We propose measurement-based conditional generation of the superposition of mesoscopic states of a nanomechanical resonator. We consider a two-level quantum mechanical system (qubit) coupled with a nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of the nanomechanical resonator depending on the state of the qubit, is realized by driving the qubit through two resonant fields or a single field with controlled phase. The measurement of the state of the qubit produces superposition states of the nanomechanical resonator. We show that the quantum interference between the generated states in the superposition may lead to an arbitrary large displacement in the resonator. We also discuss decoherence of the generated states using the Wigner function.

Light propagation in a nonlinear optical medium is nonreciprocal for spatially asymmetric linear permittivity. We examine the physical mechanism and properties of such nonreciprocity (NR). For this, we calculate the transmission of light through two models of a nonlinear optical isolator consisting of (a) a two-level atom and (b) a driven $\mathrm{\Lambda }$-type three-level atom coupled asymmetrically to light inside open waveguides. We find a higher NR in the model (b) than in the model (a) due to a stronger optical nonlinearity in the former. We determine the critical intensity of incident light for maximum NR and a dependence of the corresponding NR on asymmetry in the coupling. Surprisingly, we find that it is mainly coherent elastic scattering compared to incoherent scattering of incident light which causes maximum NR near the critical intensity. We also show a higher NR of an incident light in the presence of an additional weak light at the opposite port.

We revisit the confinement-induced $p$-wave resonance in quasi-one-dimensional (quasi-1D) atomic gases and study the induced molecules near resonance. We derive the reduced 1D interaction parameters and show that they can well predict the binding energy of shallow molecules in quasi-1D system. Importantly, these shallow molecules are found to be much more spatially extended compared to those in three dimensions (3D) without transverse confinement. Our results strongly indicate that a $p$-wave interacting atomic gas can be much more stable in quasi-1D near the induced $p$-wave resonance, where most weight of the molecule lies outside the short-range regime and thus the atom loss could be suppressed.

We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical fluctuating field. We find that for short interaction times the dynamics of the open system is described by a Gaussian noise map for several different interaction models and independently on the temperature of the environment. In order to go beyond a qualitative understanding of the origin and physical meaning of the above short-time constraint, we take a general viewpoint and, based on an algebraic approach, suggest that any quantum environment can be described by classical fields whenever global symmetries lead to the definition of environmental operators that remain well defined when increasing the size, i.e., the number of dynamical variables, of the environment. In the case of the bosonic environment this statement is exactly demonstrated via a constructive procedure that explicitly shows why a large number of environmental dynamical variables and, necessarily, global symmetries, entail the set of conditions derived in the first part of the work.

We give a path-integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hslash$. The largest power of $\hslash$ required to describe the evolution is a traditional measure of classicality. We show that the action of the Clifford operators on stabilizer states can be fully described by a single contribution of a path integral truncated at order ${\hslash }^0$ and so are “classical,” just like propagation of Gaussians under harmonic Hamiltonians in the continuous case. Such operations have no dependence on phase or quantum interference. Conversely, we show that supplementing the Clifford group with gates necessary for universal quantum computation results in a propagator consisting of a finite number of semiclassical path-integral contributions truncated at order ${\hslash }^1$, a number that nevertheless scales exponentially with the number of qudits. The same sum in continuous systems has an infinite number of terms at order ${\hslash }^1$.

We investigate the interatomic Coulombic decay (ICD) in argon dimers induced by electron-impact ionization ($E_0=90\mathrm{eV}$) using a multiparticle coincidence experiment in which the momentum vectors and, consequently, the kinetic energies for electrons and fragment ions are determined. The signature of the ICD process is obtained from a correlation map between ejected electron energy and kinetic energy release (KER) for ${\mathrm{Ar}}^{+}+{\mathrm{Ar}}^{+}$ fragment ions where low-energy ICD electrons can be identified. Furthermore, two types of ICD processes, termed fast and slow interatomic decay, are separated by the ICD initial-state energies and projectile energy losses. The dependence of the energies of emitted low-energy ICD electrons on the initial-state energy is studied. ICD electron energy spectra and KER spectra are obtained separately for fast and slow decay processes where the KER spectra for the slow decay channel are strongly influenced by nuclear motion. The KER and ICD electron energy spectra are well reproduced by ab initio calculations.

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the $\mu \mathrm{Gal}$ regime ($1\mu \mathrm{Gal}={10}^{-8}\mathrm{m}/{\mathrm{s}}^2\approx {10}^{-9}\mathrm{g}$). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as $2.04\mu \mathrm{Gal}$. The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

The one-body density matrix (OBDM) is a fundamental contraction of the Bose-Einstein condensate wave function, encapsulating its one-body properties. It serves as a major analysis tool with which the condensed component of the density can be identified. Despite its cardinal importance, calculating the ground-state OBDM of trapped interacting bosons is a challenge and to date OBDM calculations have been published only for homogeneous systems or for trapped weakly interacting bosons. In this paper we discuss an approach for computing the OBDM based on a double-walker diffusion Monte Carlo random walk coupled with a stochastic permanent calculation. We here describe the method and study some of its statistical convergence and properties applying it to some model systems.

We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $\rho$ and the wave number of resonant light $k$ satisfy $\rho k^{-3}\gtrsim 1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes strongly correlated. The deviations from mean-field theory appear to scale with the parameter $\rho k^{-3}$, and we demonstrate noticeable effects already at $\rho k^{-3}\simeq {10}^{-2}$. In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and “cooperative Lamb shift,” but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.

We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.

It is argued that a weak value of an observable is a robust property of a single pre- and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system preselected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre- and postselected in mixed states are considered.

Exploiting the master equations in the Lindblad form, we establish a sufficient and necessary condition for a Markovian dynamics to be unital. Based on this condition, we analyze the dynamical property of quantum Rényi entropy and propose a characterization of quantum non-Markovianity for unital dynamics in terms of Rényi entropy, which contains the previous criteria of non-Markovianity via von Neumann entropy and linear entropy as particular cases. The effectiveness of this measure in capturing the backflow of information from the environment is illustrated through several typical unital dynamics.

We introduce and analyze graph-associated entanglement cost, a generalization of the entanglement cost of quantum states to multipartite settings. We identify a necessary and sufficient condition for any multipartite entangled state to be constructible when quantum communication between the multiple parties is restricted to a quantum network represented by a tree. The condition for exact state construction is expressed in terms of the Schmidt ranks of the state defined with respect to edges of the tree. We also study approximate state construction and provide a second-order asymptotic analysis.

We present calculations of electron-capture cross sections in collisions of ${\mathrm{H}}^{+}$ with BeH molecules in the energy range $25\mathrm{eV}<E<10\mathrm{keV}$. We discuss the validity of the models employed to describe nonadiabatic ion-molecule collisions, specifically the eikonal approximation, the Franck-Condon approximation, and the isotropic approximation to obtain orientation-averaged cross sections, which is based on the infinite-order sudden approximation. The calculation using the Franck-Condon approximation leads to a total electron-capture cross section that is practically independent of the collision energy with a value of around ${25\AA }^2$. The calculations using the more accurate sudden vibrational approximation indicate that the Franck-Condon approximation overestimates the electron-capture cross section by at most 20%. At $E<1$ keV, the main product of the electron-capture process is the formation of ${\mathrm{BeH}}^{+}\left(2{}^1{\mathrm{\Sigma }}^{+}\right)+\mathrm{H}\left(1s\right)$. At higher energies, the cross sections for formation of ${\mathrm{BeH}}^{+}\left(2{}^1{\mathrm{\Sigma }}^{+}\right)+\mathrm{H}\left(1s\right)$ and ${\mathrm{BeH}}^{+}\left(1{}^3{\mathrm{\Sigma }}^{+}\right)+\mathrm{H}\left(1s\right)$ are practically identical. The Coriolis couplings are particularly relevant to the mechanism of this reaction, which precludes the merging of semiclassical (including Coriolis couplings) and quantal results (neglecting Coriolis couplings) in the energy range of the present calculation.

We theoretically investigate the electron-tunneling process for a helium atom irradiated by an elliptical strong laser field. The momentum distribution for an electron ionized during the cycle when the laser intensity reaches its maximum is captured, such that we can ignore the interference between the wave packets ionized in different laser cycles and precisely determine the center of the momentum distribution. The quantum mechanical prediction of the center position is further compared to the semiclassical single-trajectory simulation as well as the experimental data. We find that the electron momentums along the minor axis of the laser polarization show good agreement with the nonadiabatic semiclassical calculation for a wide range of laser intensities, indicating the existence of a nonzero lateral momentum when the electron exits the barrier. On the other hand, the offset angles obtained by our quantum mechanical approach for different laser intensities are larger than the nonadiabatic semiclassical results, indicating the importance of the quantum effects during the electron's under-the-barrier dynamics.

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\delta$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasimomenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength ${\gamma }_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

A new generation of cold atom experiments trapping atomic mixtures in species-selective optical potentials opens up the intriguing possibility to create systems in which different atoms live in different spatial dimensions. Inspired by this, we investigate a mixed-dimensional Bose polaron consisting of an impurity particle moving in a two-dimensional (2D) layer immersed in a 3D Bose-Einstein condensate (BEC), using a theory that includes the mixed-dimensional vacuum scattering between the impurity and the bosons exactly. We show that similarly to the pure 3D case, this system exhibits a well-defined polaron state for attractive boson-impurity interaction that evolves smoothly into a mixed-dimensional dimer for strong attraction, as well as a well-defined polaron state for weak repulsive interaction, which becomes overdamped for strong interaction. We furthermore find that the properties of the polaron depend only weakly on the gas parameter of the BEC as long as the Bogoliubov theory remains a valid description for the BEC. This indicates that higher-order correlations between the impurity and the bosons are suppressed by the mixed-dimensional geometry in comparison to a pure 3D system, which led us to speculate that the mixed-dimensional polaron has universal properties in the unitarity limit of the impurity-boson interaction.

Here the Abraham-Minkowski controversy on the correct definition of the light momentum in a macroscopic medium is revisited with the purpose to highlight that an effective medium formalism necessarily restricts the available information on the internal state of a system, and that this is ultimately the reason why the dilemma has no universal solution. Despite these difficulties, it is demonstrated that in the limit of no material absorption and under steady-state conditions, the time-averaged light (kinetic) momentum may be unambiguously determined by the Abraham result, both for bodies at rest and for circulatory flows of matter. The implications of these findings are discussed in the context of quantum optics of moving media, and we examine in detail the fundamental role of the Minkowski momentum in such a context.

The optomechanics can generate fantastic effects of optics due to appropriate mechanical control. Here we theoretically study effects of slow and fast lights in a single-sided optomechanical cavity with an external force. The force-induced transparency of slow and fast lights and the force-dependent conversion between the slow and fast lights result from effects of the rotating-wave approximation (RWA) and the anti-RWA, which can be controlled by properly modifying the effective cavity frequency due to the external force. These force-induced phenomena can be applied to control the light group velocity and to detect the force variation, which are feasible using current laboratory techniques.