We present theoretical and experimental results showing that a thermal ghost imaging system can produce images of high quality even when it uses detectors so slow that they respond only to intensity-averaged (that is, “blurred”) speckle patterns, as long as the collected signal variation is predominantly caused by the random fluctuation of the incident speckle field rather than other noise sources. In our experimental study, we show that the quality of the ghost image is not degraded when as many as 25 speckle patterns are averaged together for each measurement. This surprising result comes from the fact that the averaging of speckle patterns leads to a decrease in the contrast but not in the kurtosis, and the image quality of a ghost imaging system is dependent on the kurtosis rather than the contrast ratio of the illuminating field. These results suggest that a broad class of imaging systems based on the use of speckle techniques can be implemented even using detectors that respond slowly on the time scale of the fluctuating speckle pattern.

We present an experimental study of temporal retardation combined with temporal compression of weak laser pulses. The effect is optically controlled by the presence of another light pulse, although no coherent control is required. Probe pulse delays up to 13 ns and maximum compression factor of 3 were observed using few-ns-long laser pulses. We also present a theoretical model of pulse propagation that is able to reproduce the experimental results with fairly good accuracy.

We present results of our experimental investigations of nonlinear ground-state pump-probe spectroscopy in ultracold ${}^{85}$Rb collected in a magneto-optical trap. These measurements represent an extension of a similar pump-probe spectroscopy in a two-level atomic system when strongly driven by a near-resonant pump beam. In the present three-level system, coherence-induced gain at the probe laser frequency can be observed at specific frequencies within the spectrum. The absorption or gain spectra that we observe resemble those of the two-level gain spectra, but different interference processes lead to features that are not present in the two-level case. We describe our measurements of this interaction in this work.

We theoretically demonstrate the influence of dark and bright states on vacuum Rabi splitting (VRS) and optical bistability (OB) of the multi-wave-mixing (MWM) process in a collective four-level atomic-cavity coupling system. We numerically investigate the multidressed VRS and OB behavior of the zero- and high-order transmitted cavity modes of MWM signals. A further study demonstrates that VRS and self-Kerr nonlinearity OB can coexist and compete with each other in a cascade relationship, based on which we achieve the goal to control VRS and OB simultaneously through the dark state in the atomic system.

We provide an analytical expression for the energy gradient of electronically excited states within the combined time-dependent density-functional theory and the dynamical density-response formalism, called the Casida formalism. This is achieved by obtaining the nuclear coordinate derivatives of the Kohn-Sham eigenvalues and orbitals through density-functional perturbation theory (DFPT). The DFPT-based method was found successfully applied to obtain potential energy surfaces of small molecules (${\text{N}}_2$ and $\text{CO}$) and conduct a molecular dynamics simulation of a benzene molecule, thereby revealing the slow convergence problem associated with the singular matrix appearing in DFPT.

It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete positive operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather nontrivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.

We present a Lie-algebraic classification and detailed construction of the dynamical invariants, also known as Lewis-Riesenfeld invariants, of the four-level systems including two-qubit systems which are most relevant and sufficiently general for quantum control and computation. These invariants not only solve the time-dependent Schrödinger equation of four-level systems exactly but also enable the control, and hence quantum computation based on which, of four-level systems fast and beyond adiabatic regimes.

Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of nonclassical correlations of an arbitrary quantum system based on its minimal distance from the set of classical states, in terms of teleportation fidelity for general two-qubit and ($d\otimes d$)-dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two-qubit state must violate Bell's inequality. This is illustrated by an open-system model of a dissipative two-qubit state. For the ($d\otimes d$)-dimensional states the lower bound of discord is shown to be obtainable from an experimentally measurable witness operator.

We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3.

The selection of basic variables in current-density-functional theory and formal properties of the resulting formulations are critically examined. Focus is placed on the extent to which the Hohenberg-Kohn theorem, constrained-search approach, and Lieb's formulation (in terms of convex and concave conjugation) of standard density-functional theory can be generalized to provide foundations for current-density-functional theory. For the well-known case with the gauge-dependent paramagnetic current density as a basic variable, we find that the resulting total energy functional is not concave. It is shown that a simple redefinition of the scalar potential restores concavity and enables the application of convex analysis and convex (or concave) conjugation. As a result, the solution sets arising in potential-optimization problems can be given a simple characterization. We also review attempts to establish theories with the physical current density as a basic variable. Despite the appealing physical motivation behind this choice of basic variables, we find that the mathematical foundations of the theories proposed to date are unsatisfactory. Moreover, the analogy to standard density-functional theory is substantially weaker as neither the constrained-search approach nor the convex analysis framework carry over to a theory making use of the physical current density.

We investigate the scattering dynamics governed by the long-range van der Waals plus dipole-dipole interaction potential, $-C_6/R^6-C_3/R^3$, which describes the long-range interaction between two polar molecules in an electric field. In the spirit of quantum defect theory, a set of parameters which are nearly constants in the threshold regime is defined to characterize the scattering process. Using appropriate boundary conditions for the scattering wave functions and relevant parameters, we explore the quantum reflection by and quantum tunneling through the long-range potential. As a sample application, the reactive collision rates of ${}^{40}$K${}^{87}$Rb $+$ ${}^{40}$K${}^{87}$Rb are calculated.

We present a theory for manipulation of $d$-wave interaction of cold atoms with two lasers strongly driving two photoassociative transitions. The theory predicts the occurrence of a coherence between two excited ro-vibrational bound states due to the photoassociative dipole couplings of ground-state $d$-wave scattering state to the bound states. We show that this excited-state coherence significantly influences atom-atom interaction. In particular, this leads to the enhancement of $d$-wave elastic scattering and to the suppression of inelastic scattering. In the presence of an $s$-wave magnetic Feshbach resonance, the two lasers can couple the $s$-wave resonance with the $d$-wave scattering state, leading to the further enhancement in $d$-wave scattering at relatively low energy. Our numerical calculations based on realistic parameters show that $d$-wave manipulation would be most effective in case of atoms having excited diatomic states with narrow natural linewidth. We estimate that at an energy of 100 $\mu$K the inelastic scattering rate in Yb can be reduced to 20 s${}^{-1}$ while the elastic scattering rate can be two orders of magnitude larger.

We present an all-optical method to load ${}^{174}$Yb atoms into a single layer of an optical trap near the surface of a solid immersion lens which improves the numerical aperture of a microscope system. Atoms are transported to a region 20 $\mu$m below the surface using a system comprised by three optical dipole traps. The “optical accordion” technique is used to create a condensate and compress the atoms to a width of 120 nm and a distance of 1.8 $\mu$m away from the surface. Moreover, we are able to verify that after compression the condensate behaves as a two-dimensional quantum gas.

We demonstrate an extension of the x-ray grating interferometer three modal imaging method to a generalized stepping scheme using a phase object with small, random features. The method allows the recovery of the absorption, scattering, and two-dimensional phase image of the sample from a raster scan of the phase object. An additional extension of the method to recover the effective wave-front curvature is also described. The technique provides fine sensitivity and high spatial resolution and has only low requirements on spatial and longitudinal coherence of the x-ray beam. Imaging modes and processing methods are explained, and an experimental demonstration of the technique is provided by imaging a feather and the quantitative characterization of a compound refractive lens.

Starting from a generalization of the quantum trajectory theory [based on the stochastic Schrödinger equation (SSE)], non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows a consistent theory of quantum measurement in continuous time to be developed for these non-Markovian quantum trajectory models. In this context, the notions of “instrument,” “a priori,” and “a posteriori” states can be introduced. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non-Markovian effects come from the random environment, colored noises, randomness in the stimulating light, and delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied, and we show how these quantities are sensitive to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescent light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics.

We propose a protocol for a two-qubit quantum phase gate based upon the reflection of photon pulses from a quantum dot in a cavity. Depending on the state of the quantum dot the reflected photons acquire a conditional phase shift. The key ingredient is the ultrafast control of the quantum dot energies by electric fields, which allows for tuning the exciton and biexciton successively into resonance with the cavity mode. The complete dynamics of the gate are simulated, revealing a fidelity of about 0.9. The proposed scheme uses position coding and is therefore well suited to the implementation in an integrated photonic quantum processor.

We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in quantum information theory. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under some specific state rotations. In the two-state case, the connection between quantum discord and dimension witness is graphically discussed and intriguingly, our results illustrate that these two quantities are monotonically related to each other. For state encodings in the real $|0\rangle -|1\rangle$ plane, we derive an explicit analytical expression of the geometric discord and find that geometric discord reaches the maximal value for the optimal encoding strategy. However, for arbitrary state encodings in the Bloch sphere, our numerical simulations reveal that maximal geometric discord could not coincide with optimal $2\to 1$ QRAC.

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the form of linear constraints on the density matrix, the sequence of tests can prove that either all states satisfying the constraints are entangled or there is at least one separable state that satisfies them. The algorithm works even if the values of the constraints are only known to fall in a certain range. If the states are entangled, an entanglement witness is constructed and lower bounds on entanglement measures and related quantities are provided; if a separable state satisfies the constraints, a separable decomposition is provided to certify this fact.

Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over the transverse-electric and transverse-magnetic reflection coefficients associated with the surface, in analogy to the Lifshitz formula for the Casimir effect. We discuss the applications and potential limitations of this formula, and provide exact results for several models of the surface.

For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large $s$-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous one. We point out that a third type of trimer, “crossover trimers,” exists universally regardless of short-range details of the potential. These crossover trimers have neither discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the Kartavtsev-Malykh trimers, Efimov trimers, crossover trimers, and nonuniversal trimers in terms of the mass ratio and the $s$-wave scattering length by investigating the scaling property and universality (i.e., independence on short-range details) of the trimers.