Rényi uncertainty relations are shown to have significant importance in quantum phase transitions. They detect the quantum phase transition in the Dicke model. The Rényi entropy sum is more appropriate for describing quantum fluctuations than the standard variance products.

We have created a quantum degenerate Bose-Fermi mixture of ${}^{23}$Na and ${}^{40}$K with widely tunable interactions via broad interspecies Feshbach resonances. Over 30 Feshbach resonances between ${}^{23}$Na and ${}^{40}$K were identified, including $p$-wave multiplet resonances. The large and negative triplet background scattering length between ${}^{23}$Na and ${}^{40}$K causes a sharp enhancement of the fermion density in the presence of a Bose condensate. As explained via the asymptotic bound-state model, this strong background scattering leads to wide Feshbach resonances observed at low magnetic fields. Our work opens up the prospect to create chemically stable, fermionic ground-state molecules of ${}^{23}$Na-${}^{40}$K, where strong, long-range dipolar interactions would set the dominant energy scale.

We study the time evolution of trace distance between the quantum states which evolve from two kinds of initial states, a correlated Gibbs state and its uncorrelated marginal state. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We find that the trace distance increases above its initial value for any and all parameter settings when a weak external field is applied to the two-level system. This indicates that we can explore the existence of initial system-environment correlations with the breakdown of the contractivity induced by the external field.

We develop a general optimization strategy for performing a chosen unitary or nonunitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a chosen function of the system state, which quantifies the task success (score), such as fidelity, purity, or entanglement. If the time dependence of the system Hamiltonian is fast enough to be comparable to or shorter than the response time of the bath, then the resulting non-Markovian dynamics is shown to optimize the chosen task score to second order in the coupling to the bath. This strategy can protect a desired unitary system evolution from bath-induced decoherence, but can also take advantage of the system-bath coupling so as to realize a desired nonunitary effect on the system.

In a recent paper [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed-point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density-functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case because it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an explicit relation between the boundary conditions on the density and the convergence properties of the fixed-point procedure via the spectral properties of the associated Sturm-Liouville operator. We show precisely under which conditions discrete and continuous spectra arise and give explicit examples. These conditions are then used to show that, in the most physically relevant cases, the fixed-point procedure converges. This is further demonstrated with an example.

We have observed pseudodoublets representing a partly resolved fine structure of rovibronic lines in the visible part of the ${\text{D}}_2$ emission spectrum. They are characterized by splitting values of about $0.2$ cm${}^{-1}$ and relative intensity of the doublet components close to $2.0$. It is shown that they are determined by triplet splitting in lower rovibronic levels of various ${}^3{\Lambda }_g^{\pm }\to c^3{\Pi }_u^{-}$ electronic transitions. It is proposed to use the existence of such partly resolved fine-structure patterns for identification of numerous unassigned spectral lines of the ${\text{D}}_2$ molecule coming from a great variety of triplet “gerade” electronic states to vibrorotational levels of the $c^3{\Pi }_u^{-}$ state.

We studied the collective modes of a Bose-Einstein condensate (BEC) with spin-orbit coupling. We developed the hydrodynamic equations for spin-orbit coupled BECs and used them to study collective modes in the plane-wave phase and large Rabi coupling regime for both a uniform BEC and a BEC in a harmonic trap. In the homogeneous situation, we obtained energy spectra of elementary excitations and found that the spin-orbit coupling can increase the effective mass of the atoms, which will suppress the sound velocity. The spin-orbit coupling can also change the spin mixing, which will modify the interaction energy, and may lead to an enhancement of sound velocity. The competition between these two effects gives the behavior of sound velocity. In a harmonic trap, we found that the dipole mode and the breathing mode are coupled together in the plane-wave phase, and these two modes have a $\pi /2$ phase difference, because the spin-orbit coupling and the interaction are not invariant under spin rotation. However, in the large Rabi coupling regime, the dipole mode and the breathing mode are decoupled due to the symmetry restriction.

We study the interpolation from occupation number Fock states to Schrödinger cat states on systems modeled by a two-mode Bose-Hubbard Hamiltonian, like, for instance, bosons in a double well or superconducting Cooper pair boxes. In the repulsive interaction regime, by a simplified single particle description, we calculate analytically energy, number fluctuations, stability under coupling to a heat bath, entanglement entropy, and Fisher information, all in terms of hypergeometric polynomials of the single particle overlap parameter. Our approach allows us to find how those quantities scale with the number of bosons. In the attractive interaction regime we calculate the same physical quantities in terms of the imbalance parameter, and find that the spontaneous symmetry breaking, occurring at interaction $U_c$, predicted by a semiclassical approximation, is valid only in the limit of infinite number of bosons. For a large but finite number we determine a characteristic strength of interaction $U_c^{*}$, which can be promoted as the crossover point from coherent to incoherent regimes and can be identified as the threshold of fragility of the cat state. Moreover, we find that the Fisher information is always in direct ratio to the variance of on-site number of bosons, for both positive and negative interactions. We finally show that the entanglement entropy is maximum close to $U_c^{*}$ and exceeds its coherent value within the whole range of interaction between $2U_c$ and zero.

We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of $N$ noninteracting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when onsite interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adiabaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary basis needed to demonstrate CTAP, which dramatically increases the number of particles that can be efficiently considered. Finally, we compare the results of the Bose-Hubbard model to a mean-field three-mode Gross-Pitaevskii analysis for the equivalent system.

It has recently been predicted and experimentally demonstrated that the refractive index of a vapor may be enhanced while maintaining vanishing absorption by using the interference of two Raman transitions, one absorptive and one amplifying in nature. In this paper, we present a detailed experimental study of this technique in a 1-mm-long rubidium (Rb) vapor cell with densities exceeding ${10}^{14}$ cm${}^{-3}$. We study the optimization of the achieved refractive index as various experimental parameters are varied and discuss a number of limitations of the current experiments. We also present a detailed discussion of possible experimental improvements and future prospects of this technique.

We study multipartite superdense coding in the presence of a covariant noisy channel. We investigate the case of many senders and one receiver, considering both unitary and nonunitary encoding. We study the scenarios where the senders apply local encoding or global encoding. We show that, up to some preprocessing on the original state, the senders cannot do better encoding than local, unitary encoding. We then introduce general Pauli channels as a significant example of covariant maps. Considering Pauli channels, we provide examples for which the superdense coding capacity is explicitly determined.

Circular and linear dichroism in the angular distributions of photoelectrons in multiphoton ionization of unpolarized atoms by a combination of two short pulses in the extreme ultraviolet (XUV) and infrared (IR) range is theoretically considered. A noticeable circular dichroism is predicted in the case when both XUV and IR pulses are circularly polarized. Here the dichroism may be observed not only in angle-resolved but also in angle-integrated experiments. When the XUV photons are linearly polarized while the IR pulses are circularly polarized, the circular dichroism can be observed only in angle-resolved experiments. In this case the dichroism averaged over a spectral line is small. When both pulses are linearly polarized, the photoelectron yield strongly depends on the angle between the polarizations, which leads to the considerable linear dichroism.

The response of the ${{\mathrm{D}}_3}^{+}$ and ${{\mathrm{H}}_3}^{+}$ molecules to an intense, ultrashort laser pulse is investigated with a quasiclassical model to provide details of our previous short report [Phys. Rev. Lett. 106, 203001 (2011)]. The stable, lowest-energy configuration of two electrons and three deuterons (or three protons) is realized by certain auxiliary, momentum-dependent potentials. The time evolution of the molecule in the external driving field leading to the dissociation and ionization is calculated by numerically solving the classical Hamiltonian equations of motion. It is shown that the theoretical results reproduce qualitatively characteristic features of the experimental angular distributions and kinetic energy release spectra [Phys. Rev. Lett. 103, 103004 (2009)].

We study instabilities of single-species fermionic atoms in the $p$-orbital bands in two-dimensional optical lattices at noninteger filling against interactions. Charge density wave and orbital density wave orders with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superfluid phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible phase transitions from orbital stripe order to liquid-crystal phases and obtain the phase diagram. The condition of nearly-perfect Fermi-surface nesting, which is key to the above results, is shown robustly independent of fermion fillings in such $p$-orbital systems, and the $(2k_F,\pm 2k_F)$ momentum of density wave oscillation is highly tunable. Such remarkable features show the promise of making those exotic orbital phases, which are of broad interest in condensed-matter physics, experimentally realizable with optical lattice gases.

The determination of eigenpolarizations is a crucial issue in the study of functional nanomaterials and nanostructures for polarization control, such as the newly emergent chiral metamaterials with artificial optical activity. Here we propose the approaches for determining the eigenpolarizations in an arbitrary diffraction order of any planar periodic structure (PPS) under arbitrary incidence. First, a simple analytical approach based on symmetry considerations is developed for discriminating the eigenpolarizations of the directly transmitted light of any PPS under normal incidence, by dividing the PPSs into 10 categories according to the group theory. Then a general numerical approach is established to rigorously solve the eigenpolarizations of any diffraction order of a PPS under any angle of incidence. Examples are demonstrated to show the effectiveness of the approaches.

We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of spatial symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions from inner core electrons. The material is assumed to have a nonzero, third-order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk silicon we predict that cavity environments modify the dependence of second harmonic generation on incident angle, while improving third harmonic conversion efficiency by several orders of magnitude relative to bulk silicon. This occurs despite the fact that the harmonic signals may be tuned to a wavelength range where the dielectric function of the material is negative: A phase-locking mechanism binds the generated signals to the pump and inhibits their absorption. These results point the way to alternative uses and flexibility of materials such as silicon as nonlinear media in the visible and UV ranges.

We show theoretically how quantum interference between linearly coupled modes with weak local nonlinearity allows the generation of continuous variable entanglement. By solving the quantum master equation for the density matrix, we show how the entanglement survives realistic levels of pure dephasing. The generation mechanism forms a paradigm for entanglement generation in arrays of coupled quantum modes.

We report on the experimental realization of a robust and efficient magneto-optical trap for erbium atoms, based on a narrow cooling transition at 583 nm. We observe up to $N=2\times {10}^8$ atoms at a temperature of about $T=15$ $\mu$K. This simple scheme provides better starting conditions for direct loading of dipole traps as compared to approaches based on the strong cooling transition alone, or on a combination of a strong and a narrow kHz transition. Our results on Er point to a general, simple, and efficient approach to laser cool samples of other lanthanide atoms (Ho, Dy, and Tm) for the production of quantum-degenerate samples.

In this paper, we consider two related problems, unambiguous discrimination of quantum mixed states and unambiguously conveying classical messages using Einstein-Podolsky-Rosen (EPR) pairs. The main technical contributions are as follows. First, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary $N$ mixed quantum states with given a priori probability, which can be directly used to the unambiguous communication setting. Second, we propose a sufficient condition to show that a new upper bound can be achievable, and construct examples to clarify the relationship between the upper bound we derive and the existing upper bounds presented by other authors. Third, in the issue of conveying classical messages using EPR pairs, we also derive an upper bound on the success probability for unambiguously decoding, where Alice wants to convey $n$ bit classical information to Bob by sending $m$ quantum bits.