We have measured the binding energy of ${}^7$Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683 (2009)]. We find the measured locations of the three- and four-body Efimov features to be consistent with universal theory at the 20%–30% level.

We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and antiferromagnetic spin-exchange interaction. The density distributions of spin-singlet-paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations, which are derived based on the local density approximation and the Bethe ansatz exact results for a homogeneous system. Nonmonotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the radius-polarization phase diagram at strong interaction and find the critical polarization, which paves the way to directly observe the exotic singlet pairing in spinor gas experimentally.

We observe theoretically and experimentally the phenomenon of spontaneous symmetry breaking of strongly localized nonlinear optical modes at the microwatt level in a one-dimensional photonic lattice with a single coupling defect.

We experimentally investigate odd-order harmonic generation in molecular gases produced by circularly polarized laser fields. While forbidden in isotropic medium, this effect is allowed by symmetry breaking resulting from nonadiabatic laser-induced molecular alignment. The demonstration is provided by generating the third harmonic in CO${}_2$ molecules. Attractive properties and challenging potential applications are discussed in the context of higher-order harmonic generation.

Metamaterial is promising for enhancing the capability of plasmonic devices. We consider a cylindrical waveguide with three-level $\Lambda$ atoms embedded in the dielectric core. By comparing metal cladding vs metamaterial cladding of a waveguide with $\Lambda$ atoms in the core, we show that, for a fixed amount of slowing of light due to electromagnetically induced transparency, the metamaterial cladding outperforms in terms of the inherent loss.

We determine the cumulants of electromagnetic energy transmitted through one-dimensional disordered medium with absorption or amplification. For this purpose we derive the Keldysh nonlinear $\sigma$ model action with a source term that generates the energy current fluctuations. The fluctuations over the ensemble of disorder realizations are found to decrease (increase) with increasing absorption (amplification). In the conservative medium the fluctuations can be related to the Dorokhov's distribution of transmission coefficients.

We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.

The calculation of the fundamental limits of nonlinear susceptibilities posits that when a quantum system has a nonlinear response at the fundamental limit, only three energy eigenstates contribute to the first and second hyperpolarizability. This is called the three-level ansatz and is the only unproven assumption in the theory of fundamental limits. In light of the observation that the measured nonlinear response of a majority of molecules falls far short of these limits, the three-level ansatz warrants closer scrutiny. All calculations that are based on direct solution of the Schrödinger equation, including systems of arbitrarily placed electrons and nuclei in external electromagnetic fields and interacting electrons in an arbitrary potential, whose configuration space is sampled using numerical optimization techniques, yield intrinsic hyperpolarizabilities less than 0.709 and intrinsic second hyperpolarizabilities less than 0.6. In this work, we show that relaxing the three-level ansatz and allowing an arbitrary number of states to contribute leads to divergence of the optimized intrinsic hyperpolarizability in the limit of an infinite number of states, what we call the many-state catastrophe. This is not surprising given that the divergent systems are most likely not derivable from the Schrödinger equation, yet obey the sum rules. The sums rules are the second ingredient in limit theory and apply also to systems with more general Hamiltonians. These “exotic Hamiltonians” may not model any real systems found in nature. Indeed, a class of transition moments and energies that come form the sum rules do not have a corresponding Hamiltonian that is expressible in differential form. In this work, we show that the three-level ansatz acts as a constraint that excludes many of the nonphysical Hamiltonians and prevents the intrinsic hyperpolarizability from diverging. We argue that this implies that the true fundamental limit is smaller than previously calculated. Since the three-level ansatz does not lead to the largest possible nonlinear response, contrary to its assertion, we propose the intriguing possibility that the three-level ansatz is true for any system that obeys the Schrödinger equation, yet this assertion may be unprovable.

We analyze the statistical properties of entanglement for pairs and triples of entangled qubits subject to a random disturbance followed by restoration. After the random disturbance, which is modeled as a null-result weak measurement, the state is restored by applying a static measurement reversal. We then show that the fidelity of the resulting state, and therefore its entanglement, can be restored with a high success, despite the statistical fluctuations of the disturbance. In particular, we show that the variance of the entanglement of an ensemble of restored states is substantially reduced, despite large disturbances. We conclude with a proposed experimental implementation.

We consider an open quantum system consisting of four atoms which are placed in a damped cavity. Through a dissipative dynamics process, a $W$ state can be converted into a Greenberger-Horne-Zeilinger state with deterministic probability. In addition, the interaction time need not be controlled strictly in the dynamics process. The protocol may open up a promising perspective for quantum state conversion between different classes of entanglement and cavity quantum electrodynamics systems.

Dipolar Bose-Einstein condensates may present a rotonlike dispersion minimum, which has yet to be observed in experiments. We discuss a simple method to reveal roton excitations based on the response of quasi-two-dimensional dipolar condensates against a weak lattice potential. By employing numerical simulations for realistic scenarios, we analyze the response of the system as a function of both the lattice spacing and the $s$-wave scattering length, showing that the roton minimum may be readily revealed in current experiments by the resonant population of Bragg peaks in time-of-flight measurements.

We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples.

A method for construction of multipartite Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. An iterative method for deriving $(N+1)$-partite CHSH-type Bell inequalities from $N$-partite ones is derived. As an application, compact Bell inequalities for eight observers involving just four correlation functions are proposed. They require much less experimental effort than standard methods and thus are experimentally friendly in multiphoton experiments.

Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size of the quantum system. We also explain why the bounds should be valid in large generality and illustrate the method via numerical examples.

Using different optical setups based on squeezed state and photon subtraction we show how optical entanglement between a macroscopic and a microscopic state—the so-called Schrödinger cat state or micro-macro state—can be generated. The entangled state is heralded and is thus produced a priori in contrast to previous proposals. We define the macroscopicity of the macroscopic part of the state as their mean distance in phase space and the success rate in discriminating them with homodyne detection, and subsequently, based on these measures we investigate the macroscopicity of different states. Furthermore, we show that the state can be used to map a microscopic qubit onto a macroscopic one thereby linking a qubit processor with a qumode processor.

Calculations based on the projection method and using explicitly correlated Gaussians are used to confirm the existence of positron attachment to two doubly excited states of helium. The $e^{+}$He($2s^2$ ${}^1{S}^e$) and $e^{+}$He($3s^2$ ${}^1{S}^e$) states have binding energies of 0.449 and 0.286 eV. These estimates of the resonance energies are nearer to the variational limit than previous calculations. These states will exist as resonances in the $e^{+}$-He scattering continuum, and complex rotation calculations have been used to estimate their widths.

We theoretically predict a topological matter—topological inhomogeneous Fulde-Ferrell superfluid—in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near $s$-wave Feshbach resonances. The realization of such a spin-orbit-coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a nontrivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.

The near-threshold lasing modes of active microcavities and the corresponding passive resonances of the bare cavities, obtained using the Schrödinger-Bloch model and the boundary element method, respectively, are known to possess almost identical wave intensity patterns. Here, we investigate how much they resemble each other in phase space. It is shown that a clear distinction between them can be seen in the Husimi function, a phase-space representation of the resonance mode, despite their almost identical appearance in configuration space. For optical microcavities, one can distinguish two Husimi functions inside the cavity, namely one describing the wave components incident to the boundary and the other one describing (reflected) components emerging from the boundary but remaining inside the cavity. They are referred to as incident and emerging Husimi functions, respectively. We find the incident and emerging Husimi functions of the lasing mode to show a pronounced asymmetric localization in phase space, whereas the corresponding passive-case quantities look very similar. This can be understood by adding the amplification process, inherent and characteristic for the laser, to the passive mode. We also discuss possible effects of the resulting nonlinear dynamics for a single lasing mode as well as for two-mode lasing that is relevant at higher pumping strength. We demonstrate its consequences in terms of the Husimi functions that we find to be the adequate tool to illustrate features of the amplification process.

We discuss multiheterodyne interference between the laser beams of optical frequency-comb (FC) and single-frequency (SF) lasers. The beat signal generated by the interference contains a dc component, discrete-frequency elements with the same frequency interval generated by interference between the two elements of the FC laser, and elements generated by the interference between the FC and the SF lasers. The beat-signal elements between them can be used for absorption spectroscopy around the SF-laser frequency, which is called frequency-comb interference spectroscopy (FCIS). In this paper, we compare the beat-signal spectrum predicted through theoretical descriptions of multiheterodyne interference with experimental results to improve understanding of FCIS and similar techniques. Our FCIS experiments use a probing Ti:sapphire mode-locked laser, which is the beam experiencing absorption, and a reference diode laser. We also discuss the potential of this method to measure the small shift in absorption profiles using the measurement results of argon metastable atoms.

We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as $m{m}^{\prime }$ states) as compared to the maximally path-entangled NOON states in the presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the $m{m}^{\prime }$ states, which are more robust than the NOON state against photon loss, perform equally well when subject to such fluctuations. We derive the quantum Fisher information with the phase-fluctuation noise and show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramér-Rao bound in the presence of such noise, suggesting that parity detection is an optimal detection strategy.