equations of motion of the spin vector and nematic tensor. To confirm these power laws, we perform a numerical calculation of the spin-1 spinor GP equations in a two-dimensional uniform system. In case (i), the $-7/3$ power law tends to appear in the high-wave-number region, but the spectrum in the low-wave-number region deviates from the $-1$ power law. In contrast, both the $-1$ and $-7/3$ power laws tend to appear in case (ii).

Motivated by recent experiments with ultracold fermionic atoms in optical lattices, we study finite temperature magnetic correlations, as singlet and triplet correlations, and the double occupancy in the one-dimensional Hubbard model. We point out that for intermediate interaction strengths the double occupancy has an intriguing doubly nonmonotonic temperature dependence due to the competition between spin and charge modes, related to the Pomeranchuk effect. Furthermore, we determine properties of magnetic correlations in the temperature regimes relevant for current cold atom experiments and discuss effects of the trap on spatially integrated observables. We estimate the entropy and the temperature reached in the experiment by Greif, Uehlinger, Jotzu, Tarruell, and Esslinger [Science 340, 1307 (2013)].

We study the superfluid-to-Mott-insulator transition of a mixture of heavy bosons and light fermions loaded in an optical lattice. We focus on the effect of the light fermions on the dynamics of the heavy bosons. It is shown that when the lattice potential is sufficiently deep to confine the bosons to one dimension but allow the fermions to freely move in three dimensions (i.e., a mixed-dimensionality lattice), the fermions act as an ohmic bath for bosons, leading to screening and dissipation effects on the bosons. Using a perturbative renormalization-group analysis, it is shown that the fermion-induced dissipative effects have no appreciable impact on the transition from the superfluid-to-Mott-insulator state at integer filling. On the other hand, dissipative effects are found to be very important in the half-filled case near the critical point. In this case, in the presence of a finite incommensurability that destabilizes the Mott phase, the bosons can still be localized by virtue of dissipative effects.

We experimentally investigate the two-dimensional condensate (optical dropletlike) soliton formation and dynamics of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence, under competition between the third- and fifth-order nonlinear susceptibilities. With such competing nonlinearities, mutual transformations among dropletlike fundamental, dipole, and azimuthally modulated vortex FWM solitons are observed. The influence of nonlinear competition on the photonic band gap is also investigated. All the results are obtained under low powers.

We study the quantum dynamics of an open network of two-level systems which is coupled to a correlated common environment represented by a bosonic field in a thermal equilibrium state. Extensive numerical simulations of the full second-order time-convolutionless quantum master equation for the density matrix of various types of networks are performed, in order to investigate dissipation and decoherence processes and, in particular, their dependence on the spatial separation of the network sites and on the speed of the bosonic field modes. In the limit of an infinite speed the influence of the environment disappears due to the emergence of a decoherence-free subspace, while the limit of zero speed corresponds to the case in which the network sites are coupled to independent reservoirs, a case which is much easier to treat numerically. The main result of the paper is a general intuitive criterion which states that the simpler model of independent reservoirs can be used as long as the network relaxation time is smaller than the time it takes for the modes to travel the minimal distance between the network sites.

Many techniques in quantum control rely on frequency separation as a means for suppressing unwanted couplings. In its simplest form, the mechanism relies on the low bandwidth of control pulses of long duration. Here we perform a higher-order quantum-mechanical treatment that allows for higher precision and shorter times. In particular, we identify three kinds of off-resonant effects: (i) simultaneous unwanted driven couplings (e.g., due to drive crosstalk), (ii) additional (initially undriven) transitions such as those in an infinite ladder system, and (iii) sideband frequencies of the driving wave form such as we find in corrections to the rotating-wave approximation. With a framework that is applicable to all three cases, in addition to the known adiabatic error responsible for a shift of the energy levels we typically see in the spectroscopy of such systems, we derive error terms in a controlled expansion corresponding to higher-order adiabatic effects and diabatic excitations. We show, by also expanding the driving wave form in a basis of different order derivatives of a trial function (typically a Gaussian) these different error terms can be corrected for in a systematic way, hence strongly improving quantum control of systems with dense spectra.

Optical lattices are typically used to modify the dispersion relation of the matter wave, in particular, to ensure resonant conditions for multiwave interactions. Here we propose an alternative mechanism of wave interactions. It can be implemented using a nonlinear lattice and modifies the momentum conservation law of the interacting atoms, leaving the energy conservation unchanged. We propose to apply this phenomenon to construct an atom laser via a resonant four-wave mixing process.

We study the current dynamics of coupled atomic condensates flowing in two ring-shaped optical potentials. We provide a specific setup where the ring-ring coupling can be tuned in an experimentally feasible way. It is demonstrated that the imaginary time effective action of the system in a weak coupling regime provides a two-level-system dynamics for the phase slip across the two rings. Through two-mode Gross- Pitaevskii mean-field equations, the real-time dynamics of the population imbalance and the phase difference between the two condensates is thoroughly analyzed analytically, as a function of the relevant physical parameters of the system. In particular, we find that the macroscopic quantum self-trapping phenomenon is induced in the system if the flowing currents assume a nonvanishing difference.

We propose and investigate the quasi-phase-matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled lithium niobate. Laguerre-Gaussian (LG) modes are used to represent the orbital angular momentum (OAM) states, characterized with the azimuthal and radial indices. Typical three-wave nonlinear interactions among the involved OAM modes are studied with the help of coupling wave equations. Being different from normal QPM process where the energy and quasimomentum conservations are satisfied, both of the azimuthal and radial indices of the OAM states stay constant in most of the cases. However, abnormal change of the radial index is observed when there is asynchronous nonlinear conversion in different parts of the beams. The QPM nonlinear evolution of fractional OAM states is also discussed showing some interesting properties. In comparison with the traditional birefringent phase matching, the QPM technique avoids the undesired walk-off effect to reserve high-quality LG modes. We believe the QPM is an effective way to convert, amplify, and switch OAM states in various optical vortex related applications.

Dissociative ionization of N${}_2$Ar was experimentally studied in an intense femtosecond laser field. The break of the weak van der Waals bond generates an argon atomic ion and a nitrogen molecular ion. Both of them can recapture the tunneling electron. The probability measurement indicates that the tunneling electron prefers to be recaptured by the atomic ion.

Phase shift estimation with uncertainty below the Heisenberg limit, $\Delta {\varphi }_{\mathrm{HL}}\propto 1/{\overline{N}}_T$, where ${\overline{N}}_T$ is the total average number of particles employed, is a mirage of linear quantum interferometry. Recently, Rivas and Luis, [New J. Phys. 14, 093052 (2012)] proposed a scheme to achieve a phase uncertainty $\Delta \varphi \propto 1/{\overline{N}}_T^k$, with $k$ an arbitrary exponent. This sparked an intense debate in the literature which, ultimately, does not exclude the possibility to overcome $\Delta {\varphi }_{\mathrm{HL}}$ at specific phase values. Our numerical analysis of the Rivas and Luis proposal shows that sub-Heisenberg uncertainties are obtained only when the estimator is strongly biased. No violation of the Heisenberg limit is found after bias correction or when using a bias-free Bayesian analysis.

We draw attention to the existence of “genuine” fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation within a one-way sequential recipe in which an ancillary system interacts locally and only once with each qubit in a row. Given the known “no-go” associated with such a theoretically and experimentally desirable decomposition, various figures of merit are introduced to analyze the optimal “fidelity” with which an arbitrary genuinely entangling operation may admit such a sequential decomposition. An efficient variational matrix-product-operator protocol is invoked in order to obtain numerically the minimal values of the fidelity gaps incurred upon the sequential decomposition of genuine entanglers. We call the values of the gaps so obtained “genuine” in light of possible connections to the concept of the genuine multipartite entanglement and since they turn out to be independent of the ancilla dimension and the initial states the associated isometries or unitaries act upon.

We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$-dimensional maximally entangled states can be perfectly distinguished using measurements with a positive partial transpose (PPT) and can be distinguished with one-way LOCC with high probability. These results circle around the question of whether there exist three maximally entangled states which cannot be distinguished using the full power of LOCC; we discuss possible approaches to answer this question.

The complementarity of two observables is often captured in uncertainty relations, which quantify an inevitable trade-off in knowledge. Here we study complementarity in the context of an information-processing task: we link the complementarity of two observables to their usefulness for superdense coding (SDC). In SDC, Alice sends two classical dits of information to Bob by sending a single qudit. However, we show that encoding with commuting unitaries prevents Alice from sending more than one dit per qudit, implying that complementarity is necessary for SDC to be advantageous over a classical strategy for information transmission. When Alice encodes with products of Pauli operators for the $X$ and $Z$ bases, we quantify the complementarity of these encodings in terms of the overlap of the $X$ and $Z$ basis elements. Our main result explicitly solves for the SDC capacity as a function of the complementarity, showing that the entropy of the overlap matrix gives the capacity, when the preshared state is maximally entangled. We generalize this equation to resources with symmetric noise such as a preshared Werner state. In the most general case of arbitrary noisy resources, we obtain an analogous lower bound on the SDC capacity. Our results shed light on the role of complementarity in determining the quantum advantage in SDC and also seem fundamentally interesting since they bear a striking resemblance to uncertainty relations.

We present spectroscopic measurements of seven vibrational levels $v=29–35$ of the $A\left(1^1{\Sigma }_u^{+}\right)$ excited state of Li${}_2$ molecules by the photoassociation of a degenerate Fermi gas of ${}^6$Li atoms. The absolute uncertainty of our measurements is $\pm 0.00002$ cm${}^{-1}$ ($\pm 600$ kHz) and we use these new data to further refine an analytic potential for this state. This work provides high accuracy photoassociation resonance locations essential for the eventual high-resolution mapping of the $X\left(1^1{\Sigma }_g^{+}\right)$ state enabling further improvements to the $s$-wave scattering length determination of Li and enabling the eventual creation of ultracold ground-state ${}^6$Li${}_2$ molecules.

We have extended the convergent close-coupling method to investigate electron scattering from the vibrationally excited molecular hydrogen ion H${{}_2}^{+}$, within the Born-Oppenheimer approximation. Results are presented for proton-production and dissociative-ionization cross sections. The comparison with experiment is excellent across the energy range from near threshold to 1 keV.

Due to atomic interactions and dispersion in the total atom number, the order parameter of a pair-condensed Fermi gas experiences a collapse in a time that we derive microscopically. As in the bosonic case, this blurring time depends on the derivative of the gas chemical potential with respect to the atom number and on the variance of that atom number. The result is obtained first using linearized time-dependent Bogoliubov–de Gennes equations, then in the random-phase approximation, and then it is generalized to beyond the mean field. In this framework, we construct and compare two phase operators for the paired fermionic field: The first one, issuing from our study of the dynamics, is the infinitesimal generator of adiabatic translations in the total number of pairs. The second one is the phase operator of the amplitude of the field of pairs on the condensate mode. We explain that these two operators differ due to the dependence of the condensate wave function on the atom number.

We consider the fluctuations in atom number that occur within finite-sized measurement cells in a trapped Bose-Einstein condensate. These approximate the fluctuation measurements made in current experiments with finite-resolution in situ imaging. A numerical scheme is developed to calculate these fluctuations using the quasiparticle modes of a cylindrically symmetric three-dimensionally trapped condensate with either contact or dipole-dipole interactions. We use this scheme to study the properties of a pancake-shaped condensate using cylindrical cells. The extension of the theory to washer-shaped cells with azimuthal weighting is made and used to discriminate between the low-energy roton modes in a dipolar condensate according to their projection of angular momentum. Our results are based on the Bogoliubov approach valid for zero and small finite temperatures.