We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuous-variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states and show that the full structure of inseparability classes cannot be discriminated based on the extractable work. This suggests that bipartite entanglement is the fundamental resource underpinning work extraction.

We theoretically study cooling of flexural modes of a mechanical oscillator by Bose-Einstein-condensate (BEC) atoms (Rb87) trapped in a magnetic trap. The mechanical oscillator with a tiny magnet attached on one of its free ends produces an oscillating magnetic field. When its oscillating frequency matches certain hyperfine Zeeman energy of Rb87 atoms, the trapped BEC atoms are coupled out of the magnetic trap by the mechanical oscillator, flying away from the trap with stolen energy from the mechanical oscillator. Thus the mode temperature of the mechanical oscillator is reduced. The mode temperature of the steady state of mechanical oscillator, measured by the mean steady-state phonon number in the flexural mode of the mechanical oscillator, is analyzed. It is found that ground state (phonon number less than 1) may be accessible with optimal parameters of the hybrid system of mechanical oscillator and trapped BEC atoms.

We investigate laser-induced quantum interference phenomena in superradiance processes evolving in an ensemble of initially excited $\mathrm{\Lambda }$-type closely packed three-level emitters. The lower doublet levels are pumped with a coherent laser field. Due to constructive quantum interference effects, the superradiance occurs in a much weaker atomic transition, which is not the case in the absence of the coherent driving. This result may be of visible relevance for enhancing ultraweak transitions in atomic or atomiclike systems or for high-frequency lasing effects.

The induced transparency was proposed recently in X. Guo et al. [Phys. Rev. Lett. 117, 123902 (2016)] based on a three-wave mixing system. In this paper, we find the double- and multitransparency window can also be observed in this system. The zero-absorption point and profile of the transparency window and the transform of single- and double-transparency window can be controlled by only adjusting the detunings between the laser and the corresponding cavity modes, which is different from the previous studies. A practical application of the three-wave-mixing-induced transparency is to measure the nonlinear coefficient, and the controllable absorption profiles can be employed to engineer a high quality factor of the cavity.

Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase shift due to a sample which has an associated optical loss, and compare phase estimation strategies using classical and nonclassical probe states. These comparisons are based on the attainable (quantum) Fisher information calculated per number of photons absorbed or scattered by the sample throughout the sensing process. We find that for a given number of incident photons upon the unknown phase, nonclassical techniques in principle provide less than a $20\%$ reduction in root-mean-square error (RMSE) in comparison with ideal classical techniques in multipass optical setups. Using classical techniques in a different optical setup that we analyze, which incorporates additional stages of interference during the sensing process, the achievable reduction in RMSE afforded by nonclassical techniques falls to only $\simeq 4\%$. We explain how these conclusions change when nonclassical techniques are compared to classical probe states in nonideal multipass optical setups, with additional photon losses due to the measurement apparatus.

For pure symmetric three-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal{C}$, the three-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for symmetric $n$-qubit states derived from their Majorana representation, we derive the explicit achievable region of triples $(\mathcal{C},\tau ,\kappa )$.

The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the $s$-wave scattering length. For weakly interacting bosons we derive nonuniversal corrections to this equation of state taking into account finite-range effects of the interatomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities such as pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.

We study the effects of repulsive on-site interactions on the broadening of the localized Wannier functions used for calculating the parameters to describe ultracold atoms in optical lattices. For this, we replace the common single-particle Wannier functions, which do not contain any information about the interactions, by two-particle Wannier functions obtained from an exact solution which takes the interactions into account. We then use these interaction-dependent basis functions to calculate the Bose-Hubbard model parameters, showing that they are substantially different both at low and high lattice depths from the ones calculated using single-particle Wannier functions. Our results suggest that density effects are not negligible for many parameter ranges and need to be taken into account in metrology experiments.

A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.

A two-level quantum emitter with broken inversion symmetry simultaneously driven by an optical field and a microwave field that couples to the permanent dipole's moment is presented. We focus to a situation where the angular frequency of the microwave field is chosen such that it closely matches the Rabi frequency of the optical field, the so-called Rabi resonance condition. Using a series of unitary transformations we obtain an effective Hamiltonian in the double-dressed basis which results in easily solvable Bloch equations which allow us to derive analytical expressions for the spectrum of the scattered photons. We analyze the steady-state population inversion of the system which shows a distinctive behavior at the Rabi resonance with regard to an ordinary two-level nonpolar system. We show that saturation can be produced even in the case that the optical field is far detuned from the transition frequency, and we demonstrate that this behavior can be controlled through the intensity and the angular frequency of the microwave field. The spectral properties of the scattered photons are analyzed and manifest the emergence of a series of Mollow-like triplets which may be spectrally broadened or narrowed for proper values of the amplitude and/or frequency of the low-frequency field. We also analyze the phase-dependent spectrum which reveals that a significant enhancement or suppression of the squeezing at certain sidebands can be produced. These quantum phenomena are illustrated in a recently synthesized molecular complex with high nonlinear optical response although they can also occur in other quantum systems with broken inversion symmetry.

We establish the multiparameter quantum Cramér-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using a linear imaging system. For equally bright sources, the Cramér-Rao bound is independent of their separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost importance in realistic scenarios, such as observational astronomy.

We address side-channel leakage in a trusted preparation station of continuous-variable quantum key distribution with coherent and squeezed states. We consider two different scenarios: multimode Gaussian modulation, directly accessible to an eavesdropper, or side-channel loss of the signal states prior to the modulation stage. We show the negative impact of excessive modulation on both the coherent- and squeezed-state protocols. The impact is more pronounced for squeezed-state protocols and may require optimization of squeezing in the case of noisy quantum channels. Further, we demonstrate that the coherent-state protocol is immune to side-channel signal state leakage prior to modulation, while the squeezed-state protocol is vulnerable to such attacks, becoming more sensitive to the noise in the channel. In the general case of noisy quantum channels the signal squeezing can be optimized to provide best performance of the protocol in the presence of side-channel leakage prior to modulation. Our results demonstrate that leakage from the trusted source in continuous-variable quantum key distribution should not be underestimated and squeezing optimization is needed to overcome coherent state protocols.

The isotopic effects in reactions of ${\mathrm{O}}^{-}$ ions with ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ have been studied experimentally using a cryogenic 22-pole radio-frequency ion trap. The rate coefficients for associative detachment leading to ${\mathrm{H}}_2\mathrm{O}+e^{-}$ and to ${\mathrm{D}}_2\mathrm{O}+e^{-}$ and for atom transfer reactions leading to formation of ${\mathrm{OH}}^{-}$ and ${\mathrm{OD}}^{-}$ ions were determined at temperatures ranging from 15 to 300 K. The measured temperature dependencies of the rate coefficients for both channels of reactions of ${\mathrm{O}}^{-}$ with ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are compared with the results of the classical trajectory Monte Carlo simulation of the ${\mathrm{O}}^{-}+{\mathrm{H}}_2$ and ${\mathrm{O}}^{-}+{\mathrm{D}}_2$ collisions using the newly calculated potential energy surfaces. The measured temperature dependencies of the reaction rate coefficients for associative detachment are in very good agreement with the calculated ones. Agreement between experimental and calculated temperature dependencies of the rate coefficients of atom transfer reactions is off at most by a factor of 3 and the isotope effect is reproduced.

We theoretically investigate a scattering configuration in Compton scattering, in which the orientation of the electron spin is reversed and, simultaneously, the photon polarization changes from linear polarization into circular polarization. The intrinsic angular momentum of electron and photon are computed along the coincident propagation direction of the incoming and outgoing photon. We find that this intrinsic angular momentum is not conserved in the considered scattering process. We also discuss the generation of entanglement for the considered scattering setup and present an angle-dependent investigation of the corresponding differential cross section, Stokes parameters, and spin expectation.

We study theoretically the creation of knot structures in the polar phase of spin-1 Bose-Einstein condensates using the counterdiabatic protocol in an unusual fashion. We provide an analytic solution to the evolution of the external magnetic field that is used to imprint the knots. As confirmed by our simulations using the full three-dimensional spin-1 Gross-Pitaevskii equation, our method allows for the precise control of the Hopf charge as well as the creation time of the knots. The knots with Hopf charge exceeding unity display multiple nested Hopf links.

A scheme for strong coupling between a single atomic spin and the rotational mode of levitating nanoparticles is proposed. The idea is based on spin readout of nitrogen-vacancy centers embedded in aspherical nanodiamonds levitating in an ion trap. We show that the asymmetry of the diamond induces a rotational confinement in the ion trap. Using a weak homogeneous magnetic field and a strong microwave driving we then demonstrate that the spin of the nitrogen-vacancy center can be strongly coupled to the rotational mode of the diamond.

The Smith-Purcell effect, observed when an electron beam passes in the vicinity of a periodic structure, is a promising platform for the generation of electromagnetic radiation in previously unreachable spectral ranges. However, most of the studies of this radiation were performed on simple periodic gratings, whose radiation spectrum exhibits a single peak and its higher harmonics predicted by a well-established dispersion relation. Here, we propose a method to shape the spatial and spectral far-field distribution of the radiation using complex periodic and aperiodic gratings. We show, theoretically and experimentally, that engineering multiple peak spectra with controlled widths located at desired wavelengths is achievable using Smith-Purcell radiation. Our method opens the way to free-electron-driven sources with tailored angular and spectral responses, and gives rise to focusing functionality for spectral ranges where lenses are unavailable or inefficient.

The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms $E^{\left(k\right)},k=1,2,\cdots M$ resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by ${\mu }^k$ ($\mu$ being the perturbation parameter) we form the sum $E\left(\mu \right)={\sum }_k{\mu }^k{E}^{\left(k\right)}$ for small $\mu$ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function $E\left(\mu \right)$ to $\mu =1$ yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.