We demonstrate the deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-not gate. Parity oscillation measurements reveal a Bell state fidelity of $F=0.58\pm 0.04$, which is above the entanglement threshold of $F=0.5$, without any correction for atom loss, and $F=0.71\pm 0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.

We show that the probability of the collision-induced absorption of nonresonant microwave photons by a gas of ultracold molecules is dramatically enhanced near a Feshbach scattering resonance. This can be used for detecting Feshbach resonances of ultracold molecules by measuring the microwave field absorption and for tuning the elastic scattering cross sections of ultracold molecules by varying the frequency and intensity of the microwave field in a wide range of the field parameters.

We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of three-dimensional lattice geometries this coupling is shown to affect only clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390-nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of ${10}^{-18}$ and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex geometries or other atomic systems, this shift could potentially be a limiting factor in clock accuracy.

We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann $\zeta$ function $\zeta (s,a)$. Indeed, the autocorrelation function at a time $t$ is determined by $\zeta (\sigma +i\tau ,a)$, where $\sigma$ is governed by the temperature of the thermal phase state and $\tau$ is proportional to $t$. We use the JWKB method to solve the inverse spectral problem for a general logarithmic energy spectrum; that is, we determine a family of potentials giving rise to such a spectrum. For large distances, all potentials display a universal behavior; they take the shape of a logarithm. However, their form close to the origin depends on the value of the Hurwitz parameter $a$ in $\zeta (s,a)$. In particular, we establish a connection between the value of the potential energy at its minimum, the Hurwitz parameter and the Maslov index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann $\zeta$ wave-packet dynamics using cold atoms in appropriately tailored light fields.

An implementation of the topological cluster-state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for nonlinear devices to create a lattice of entangled photons. Whereas the thresholds found for computational errors are quite satisfactory (above ${10}^{-3}$), the estimates of the minimum efficiencies needed for the detectors and quantum dots are beyond current technology’s reach. This is because we rely heavily on probabilistic entangling gates, which introduces loss into the scheme irrespective of detector and quantum-dot efficiencies.

In this paper, we investigate the relationship between the minimum-error probability $Q_E$ of ambiguous discrimination and the optimal inconclusive probability $Q_U$ of unambiguous discrimination. It is known that for discriminating two states, the inequality $Q_U⩾2Q_E$ has been proved in the literature. The main technical results are as follows: (1) We show that, for discriminating more than two states, $Q_U⩾2Q_E$ may not hold again, but the infimum of $Q_U/Q_E$ is $1,$ and there is no supremum of $Q_U/Q_E$, which implies that the failure probabilities of the two schemes for discriminating some states may be narrowly or widely gapped. (2) We derive two concrete formulas of the minimum-error probability $Q_E$ and the optimal inconclusive probability $Q_U$, respectively, for ambiguous discrimination and unambiguous discrimination among arbitrary $m$ simultaneously diagonalizable mixed quantum states with given prior probabilities. In addition, we show that $Q_E$ and $Q_U$ satisfy the relationship that $Q_U⩾\frac{m}{m-1}{Q}_E$.

We investigate the entanglement entropy of a block of $L$ sites in quasifree translation-invariant spin chains concentrating on the effect of reflection-symmetry breaking. The Majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these, it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large $L$ asymptotics of the entropy are calculated analytically for general gauge-invariant models, which have, until now, been done only for the reflection-symmetric sector. Analytical results are also derived for certain nongauge-invariant models (e.g., for the Ising model with Dzyaloshinskii-Moriya interaction). We also study numerically finite chains of length $N$ with a nonreflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first $L$ spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for noncritical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the saturation entropy as we approach the critical line. The paper also provides a concise but extensive review of the block-entropy asymptotics in translation-invariant quasifree spin chains with an analysis of the nearest-neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.

In a solid-state circuit QED system, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of a moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved feedback scheme. We show that this is essential to achieve a desirable control effect by the use of dispersive measurement.

Several families of states such as Werner states, Bell-diagonal states, and Dicke states are useful in understanding multipartite entanglement. Here we present a $(2^{N+1}-1)$-parameter family of $N$-qubit “$X$ states” that embraces all those families, generalizing previously defined states for two qubits. We also present the algebra of the operators that characterize the states and an iterative construction for this algebra, a subalgebra of su$(2^N)$. We show how a variety of entanglement witnesses can detect entanglement in such states. Connections are also made to structures in projective geometry.

We consider the Casimir-Polder potential of particles placed inside a metallic cylindrical cavity at finite temperatures, taking account of thermal nonequilibrium effects. In particular, we study how the resonant (thermal nonequilibrium) potential and transition rates can be enhanced by fine tuning the radius of the cavity to match the transition wavelength of the dominant transitions of the particle. Numerical calculations show that the cavity-induced energy-level shift of atoms prepared in low-lying Rydberg states can be enhanced beyond 30 kHz, which is within the range of observability of modern experiments. Because the magnitude of the resonance peaks depends sensitively on the low-frequency dissipation of the cavity metal, experiments in this setup could be a critical test of the disputed thermal correction to the Casimir force between metal plates.

In this paper we calculate the Casimir energy for a massless fermionic field confined inside a three-dimensional rectangular box. We use the MIT bag model boundary condition for the confinement. We use the direct mode summation method along with the Abel-Plana summation formula to compute the Casimir energy, without any use of regularization or analytic continuation techniques. We obtain a negative Casimir energy, as opposed to the previously reported result for the interior of a three-dimensional sphere.

Ab initio calculations for the strongly exoergic ${\mathrm{Li}}_2+\mathrm{F}$ harpoon reaction are presented using density-functional theory, complete active space self-consistent field, and multireference configuration interaction methods to argue that this reaction would be an ideal candidate for investigation with ultracold molecules. The lowest six states are calculated with the aug-correlation-consistent polarized valence triple-zeta basis set and at least two can be accessed by a ground rovibronic ${\mathrm{Li}}_2$ molecule with zero collision energy at all reaction geometries. The large reactive cross section (characteristic of harpoon reactions) and chemiluminescent products are additional attractive features of these reactions.

We investigate imaging of the spatial spin distribution of atoms in optical lattices using nonresonant light scattering. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. Furthermore, we show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.

We theoretically investigate the scattering of an attosecond electron wave packet launched by an attosecond pulse under the influence of an infrared laser field. As the electron scatters inside a spatially extended system, the dressing laser field controls its motion. We show that this interaction, which lasts just a few hundreds of attoseconds, clearly manifests itself in the spectral interference pattern between different quantum pathways taken by the outgoing electron. We find that the Coulomb-Volkov approximation, a standard expression used to describe laser-dressed photoionization, cannot properly describe this interference pattern. We introduce a quasiclassical model, based on electron trajectories, which quantitatively explains the laser-dressed photoelectron spectra, notably the laser-induced changes in the spectral interference pattern.

We present a compact cold-atom clock configuration where isotropic laser cooling, microwave interrogation, and clock signal detection are successively performed inside a spherical microwave cavity. For ground operation, a typical Ramsey fringe width of 20 Hz has been demonstrated, limited by the atom cloud’s free fall in the cavity. The isotropic cooling light’s disordered properties provide a large and stable number of cold atoms, leading to a high signal-to-noise ratio limited by atomic shot noise. A relative frequency stability of $2.2\times {10}^{-13}{\tau }^{-1/2}$ has been achieved, averaged down to $4\times {10}^{-15}$ after $5\times {10}^3$ s of integration. Development of such a high-performance compact clock is of major relevance for on-board applications, such as satellite-positioning systems. As a cesium clock, it opens the door to a new generation of compact primary standards and timekeeping devices.

We investigate the mean-field ground state of a homogeneous three-component attractive Fermi gas at zero temperature. This is achieved by deriving a set of Bogoliubov–de Gennes (BdG) equations of the three-component system, including pairing both order parameters ${\Delta }_{\mathit{ij}}$ and coherence order parameters $\langle {\psi }_i^{†}{\psi }_j\rangle$ ($i\ne j$), where ${\psi }_j$ is the field operator for spin level $j$. Ward-Takahashi identities are obtained to constrain these order parameters. In addition, we present an explicit analytic mean-field solution for symmetric systems and verify that the quasiparticle excitations consist of both gapped and gapless spectra, which correspond to the excitations of paired and unpaired atoms. We further point out that the omission of $\langle {\psi }_i^{†}{\psi }_j\rangle$ in BdG equations could lead to an overestimation of ${\Delta }_{\mathit{ij}}$ in the strong coupling regime.

Squeezed states and macroscopic superpositions of coherent states have been predicted to be generated dynamically in Bose Josephson junctions. We solve exactly the quantum dynamics of such a junction in the presence of a classical noise coupled to the population-imbalance number operator (phase noise), accounting for, for example, the experimentally relevant fluctuations of the magnetic field. We calculate the correction to the decay of the visibility induced by the noise in the non-Markovian regime. Furthermore, we predict that such a noise induces an anomalous rate of decoherence among the components of the macroscopic superpositions, which is independent of the total number of atoms, leading to potential interferometric applications.

The dynamic structure factor of a normal Fermi gas is investigated by using the moment method for the Boltzmann equation. We determine the spectral function at finite temperatures over the full range of crossover from the collisionless regime to the hydrodynamic regime. We find that the Brillouin peak in the dynamic structure factor exhibits a smooth crossover from zero to first sound as functions of temperature and interaction strength. The dynamic structure factor obtained using the moment method also exhibits a definite Rayleigh peak ($\omega ~0$), which is a characteristic of the hydrodynamic regime. We compare the dynamic structure factor obtained by the moment method with that obtained from the hydrodynamic equations.

We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schrödinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.

We show that dark-state resonances can be a fundamental mechanism for the entanglement between light and matter. While two optical fields trap an ensemble of three-level $\Lambda$ atoms into the dark state, the coherence is created between the two metastable states, and the two fields undergo no absorption. The trapped atoms behave like a coherently coupled two-party reservoir and act on the two fields. As a result, Einstein-Podolsky-Rosen entanglement is obtainable between the atomic ensemble and one collective field under proper parameter conditions. Long-lived atomic coherence and no need of nonclassical input light are the advantages for quantum communications between light and matter based on the present mechanism.