In a weak measurement with postselection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of an observable. However, there are some controversies whether weak-value amplification is practically useful in increasing the sensitivity of the measurement, in which fundamental quantum noise dominates. In this paper, we investigate the sensitivity limit of an optical interferometer when weak-value amplification is implemented, properly accounting for quantum shot noise and radiation-pressure noise. To do so, we formulate weak-value amplification in the Heisenberg picture instead of in the Schrödinger picture, which is conventionally used. This formulation enables us to understand intuitively what happens when the measurement outcome is postselected and the weak value is amplified. As a result, we find that the sensitivity limit is given by the standard quantum limit that is the same as in a standard interferometry. We also discuss a way to circumvent the standard quantum limit.

We generalize and extend the stochastic path-integral formalism and action principle for continuous quantum measurement introduced in Chantasri, Dressel, and Jordan [Phys. Rev. A 88, 042110 (2013)], where the optimal dynamics, such as the most likely paths, is obtained by extremizing the action of the stochastic path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behavior of continuous quantum measurement. Examples are given for the qubit case. For qubit measurement with zero-qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time-correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.

Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimentally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally noncontextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.

We study a tripartite quantum system consisting of a coplanar-waveguide (CPW) resonator and a nanomechanical resonator (NAMR) connected by a flux qubit, where the flux qubit has a large detuning from both resonators. By a unitary transformation and a second-order approximation, we obtain a strong and controllable (i.e., magnetic-field-dependent) effective coupling between the NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting can be observed from the voltage-fluctuation spectrum of the CPW resonator. We further study the properties of single-photon transport as inferred from the reflectance or equivalently the transmittance. We show that the reflectance and the corresponding phase-shift spectra both exhibit doublet of narrow spectral features due to vacuum Rabi splitting. By tuning the external magnetic field, the reflectance and the phase shift can be varied from 0 to 1 and $-\pi$ to $\pi$, respectively. The results indicate that this hybrid quantum system can act as a quantum router.

We show that a squeezed bath, that acts on the central element of a harmonic chain, can drive the whole system to a steady state featuring a series of nested entangled pairs of oscillators that, ideally, covers the whole chain regardless of its size. We study how to realize this effect in various physical implementations, including optomechanical and superconducting devices, using currently available technologies. In these cases no squeezed fields are actually needed, and the squeezed bath is, instead, simulated by quantum reservoir engineering with bichromatic drives.

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the “simplex of complete graphs” in time $\mathrm{\Theta }\left(N^{3/4}\right)$. We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly $\mathrm{\Theta }\left(\sqrt{N}\right)$. To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

We present a quantum clock synchronization scheme of multiple parties which uses operation as the trigger to start the evolution of the initial state. In comparison, the existing protocols use measurement to start the evolution. We show that our protocol links the problem to a multiple-phase estimation problem, such that we have provided a general framework for the study of quantum clock synchronization. We can use the Fisher information to give the precision of the synchronization, and we explicitly show that the Heisenberg scale of synchronization is achieved in the two-party case. We prove that the measurement-triggered quantum clock synchronization is included in the operation-triggered quantum clock synchronization, so the operation-triggered quantum clock synchronization is, in general, more powerful than measurement-triggered quantum clock synchronization. We show that our protocol is very efficient in synchronizing a clock to the average time of other clocks.

A model for determining the hyperfine structure of the excited electronic states of diatomic bialkali heteronuclear molecules is formulated from the atomic hyperfine interactions and is applied to the case of bosonic ${}^{39}\mathrm{KCs}$ and fermionic ${}^{40}\mathrm{KCs}$ molecules. The hyperfine structure of the potential-energy curves of the states correlated to the $\mathrm{K}\left(4s{}^2{S}_{1/2}\right)+\mathrm{Cs}\left(6p{}^2{P}_{1/2,3/2}\right)$ dissociation limits is described in terms of different coupling schemes depending on the internuclear distance $R$. These results provide a step in the calculation of the hyperfine structure of rovibrational levels of these excited molecular states in the perspective of the identification of efficient paths for creating ultracold ground-state KCs molecules.

Radiative recombination (RR) into the $K$ shell and $L$ subshells of ${\mathrm{U}}^{92+}$ ions interacting with cooling electrons has been studied in an x-ray RR experiment at the electron cooler of the Experimental Storage Ring at GSI. The measured radiative recombination rate coefficients for electron-ion relative energies in the range 0–1000 meV demonstrate the importance of relativistic effects. The observed asymmetry of the measured $K$-RR x-ray emission with respect to the cooling energy, i.e., zero average relative velocity ($\langle v_{\mathrm{rel}}\rangle =0$), are explained by fully relativistic RR calculations. With our new approach, we show that the study of the angular distribution of RR photons for different relative energies opens new perspectives for detailed understanding of the RR of ions with cooling electrons in cold magnetized plasma.

We report a joint theoretical-experimental investigation on elastic electron scattering by acetone in the low- and intermediate-energy regions. More specifically, experimental differential, integral, and momentum-transfer cross sections are given in the 30–800 eV and ${10}^{\circ }–{120}^{\circ }$ ranges. Theoretical cross sections are reported in the 1–500 eV interval. The experimental differential cross sections were determined using a crossed electron-beam–molecular-beam geometry, whereas the absolute values of the cross sections were obtained using the relative-flow technique. Theoretically, a complex optical potential derived from a Hartree-Fock molecular wave function was used to represent the collision dynamics, and a single-center expansion method combined with the Padé approximant technique was used to solve the scattering equations. Our experimental cross-section data are in generally good agreement with the present calculated data. Also, our calculated grand-total and total absorption cross sections are in good agreement with the experimental results reported in the literature. Nevertheless, our calculations have revealed a strong shape resonance in the ${}^2{B}_2$ scattering channel not clearly seen in the experimental results. Possible reasons for this fact are also discussed.

We put forward a first-principle nonequilibrium Green's-function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin systems. The method can deal with pump fields of arbitrary strength, frequency, and duration as well as overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing pump-probe delay $\tau$ and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of dynamical correlation effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of ${\mathrm{Kr}}^{2+}$ with respect to ${\mathrm{Kr}}^{1+}$ as a function of $\tau$.

Ionization of molecular nitrogen plays an important role in the process of light-filament formation in air. In the present paper we theoretically investigated tunneling ionization of the valence $3{\sigma }_g$ and $1{\pi }_u$ shells in a ${\mathrm{N}}_2$ molecule using a strong near-infrared laser field. This research is based on our previously proposed theory of anti-Stokes-enhanced tunneling ionization with quantum accounting for the vibrationally excited states of the molecules [A. S. Kornev and B. A. Zon, Phys. Rev. A 86, 043401 (2012)]. We demonstrated that if the ${\mathrm{N}}_2$ molecule is ionized from the ground vibrational state, then the contribution of the $1{\pi }_u$ orbital is 0.5%. In contrast, for vibrationally excited states with a certain angle between the light polarization vector and the molecule axis, both shells can compete and even reverse their contributions due to the anti-Stokes mechanism. The structure constants of molecular orbitals are extracted from numerical solutions to the Hartree-Fock equations. This approach correctly takes into account the exchange interaction. Quantum consideration of vibrational motion results in the occurrence of the critical vibrational state, the tunneling ionization from which has the maximum rate. The numbers of the critical vibrational states are different for different valence shells. In addition, quantum description of vibrations changes the rate of ionization from the ground vibrational state by 20%–40% in comparison with the quasiclassical results.

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbor sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards the realization of topologically nontrivial band structures. In such a lattice the real-valued next-nearest neighbor transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three energy bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sublattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbor coupling, as well as enhanced topological band structures featuring Chern numbers higher than one leading to physics beyond the usual quantum Hall effect. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection.

Sums of matrix elements of spin-dependent two-body momentum-independent interactions and sums of their products are calculated analytically in the basis of many-body states with given total spin—the states built from spin and spatial wave functions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. As in the first part of the series [V. A. Yurovsky, Phys. Rev. A 91, 053601 (2015)], the sum dependence on the many-body states is given by universal factors, which are independent of the Hamiltonians of noninteracting particles. The sum rules are applied to perturbative analysis of energy spectra and to calculation of two-body spin-dependent local correlations.

Mixed adiabatic and diabatic passages through avoided crossings in the Stark map of cesium Rydberg atoms are employed as beam splitters and recombiners in an atom-interferometric measurement of energy-level splittings. We subject cold cesium atoms to laser-excitation, electric-field, and detection sequences that constitute an (internal-state) atom interferometer. The adiabatic state transformation in the interferometer's beam splitters enables the spectroscopy of states that are, due to selection rules, inaccessible to direct laser-spectroscopic observation. For the read-out of the interferometer we utilize state-dependent collisions, which selectively remove atoms of one kind from the detected signal. We investigate the dependence of the interferometric signal on timing and field parameters, and find good agreement with quantum simulations of the interferometer. Fourier analysis of the interferometric signals yield coherence frequencies that agree with corresponding energy-level differences in calculated Stark maps.

We study Landau damping in a Bose-Fermi superfluid mixture at finite temperatures. We find that at low temperatures, the Landau damping rate will be exponentially suppressed on both the BCS side and the BEC side of the Fermi superfluid. The momentum dependence of the damping rate is obtained, and it is quite different from the BCS side to the BEC side since the dominated low-energy excitations are different on the two sides. The relation between our result and the collective mode experiment in the recently realized Bose-Fermi superfluid mixture is also discussed.

We experimentally demonstrate the localization of excitation between hyperfine ground states of ${}^{87}\mathrm{Rb}$ atoms to as small as $\lambda /13$-wide spatial regions. We use ultracold atoms trapped in a dipole trap and utilize electromagnetically induced transparency (EIT) for the atomic excitation. The localization is achieved by combining a spatially varying coupling laser (standing wave) with the intensity dependence of EIT. The excitation is fast (150 ns laser pulses) and the dark-state fidelity can be made higher than 94% throughout the standing wave. Because the width of the localized regions is much smaller than the wavelength of the driving light, traditional optical imaging techniques cannot resolve the localized features. Therefore, to measure the excitation profile, we use an autocorrelation-like method where we perform two EIT sequences separated by a time delay, during which we move the standing wave.

We have recently developed a quantized fluctuational electrodynamics (QFED) formalism to describe the quantum aspects of local thermal balance formation and to formulate the electromagnetic field ladder operators so that they no longer exhibit the anomalies reported for resonant structures. Here we show how the QFED can be used to resolve between the left and right propagating fields to bridge the QFED and the quantum optical input-output relations commonly used to describe selected quantum aspects of resonators. The generalized model introduces a density of states concept describing interference effects, which is instrumental in allowing an unambiguous separation of the fields and related quantum operators into left and right propagating parts. In addition to providing insight on the quantum treatment of interference, our results also provide the conclusive resolution of the long-standing enigma of the anomalous commutation relations of partially confined propagating fields.

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle can be derived from the Dirac equation. The generalization of this problem to three dimensions is discussed in this paper. It shows that the three-dimensional Dirac particle in vector and scalar potentials has a confinement limit proportional to the modulus of expectation value of spin. This result obtained in Dirac equation is applicable for any Dirac particle confined in a finite region of space, even when vector and scalar potentials of quite general character are present. In addition, a Dirac particle confined in Lorentz scalar potential is discussed.