We study the measurement-device-independent quantum key distribution (MDIQKD) in practice with limited resources when there are only three different states in implementing the decoy-state method and when there are basis-dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with three different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon sources such as the coherent states or the heralded states from the parametric down-conversion. We point out that the existing result for secure MDIQKD with source coding errors does not always hold. We find that very accurate source coding is not necessary. In particular, we loosen the precision of the existing result by several orders of magnitude.

We present a simple semidefinite program whose optimal value is equal to the maximum probability of perfectly distinguishing orthogonal maximally entangled states using any PPT measurement (a measurement whose operators are positive under partial transpose). When the states to be distinguished are given by the tensor product of Bell states, the semidefinite program simplifies to a linear program. In Phys. Rev. Lett. 109, 020506 (2012), Yu, Duan, and Ying exhibit a set of four maximally entangled states in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$, which is distinguishable by any PPT measurement only with probability strictly less than 1. Using semidefinite programming, we show a tight bound of $7/8$ on this probability ($3/4$ for the case of unambiguous PPT measurements). We generalize this result by demonstrating a simple construction of a set of $k$ states in ${\mathbb{C}}^k\otimes {\mathbb{C}}^k$ with the same property, for any $k$ that is a power of 2. By running numerical experiments, we show the local indistinguishability of certain sets of generalized Bell states in ${\mathbb{C}}^5\otimes {\mathbb{C}}^5$ and ${\mathbb{C}}^6\otimes {\mathbb{C}}^6$ previously considered in the literature.

We report an upper bound to the ionization energy of ${}^{85}$Rb${}_2$ of 31$$348.0(6) cm${}^{-1}$, which also provides a lower bound to the dissociation energy $D_0$ of ${}^{85}$Rb${}_2^{+}$ of 6$$307.5(6) cm${}^{-1}$. These bounds were measured by the onset of autoionization of the excited states of ${}^{85}$Rb${}_2$ below the $5s+7p$ atomic limit. We form ${}^{85}$Rb${}_2$ molecules via photoassociation of ultracold ${}^{85}$Rb atoms and subsequently excite the molecules by single-photon uv transitions to states above the ionization threshold.

Experimental diffraction patterns produced by grazing scattering of fast helium atoms from a Ag(110) surface are used as a sensitive tool to test an ab initio potential model derived from accurate density-functional theory (DFT) calculations. The scattering process is described by means of the surface eikonal approximation, which is a distorted-wave method that includes the quantum interference between contributions coming from different projectile paths, taking into account the complete corrugation of the three-dimensional projectile-surface potential. A fairly good agreement between the theoretical and experimental momentum distributions is found for incidence along different low-indexed crystallographic directions. This agreement is indicative of the quality of the DFT potential. The effective corrugation of the interaction potential across the incidence channel is also investigated.

We investigate the possibility of cooling a mechanical oscillator to its ground state and using it to detect a weak coherent force by means of a hybrid optomechanical quantum device formed by a Bose-Einstein condensate (BEC) confined in a high quality factor optical cavity with an oscillatory end mirror. We show using the stochastic cooling technique that the atomic two-body interaction can be utilized to cool the mirror and achieve position squeezing essential for making sensitive measurements of weak forces. We further show that for certain values of the system parameters and spectral range, the atomic two-body interaction can also increase the signal-to-noise ratio and decrease the noise of the off-resonant stationary spectral measurements. We show that the minimum noise is obtained only in the presence of BEC.

We investigate theoretically nonmagnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to topologically trivial Bardeen-Cooper-Schrieffer $s$-wave superfluid, topological superfluid can host a midgap state that is bound to localized nonmagnetic impurity. For strong impurity scattering, the bound state becomes universal, with nearly zero energy and a wave function that closely follows the symmetry of that of Majorana fermions. We propose that the observation of such a universal bound state could be useful evidence for characterizing the topological nature of topological superfluids. Our prediction is applicable to an ultracold, resonantly interacting Fermi gas of ${}^{40}$K atoms with spin-orbit coupling confined in a two-dimensional optical lattice.

We investigate the spontaneous emission of a two-level system, e.g., an atom or atomlike object, coupled to a single-end, i.e., a semi-infinite, one-dimensional photonic waveguide such that one end behaves as a perfect mirror while light can pass through the opposite end with no backreflection. Through a quantum microscopic model we show that such geometry can cause nonexponential and long-lived atomic decay. Under suitable conditions, a bound atom-photon stationary state appears in the atom-mirror interspace so as to trap a considerable amount of initial atomic excitation. Yet this can be released by applying an atomic frequency shift, causing a revival of photon emission. The resilience of such effects to typical detrimental factors is analyzed.

Recently, several theoretical proposals addressed the generation of an active optical frequency standard based on atomic ensembles trapped in an optical lattice potential inside an optical resonator. Using atoms with a narrow linewidth transition and population inversion together with a “bad” cavity allows us to realize the super-radiant photon emission regime. These schemes reduce the influence of mechanical or thermal vibrations of the cavity mirrors on the emitted optical frequency, overcoming current limitation in passive optical standards. The coherence time of the emitted light is ultimately limited by the lifetime of the atoms in the optical lattice potential. Therefore these schemes would produce one light pulse per atomic ensemble without a phase relation between pulses. Here we study how phase coherence between pulses can be maintained by using several inverted atomic ensembles, introduced into the cavity sequentially by means of a transport mechanism. We simulate the light emission process using the Heisenberg-Langevin approach and study the frequency noise of the intracavity field.

Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in a noncontextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of entangled, as well as product states. Our inequality can be experimentally tested using the existing technology.

We propose a technique for performing quantum state tomography of photonic polarization-encoded multiqubit states. Our method uses a single rotating wave plate, a polarizing beam splitter, and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudocontinuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes’ parameters that represent the state. The experimental complexity, i.e., different wave plate rotation frequencies, scales linearly with the number of qubits.

By studying the topological invariance and Berry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases $Q$ to identify the topological invariance for non-Hermitian systems. We find that $Q$ can identify topological invariance in two kinds of non-Hermitian model, the two-level non-Hermitian Hamiltonian and the bipartite dissipative model. For the bipartite dissipative model, an abrupt change of the Berry phase in the parameter space reveals a quantum phase transition and is related to the exceptional points. These results give the basic relationships between the Berry phase and the quantum and topological phase transitions of non-Hermitian systems.

We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete positive operator valued measurement (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVM's are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.

We investigate the scattering properties of quantum walks by considering single and double position defects on a one-dimensional line. This corresponds to introducing, at designated positions, delta potential defects for continuous-time quantum walks and phase-defect Hadamard coins for discrete time quantum walks. The delta potential defects can be readily considered as potential barriers in discrete position space, which affect the time evolution of the system in a similar way as the quantum wave-packet dynamics in a continuous position space governed by Schrödinger's equation. Although there is no direct analogy of potential barriers in the theoretical formulation of discrete time quantum walks, in this paper we show that the phase defects in the coin space can be utilized to provide similar scattering effects. This study provides means of controlling the scattering properties of quantum walks by introducing designated position-dependent defects.

We develop a method to quantify the secret key rate for permutation-invariant protocols for coherent attacks and finite resources. The method reduces the calculation of secret key rates for coherent attacks to the calculation for collective attacks by bounding the smooth min-entropy of permutation-invariant states via the smooth min-entropy of corresponding tensor-product states. The comparison of the results to the well-known postselection technique for the BB84 and six-state protocol shows the high relevance of this method. Since our calculation of secret key rates for coherent attacks strongly depends on the way of treating collective attacks, a prospective progress in the analysis of collective attacks will immediately cause progress in our strategy.

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

It has been found that non-Gaussian operations can be applied to increase and distill entanglement between Gaussian entangled states. We propose here a method to improve the performance of entanglement-based (EB) continuous-variable quantum-key-distribution protocol by using the non-Gaussian operation, in particular, the subtraction operation, which can be implemented under current technology easily. Security analysis shows that the subtraction operation can well increase the secure distance and tolerable excess noise of the EB scheme and also the corresponding prepare-and-measure scheme.

We report on a theoretical study and experimental characterization of coherent-population-trapping (CPT) resonances in buffer-gas-filled vapor cells with push-pull optical pumping (PPOP) on Cs $D_1$ line. We point out that the push-pull interaction scheme is identical to the so-called $\mathrm{lin}\perp \mathrm{lin}$ polarization scheme. Expressions of the relevant dark states, as well as of absorption, are reported. The experimental setup is based on the combination of a distributed feedback diode laser, a pigtailed intensity Mach-Zehnder electro-optic modulator (MZ EOM) for optical sideband generation and a Michelson-like interferometer. A microwave technique to stabilize the transfer function operating point of the MZ EOM is implemented for proper operation. A CPT resonance contrast as high as 78$\%$ is reported in a cm-scale cell for the magnetic-field-insensitive clock transition. The impact of the laser intensity on the CPT-clock signal key parameters (linewidth, contrast, linewidth/contrast ratio) is reported for three different cells with various dimensions and buffer-gas contents. The potential of the PPOP technique for the development of high-performance atomic vapor-cell clocks is discussed.

In this paper, we have investigated theoretically the influence of atomic collisions on the behavior of a one-dimensional Bose-Einstein condensate inside a driven optical cavity. We develop the discrete-mode approximation for the condensate taking into account the interband transitions due to the $s$-wave scattering interaction. We show that in the Bogoliubov approximation the atom-atom interaction shifts the energies of the excited modes and also plays the role of an optical parametric amplifier for the Bogoliubov side mode which can affect its normal-mode splitting behavior. On the other hand due to the atomic collisions the resonance frequency of the cavity is shifted which leads to the decrease of the number of cavity photons and the depletion of the Bogoliubov mode. Besides, it reduces the effective atom-photon coupling parameter which consequently leads to the decrease of the entanglement between the Bogoliubov mode and the optical field.

We present an extension of Nagaoka's theorem in the SU($n$) generalization of the infinite-$U$ Hubbard model. It is shown that, when there is exactly one hole, the fully polarized states analogous to the ferromagnetic states in the SU(2) Hubbard model are ground states. For a restricted class of models satisfying the connectivity condition, these fully polarized states are the unique ground states up to the trivial degeneracy due to the SU($n$) symmetry. We also give examples of lattices in which the connectivity condition can be verified explicitly. The examples include the triangular, Kagomé, and hypercubic lattices in $d(\ge 2)$ dimensions, among which the cases of $d=2$ and 3 are experimentally realizable in ultracold atomic gases loaded into optical lattices.

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar ${}^{164}$Dy droplet bound in a trapped nondipolar ${}^{87}$Rb BEC with a variable number of ${}^{164}$Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a ${}^{164}$Dy droplet by relaxing the trap on the ${}^{164}$Dy BEC in a trapped binary ${}^{87}$Rb-${}^{164}$Dy mixture.