Microwave near-field quantum control of spin and motional degrees of freedom of ${}^{25}$Mg${}^{+}$ ions can be used to generate two-ion entanglement, as recently demonstrated in Ospelkaus et al. [Nature 476, 181 (2011)]. Here, we describe additional details of the setup and calibration procedures for these experiments. We discuss the design and characteristics of the surface-electrode trap and the microwave system and compare experimental measurements of the microwave near fields with numerical simulations. Additionally, we present a method that utilizes oscillating magnetic-field gradients to detect micromotion induced by the ponderomotive radio-frequency potential in linear traps. Finally, we discuss the present limitations of microwave-driven two-ion entangling gates in our system.

We study resonantly enhanced cascaded two-photon transitions in Doppler-broadened rubidium vapor, induced by an optical frequency comb. Cascaded two-step excitation of atoms from the ground state 5$S$${}_{1/2}$ to the final 5$D$${}_{5/2}$ state via an intermediate 5$P$${}_{3/2}$ state as well as the influence of the frequency comb repetition rate on the two-photon fluorescence signal have been investigated. It is shown that the careful choice of $f_R$ leads to enhancement of the two-photon signal with considerable increase of the final $5D_{5/2}$-state population due to velocity-selective double resonance. Since the double-resonance condition for two different rubidium isotopes is fulfilled for different $f_R$, the possibility of isotope-selective two-photon excitation is explored. The dependence of the two-photon signal on external magnetic field values and different repetition rates of the optical frequency comb is also investigated.

Many ion species commonly used for laser-cooled ion-trapping studies have a low-lying metastable ${}^2{D}_{3/2}$ state that can become populated due to spontaneous emission from the ${}^2{P}_{1/2}$ excited state. This requires a repumper laser to maintain the ion in the Doppler cooling cycle. Typically, the ${}^2{D}_{3/2}$ state, or some of its hyperfine components if the ion has nuclear spin, has a higher multiplicity than the upper state of the repumping transition. This can lead to dark states, which have to be destabilized by an external magnetic field or by modulating the polarization of the repumper laser. We propose using unpolarized, incoherent amplified spontaneous emission (ASE) to drive the repumping transition. An ASE source offers several advantages compared to a laser. It prevents the buildup of dark states without external polarization modulation even in zero magnetic field, it can drive multiple hyperfine transitions simultaneously, and it requires no frequency stabilization. These features make it very compact and robust, which is essential for the development of practical, transportable optical ion clocks. We construct a theoretical model for the ASE radiation, including the possibility of the source being partially polarized. Using ${}^{88}{\mathrm{Sr}}^{+}$ as an example, the performance of the ASE source compared to a single-mode laser is analyzed by numerically solving the eight-level density-matrix equations for the involved energy levels. Finally, a reduced three-level system is derived, yielding a simple formula for the excited-state population and scattering rate, which can be used to optimize the experimental parameters. The required ASE power spectral density can be obtained with current technology.

Ultracold atoms in optical lattices provide an ideal platform for exploring many-body physics of a large system arising from the coupling among a series of small identical systems whose few-body dynamics is exactly solvable. Using Landau-Zener (LZ) transition of bosonic atoms in double-well optical lattices as an experimentally realizable model, we investigate such few- to many-body routes by exploring the relation and difference between the small few-body (in one double well) and the large many-body (in double-well lattice) nonequilibrium dynamics of cold atoms in optical lattices. We find the many-body coupling between double wells greatly enhances the LZ transition probability. The many-body dynamics in the double-well lattice shares both similarity and difference from the few-body dynamics in one and two double wells. The sign of the on-site interaction plays a significant role in the many-body LZ transition. Various experimental signatures of the many-body LZ transition, including atom density, momentum distribution, and density-density correlation, are obtained.

We study the real-time motion of a microscopic object in a cold Fermi gas at unitary conditions by using an extended Thomas-Fermi density functional approach. We find that the spontaneous creation of singly quantized vortex-antivortex pairs occurs as a critical velocity is exceeded, which leads to a drag between the moving object and the Fermi gas. The resulting force is linear in the velocity for subsonic motion and becomes quadratic for supersonic motion.

The performance of a coherent perfect absorber (time-reversed laser) is limited by quantum and thermal noise. At zero temperature, the quantum shot noise dominates the signal for frequencies close to the resonance frequency and both vanish exactly at the resonance frequency. We compute the sensitivity of the absorbing cavity as a background-free detector, limited by finite signal or detector bandwidth.

Two-photon-counting interferometry has been realized by measuring the electrical current due to two-photon absorption in the space-charge layer of a semiconductor detector located at the output port of an interferometer. We apply this technique to study the correlation properties of twin beams issued from parametric fluorescence. We describe in detail how the different second-order correlation functions (interbeam, intrabeam) can be extracted at the femtosecond time scale from raw data. The values of these correlation functions determined by our experiments are in excellent agreement with theory. More precisely, extrabunching in twin beams is unambiguously demonstrated and theoretically described using two models: a comprehensive multimode quantum optics model and a simpler classical stochastic approach. Given the high brightness of our twin-beam source, both theories yield similar results. Finally, convenient analytical expressions of the correlation functions were derived from both theories, expressions in which we have been able to relate specific terms to accidental and exact coincidences between photons. Two-photon interferometry thus determines to which extent twin photons are twin. This technique should become a useful tool for future quantum optics developments.

We performed an experiment to observe the storage of an input probe field and an idler field generated through an off-axis four-wave mixing (FWM) process via a double-Λ configuration in a cold atomic ensemble. We analyzed the underlying physics in detail and found that the retrieved idler field came from two parts if there was no single-photon detuning for the pump pulse: Part 1 was from the collective atomic spin (the input probe field, the coupling field, and the pump field combined to generate the idler field through FWM; then the idler was stored through electromagnetically induced transparency). Part 2 was from the generated new FWM process during the retrieval process (the retrieved probe field, the coupling field, and the pump field combined to generate a new FWM signal). If there was single-photon detuning for the pump pulse, then the retrieved idler was mainly from part 2. The retrieved two fields exhibited damped oscillations with the same oscillatory period when a homogeneous external magnetic field was applied, which was caused by the Larmor spin precession. We also experimentally realized the storage and retrieval of an image of light using FWM, in which an image was added into the input signal. After the storage, the retrieved idler beams and input signal carried the same image. This image storage technique holds promise for applications in image processing, remote sensing, and quantum communication.

We discuss quantum and classical aspects of two-photon interference in light transmission through disordered media. We show that disorder is the main factor that suppresses the interference, whatever the quantum state of the incident light. Secondarily, the two-photon interference is affected by the quantum nature of light (i.e., the well-defined number of photons in the two-photon entangled and Fock states as compared to the coherent state). And finally, entanglement is a resource that allows one to prepare two-photon states with special symmetries with respect to the interchange of the photons and, in particular, the states with bosonic and fermionic symmetries. The two-photon interference is more robust for the latter states and its sign can be inverted for the fermionic state.

In this paper, we study the full statistics of photons transmitted through an optical cavity coupled to nanomechanical motion. We analyze the entire temporal evolution of the photon correlations, the Fano factor, and the effects of strong laser driving, all of which show pronounced features connected to the mechanical backaction. In the regime of single-photon strong coupling, this allows us to predict a transition from sub-Poissonian to super-Poissonian statistics for larger observation time intervals. Furthermore, we predict cascades of transmitted photons triggered by multiphoton transitions. In this regime, we observe Fano factors that are drastically enhanced due to the mechanical motion.

Quantum mechanics exhibits a very peculiar form of contextuality. Identifying and connecting the simplest scenarios in which more general theories can or cannot be more contextual than quantum mechanics is a fundamental step in the quest for the principle that singles out quantum contextuality. The former scenario corresponds to the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality. Here we show that there is a simple tight inequality, twin to the KCBS, for which quantum contextuality cannot be outperformed. In a sense, this twin inequality is the simplest tool for recognizing fully contextual quantum correlations.

Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a quantum-classical gap. These are the most elementary logical Bell inequalities. We show that the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and report violations in good agreement with the quantum predictions. Unlike other experiments testing noncontextuality inequalities with pentagonal exclusivity, the ones reported here are free of the compatibility loophole.

Understanding the rich dynamics of open quantum systems is of fundamental interest to quantum control and quantum information processing. By considering an open system of many identical two-level atoms interacting with a common bath, we show that the effects of system-bath correlations are amplified in a many-body system via the generation of a bath-dependent short time scale (inversely proportional to the number of atoms) in the system dynamics. The effects of system-bath correlations are therefore considerable even when each individual atom interacts with the bath weakly. We further show that the correlation-induced dynamical effects may still be suppressed via the dynamical decoupling approach, but they present a challenge for quantum state protection as the number of atom increases.

We study the appearance of an Abelian geometric phase in relativistic and nonrelativistic quantum dynamics of a neutral particle due to the presence of an edge dislocation. We demonstrate that the nonminimal coupling of fermions with torsion introduces a geometric phase in the wave function of the neutral particle in relativistic and in nonrelativistic quantum dynamics.

We show a geometric formulation for minimum-error discrimination of qubit states that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal a priori probabilities, we provide a systematic way of finding optimal discrimination and the complete solution in a closed form. This generally gives a bound to cases when prior probabilities are unequal. Then it is shown that the guessing probability does not depend on detailed relations among the given states, such as the angles between them, but on a property that can be assigned by the set of given states itself. This also shows how a set of quantum states can be modified such that the guessing probability remains the same. Optimal measurements are also characterized accordingly, and a general method of finding them is provided.

The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to act as a catalyst, one also speaks of randomness expansion. R. Colbeck and A. Kent [J. Phys. A 44, 095305 (2011)] proposed the first method for generating randomness from untrusted devices, but without providing a rigorous analysis. This was addressed subsequently by S. Pironio et al. [Nature (London) 464, 1021 (2010)], who aimed at deriving a lower bound on the min-entropy of the data extracted from an untrusted device based only on the observed nonlocal behavior of the device. Although that article succeeded in developing important tools for reaching the stated goal, the proof itself contained a bug, and the given formal claim on the guaranteed amount of min-entropy needs to be revisited. In this paper we build on the tools provided by Pironio et al. and obtain a meaningful lower bound on the min-entropy of the data produced by an untrusted device based on the observed nonlocal behavior of the device. Our main result confirms the essence of the (improperly formulated) claims of Pironio et al. and puts them on solid ground. We also address the question of composability and show that different untrusted devices can be composed in an alternating manner under the assumption that they are not entangled. This enables superpolynomial randomness expansion based on two untrusted yet unentangled devices.

Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private; i.e., they appear random not only to the user but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed to sample the behavior of the quantum devices and to extract uniform randomness from the raw outputs of the devices, one usually speaks of device-independent randomness expansion. The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical side information; i.e., proving randomness against quantum side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, however, will generate cryptographically secure randomness that cannot be predicted by the adversary, and thus one can, given access to free public randomness, talk about private randomness generation. The theoretical tools to quantify the generated randomness according to these criteria were already introduced in S. Pironio et al. [Nature (London) 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device-independent randomness generation.

We show that a thermal reservoir can effectively act as a squeezed reservoir on atoms that are subject to energy-level modulation. For sufficiently fast and strong modulation, for which the rotating-wave approximation is broken, the resulting squeezing persists at long times. These effects are analyzed by a master equation that is valid beyond the rotating-wave approximation. As an example we consider a two-level atom in a cavity with Lorentzian linewidth, subject to sinusoidal energy modulation. A possible realization of these effects is discussed for Rydberg atoms.

We propose a versatile approach for generating multipartite $W$ states in predesigned on-chip multiport photonic lattices. It is shown that is possible to produce photon-encoded $W$ states where exactly one photon is coherently “shared” among $N$ optical modes by judiciously adjusting the coupling coefficients involved in one-dimensional arrays of evanescently coupled single-mode waveguides. Two-dimensional waveguide configurations are also investigated as possible avenues to produce $W$ states with equal probability amplitudes and equal relative phases.

The protection of quantum states is challenging for nonorthogonal states, especially in the presence of noise. Recent research shows that this difficulty can be overcome by feedback control with weak measurements. However, the state-protection schemes proposed recently work optimally only for special quantum states. In this paper, by applying different weak measurements, we extend the idea of the state-protection scheme to include protecting general states. We calculate numerically the optimal parameters and discuss the performance of the scheme. Comparison between this extended scheme and the earlier scheme is also presented.