Quantum teleportation is one of the crucial protocols in quantum information processing. It is important to accomplish an efficient teleportation under practical conditions, aiming at a higher fidelity desirably using fewer resources. The continuous-variable (CV) version of quantum teleportation was first proposed using a Gaussian state as a quantum resource, while other attempts were also made to improve performance by applying non-Gaussian operations. We investigate the CV teleportation to find its ultimate fidelity under energy constraint identifying an optimal quantum state. For this purpose, we present a formalism to evaluate teleportation fidelity as an expectation value of an operator. Using this formalism, we prove that the optimal state must be a form of photon-number entangled states. We further show that Gaussian states are near optimal, while non-Gaussian states make a slight improvement and therefore are rigorously optimal, particularly in the low-energy regime.

For general bipartite quantum systems, many sets of locally indistinguishable orthogonal product states have been constructed so far. Here, we first present a general method to construct multipartite orthogonal product states in $d_1\otimes d_2\otimes \cdots \otimes d_n(d_{1,2,\cdots ,n}\ge 3,n\ge 4)$ by using some locally indistinguishable bipartite orthogonal product states. And we prove that these multipartite orthogonal quantum states cannot be distinguished by local operations and classical communication. Furthermore, in $d_1\otimes d_2\otimes \cdots \otimes d_n(d_{1,2,\cdots ,n}\ge 3,n\ge 5)$, we give a general method to construct a much smaller number of locally indistinguishable multipartite orthogonal product states for even and odd $n$ separately. In addition, we also present a general method to construct complete orthogonal product bases for the multipartite quantum systems. Our results demonstrate the phenomenon of nonlocality without entanglement for the multipartite quantum systems.

Photodetachment of negative ions in combined laser and low-frequency fields is investigated. The time-dependent Green's function method is used for calculation of electron flux at a macroscopic distance from the photodetachment source, typical for a photodetachment microscopy experiment. In calculating the electron flux, we use the stationary phase method for the time integral, equivalent to the semiclassical approximation, to compute the time-dependent wave function. The stationary points $t_1^{\left(i\right)}, i=1,...,n$ correspond to time instances of launching of classical trajectories arriving at the detector at a given spacetime point $(\mathbf{r},t)$. The number of trajectories $n$ contributing to the electron flux at any point in the classically allowed spacetime domain can be controlled by varying the switching interval of the high-frequency laser which initiates the photodetachment process. The divergences inherent in the electron flux in the semiclassical treatment are removed by using the uniform Airy approximation near the caustics.

We report the experimental determination of the $4s{}^2{S}_{1/2}$ $\leftrightarrow$ $3d{}^2{D}_{5/2}$ quadrupole transition matrix element in ${}^{40}\mathrm{Ca}^{+}$ by measuring the branching fraction of the $3d{}^2{D}_{5/2}$ state decaying into the ground state $4s{}^2{S}_{1/2}$ and the lifetime of the $3d{}^2{D}_{5/2}$ state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52) $e{a}_0^2$ with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.

We present experimental measurements of the steady-state ion number in a linear Paul trap (LPT) as a function of the ion-loading rate. These measurements, taken with (a) constant Paul trap stability parameter $q$, (b) constant radio-frequency (rf) amplitude, or (c) constant rf frequency, show nonlinear behavior. At the loading rates achieved in this experiment, a plot of the steady-state ion number as a function of loading rate has two regions: a monotonic rise (region I) followed by a plateau (region II). Also described are simulations and analytical theory which match the experimental results. Region I is caused by rf heating and is fundamentally due to the time dependence of the rf Paul-trap forces. We show that the time-independent pseudopotential, frequently used in the analytical investigation of trapping experiments, cannot explain region I, but explains the plateau in region II and can be used to predict the steady-state ion number in that region. An important feature of our experimental LPT is the existence of a radial cutoff ${\widehat{R}}_{\mathrm{cut}}$ that limits the ion capacity of our LPT and features prominently in the analytical and numerical analysis of our LPT-loading results. We explain the dynamical origin of ${\widehat{R}}_{\mathrm{cut}}$ and relate it to the chaos border of the fractal of non-escaping trajectories in our LPT. We also present an improved model of LPT ion-loading as a function of time.

Recently a scheme has been proposed for generating the two-dimensional Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al., Phys. Rev. A 93, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the Bogoliubov–-de Gennes simulations with a weak harmonic trap added.

A spin-orbit-coupled two-dimensional Bose gas is shown to simultaneously possess quasi- and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii-Kosterlitz-Thouless transition to a low-temperature phase with quasi-long-range order, as expected for a two-dimensional quantum gas. Additionally, the relative phase undergoes an Ising-type transition building up true long-range order, which is induced by the anisotropic spin-orbit coupling in combination with spin-dependent particle-particle interactions. Based on the Bogoliubov approach, expressions for the total- and relative-phase fluctuations are derived analytically for the low-temperature regime. Numerical simulations of the stochastic projected Gross-Pitaevskii equation give a good agreement with the analytical predictions.

We propose a realistic experiment to demonstrate a dynamic Kosterlitz-Thouless transition in ultracold atomic gases in two dimensions. With a numerical implementation of the truncated Wigner approximation we simulate the time evolution of several correlation functions, which can be measured via matter wave interference. We demonstrate that the relaxational dynamics is well described by a real-time renormalization-group approach and argue that these experiments can guide the development of a theoretical framework for the understanding of critical dynamics.

In recent years the interest in studying interactions of Rydberg atoms or ensembles thereof with optical and microwave frequency fields has steadily increased, both in the context of basic research and for potential applications in quantum information processing. We present measurements of the dispersive interaction between an ensemble of helium atoms in the $37s$ Rydberg state and a single resonator mode by extracting the amplitude and phase change of a weak microwave probe tone transmitted through the cavity. The results are in quantitative agreement with predictions made on the basis of the dispersive Tavis-Cummings Hamiltonian. We study this system with the goal of realizing a hybrid between superconducting circuits and Rydberg atoms. We measure maximal collective coupling strengths of 1 MHz, corresponding to $3\times {10}^3$ Rydberg atoms coupled to the cavity. As expected, the dispersive shift is found to be inversely proportional to the atom-cavity detuning and proportional to the number of Rydberg atoms. This possibility of measuring the number of Rydberg atoms in a nondestructive manner is relevant for quantitatively evaluating scattering cross sections in experiments with Rydberg atoms.

It has recently been demonstrated that a general three-dimensional (3D) polarization state cannot be considered an incoherent superposition of (1) a pure state, (2) a two-dimensional unpolarized state, and (3) a 3D unpolarized state [J. J. Gil, Phys. Rev. A 90, 043858 (2014)]. This fact is intimately linked to the existence of 3D polarization states with fluctuating directions of propagation, but whose associated polarization matrices R satisfy rank $\mathbf{R}=2$. In this work, such peculiar states are analyzed and characterized, leading to a meaningful general classification and interpretation of 3D polarization states. Within this theoretical framework, the interrelations among the more significant polarization descriptors presented in the literature, as well as their respective physical interpretations, are studied and illustrated with examples, providing a better understanding of the structure of polarimetric purity of any kind of polarization state.

It has recently been shown that passive lens designs can retain perfect lensing despite intrinsic loss in the comprising left-handed materials. Here we show that energy conservation is not at odds with the operation of such lossy perfect lenses: The irreversible transfer of electromagnetic power to the lossy material dictates that a smaller portion of the power emitted by the source arrives at the image, but image fidelity remains absolute. Moreover, the power that does arrive at the perfect image must drain from the system there. This is shown to apply to any layered perfect lens based on left-handed media, including the well-known Veselago lens. Combined with what is known about Maxwell's fisheye lens, our results suggest that power drainage is universal to all perfect lenses and is intrinsic to any perfect image. Properly addressing this unique power dynamics is therefore essential to any successful realization of practical perfect lenses with existing metamaterials.

Optomechanical systems driven by an effective blue-detuned laser can exhibit self-sustained oscillations of the mechanical oscillator. These self-oscillations are a prerequisite for the observation of synchronization. Here, we study the synchronization of the mechanical oscillations to an external reference drive. We study two cases of reference drives: (1) an additional laser applied to the optical cavity; (2) a mechanical drive applied directly to the mechanical oscillator. Starting from a master equation description, we derive a microscopic Adler equation for both cases, valid in the classical regime in which the quantum shot noise of the mechanical self-oscillator does not play a role. Furthermore, we numerically show that, in both cases, synchronization arises also in the quantum regime. The optomechanical system is therefore a good candidate for the study of quantum synchronization.

Quantum erasers with paths in the form of physical slits have been studied extensively and proven instrumental in probing wave-particle duality in quantum mechanics. Here we replace physical paths (slits) with abstract paths of orbital angular momentum (OAM). Using spin-orbit hybrid entanglement of photons, we show that the OAM content of a photon can be erased with a complementary polarization projection of one of the entangled pair. The result is the (dis)appearance of azimuthal fringes based on whether the “which-OAM” information was erased. We extend this concept to a delayed measurement scheme and show that the OAM information and fringe visibility are complementary.

When internal states of atoms are manipulated using coherent optical or radio-frequency (rf) radiation, it is essential to know the polarization of the radiation with respect to the quantization axis of the atom. We first present a measurement of the two-dimensional spatial distribution of the electric-field amplitude of a linearly polarized pulsed rf electric field at $\sim 25.6\mathrm{GHz}$ and its angle with respect to a static electric field. The measurements exploit coherent population transfer between the $35s$ and $35p$ Rydberg states of helium atoms in a pulsed supersonic beam. Based on this experimental result, we develop a general framework in the form of a set of equations relating the five independent polarization parameters of a coherently oscillating field in a fixed laboratory frame to Rabi rates of transitions between a ground and three excited states of an atom with arbitrary quantization axis. We then explain how these equations can be used to fully characterize the polarization in a minimum of five Rabi-rate measurements by rotation of an external bias field, or, knowing the polarization of the driving field, to determine the orientation of the static field using two measurements. The presented technique is not limited to Rydberg atoms and rf fields but can also be applied to characterize optical fields. The technique has the potential for sensing the spatiotemporal properties of electromagnetic fields, e.g., in metrology devices or in hybrid experiments involving atoms close to surfaces.

Quantum Brownian motion is a fundamental model for a proper understanding of open quantum systems in different contexts such as chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper we propose a different approach to describe this model. We provide an exact and analytic equation for the time evolution of the operators and we show that the corresponding equation for the states is equivalent to well-known results in the literature. The dynamics is expressed in terms of the spectral density, regardless of the strength of the coupling between the system and the bath. Our derivation allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations. An example is explicitly studied.

Attempts to find a quantum-to-classical correspondence in a classically forbidden region leads to nonphysical paths involving, for example, complex time or spatial coordinates. Here, we identify genuine quasiclassical paths for tunneling in terms of probabilistic correlations in sequential time-of-arrival measurements. In particular, we construct the postselected probability density $P_{\text{p.s.}}(x,\tau )$ for a particle to be found at time $\tau$ in position $x$ inside the forbidden region, provided that it later crossed the barrier. The classical paths follow from the maximization of the probability density with respect to $\tau$. For almost monochromatic initial states, the paths correspond to the maxima of the modulus square of the wave function ${\left|\psi (x,\tau )\right|}^2$ with respect to $\tau$ and for constant $x$ inside the barrier region. The derived paths are expressed in terms of classical equations, but they have no analogs in classical mechanics. Finally, we evaluate the paths explicitly for the case of a square potential barrier.

We present a Hamiltonian which can be used to convert any asymmetric state ${|\phi \rangle }_a{|\varphi \rangle }_b$ of two oscillators $a$ and $b$ into an entangled state via a single-step operation. Furthermore, with this Hamiltonian and only local operations, two oscillators, initially in any asymmetric initial states, can be entangled with a third oscillator. The prepared entangled states can be engineered with an arbitrary degree of entanglement. A discussion of the realization of this Hamiltonian is given. Numerical simulations show that, with current circuit QED technology, it is feasible to generate high-fidelity entangled states of two microwave optical fields, such as entangled coherent states, entangled squeezed states, entangled coherent-squeezed states, and entangled cat states. Our finding opens a avenue for creating not only wavelike or particlelike entanglement but also wavelike and particlelike hybrid entanglement.

This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-$\frac{1}{2}$ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.

In this work the single-electron capture and single-ionization processes are studied for proton collisions with He and Ar atoms at impact energies in the range 25–100 keV. Classical trajectory Monte Carlo simulations are benchmarked against experimental data obtained at the reaction microscope in Bariloche, Argentina, which employs the cold target recoil-ion momentum spectroscopy technique. Special emphasis is placed on describing the momentum transfer to the recoil ion for these collision systems.

We measure the temperature of a deeply degenerate Fermi gas, by using a weakly interacting sample of heavier bosonic atoms as a probe. This thermometry method relies on the thermalization between the two species and on the determination of the condensate fraction of the bosons. In our experimental implementation, a small sample of ${}^{41}\mathrm{K}$ atoms serves as the thermometer for a ${}^6\mathrm{Li}$ Fermi sea. We investigate the evaporative cooling of a ${}^6\mathrm{Li}$ spin mixture in a single-beam optical dipole trap and observe how the condensate fraction of the thermometry atoms depends on the final trap depth. From the condensate fraction, the temperature can be readily extracted. We show that the lowest temperature of 5.9(5)% of the Fermi temperature is obtained, when the decreasing trap depth closely approaches the Fermi energy. To understand the systematic effects that may influence the results, we carefully investigate the role of the number of bosons and the thermalization dynamics between the two species. Our thermometry approach provides a conceptually simple, accurate, and general way to measure the temperature of deeply degenerate Fermi gases. Since the method is independent of the specific interaction conditions within the Fermi gas, it applies to both weakly and strongly interacting Fermi gases.