Studying the conversion between transverse light modes via four-wave mixing in a heated rubidium vapor, we demonstrate and explain a transfer between azimuthal and radial mode numbers. They relate to orthogonal modal dimensions, which one would not normally expect to interact. While angular momentum conservation in this nonlinear process dictates the selection rules for the angular mode number, the role of the radial mode number is more esoteric. We demonstrate systematically that the Gouy phase is the key to understanding this conversion, leading to strikingly different conversion behavior in the thick- and thin-medium regimes. Our experimental investigation of the transition between these regimes bridges the gap between previous experiments in atomic thick media and work in nonlinear crystals. Our work sets a clear starting point to explore the thick-medium regime, allowing efficient radial-to-azimuthal and radial-to-radial mode conversion.

Measurements invariably determine the physical state of a given “observed system” with respect to an “observer system.” This implies an inescapable two-body relationality upon which physical theories must rely. There has been a growing effort to understand how quantum mechanics can accommodate the notion of reference frame in its substratum and whether such approach would respect general covariance. With regard to quantum resources, it has been shown that coherence and entanglement are not invariant upon changes of quantum reference frames. Here, we construct a theoretical framework within which a given combination of quantum resources, including not only coherence and entanglement, is shown to be a physical invariant. Under the premise of the universality of quantum phenomena, the proven covariance between quantum reference frames then implies that the total quantumness accessible to any observer in the universe is absolute.

In the last few years, the application of machine learning methods has become increasingly relevant in different fields of physics. One of the most significant subjects in the theory of open quantum systems is the study of the characterization of non-Markovian memory effects that emerge dynamically throughout the time evolution of open systems as they interact with their surrounding environment. Here we consider two well-established quantifiers of the degree of memory effects, namely, the trace distance and the entanglement-based measures of non-Markovianity. We demonstrate that using machine learning techniques, in particular, support vector machine algorithms, it is possible to estimate the degree of non-Markovianity in two paradigmatic open system models with high precision. Our approach can be experimentally feasible to estimate the degree of non-Markovianity, since it requires a single or at most two rounds of state tomography.

We develop a hybrid quantum-classical algorithm to solve an optimal population transfer problem for a molecule subject to a laser pulse. The evolution of the molecular wave function under the laser pulse is simulated on a quantum computer, while the optimal pulse is iteratively shaped via a machine learning (evolutionary) algorithm. A method to encode on the quantum computer the $n$-electrons wave function is discussed, the circuits accomplishing its quantum simulation are derived and the scalability in terms of number of operations is discussed. Performance on noisy intermediate-scale quantum devices (IBM Q X2) is provided to assess the current technological gap. Furthermore the hybrid algorithm is tested on a quantum emulator to compare performance of the evolutionary algorithm with standard ones. Our results show that such algorithms are able to outperform the optimization with a downhill simplex method and provide performance comparable to more advanced (but quantum-computer unfriendly) algorithms such as Rabitz's or gradient-based optimization.

Backaction-evading (BAE) measurements of a mechanical resonator, by continuously monitoring a single quadrature of motion, can achieve precision below the zero-point uncertainty. When this happens, the measurement leaves the resonator in a quantum squeezed state. The squeezed state so generated is however conditional on the measurement outcomes, while for most applications it is desirable to have a deterministic, i.e., unconditional, squeezed state with the desired properties. In this work we apply feedback control to achieve deterministic manipulation of mechanical squeezing in an optomechanical system subject to a continuous BAE measurement. We study in details two strategies, direct (Markovian) and state-based (Bayesian) feedback. We show that both are capable to achieve optimal performances, i.e., a vanishing noise added by the feedback loop. Moreover, even when the feedback is restricted to be a time-varying mechanical force (experimentally friendly scenario) and an imperfect BAE regime is considered, the ensuing nonoptimal feedback may still obtain significant amount of squeezing. In particular, we show that Bayesian feedback control is nearly optimal for a wide range of sideband resolution. Our analysis is of direct relevance for ultrasensitive measurements and quantum state engineering in state-of-the-art optomechanical devices.

X-ray absorption and core-ionization spectra of molecules pumped by two coherent infrared pulses with different polarizations are studied theoretically. We have found a sensitivity of the vibrational profile of x-ray probe spectra to polarizations of the IR and x-ray pulses. This polarization dependence is qualitatively different for x-ray absorption and x-ray photoelectron spectra. Measurements of this polarization dependence allow to select the difference in Franck-Condon distributions from the lowest and pumped vibrational levels of the electronic ground state. The proposed technique is exemplified numerically using x-ray absorption spectra of the pumped CO molecule. We also show that this kind of pump-probe spectroscopy can enable studies of the dynamics of molecular rotation.

In atomic gyroscopes, measuring the effective noble-gas magnetic field enables the determination of the noble-gas polarization. The enhancement factor is introduced to relate the effective magnetic field and the polarization in a certain magnetic-field environment. Earlier experiments concentrate on the strong magnetic-field environment for measuring the spin-exchange cross section precisely, so the results on the enhancement factor in the weak magnetic field are still insufficient. In our nuclear magnetic resonance gyroscope based on Cs-${}^{129}\mathrm{Xe}$ and -${}^{131}\mathrm{Xe}$, the magnetic field is usually set to 1–10 $\mu \mathrm{T}$. In this paper, we measure the effective magnetic field and the polarization of Xe atoms to estimate the Cs-Xe enhancement factor in the weak magnetic field of 2.5 $\mu \mathrm{T}$ and give the estimation of the Cs-${}^{129}\mathrm{Xe}$ enhancement factor of $(1.60\pm 0.06)\times {10}^4$.

We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACSs) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find $1/N$ corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self-trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we also find that, for a few atoms, the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also, the numerical results of SSB are better reproduced by the ACS approach than with the MF approach. Instead, the onset of MQST is correctly reproduced by ACS theory only in the large $N$ regime and, for this phenomenon, the $1/N$ correction to the MF formula is not reliable.

We consider a hybrid atom-optomechanical system consisting of a mechanical membrane inside an optical cavity and an atomic Bose-Einstein condensate outside the cavity. The condensate is confined in an optical lattice potential formed by a traveling laser beam reflected off one cavity mirror. We derive the cavity-mediated effective atom-atom interaction potential and find that it is nonuniform, site-dependent, and does not decay as the interatomic distance increases. We show that the presence of this effective interaction breaks the $Z_2$ symmetry of the system and gives rise to new quantum phases and phase transitions. When the long-range interaction dominates, the condensate breaks the translation symmetry and turns into a novel self-organized latticelike state with increasing particle densities for sites farther away from the cavity. We present the phase diagram of the system and investigate the stabilities of different phases by calculating their respective excitation spectra. The system can serve as a platform to explore various self-organized phenomena induced by the long-range interactions.

Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results obtained for the untrapped system are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

We develop a theoretical scheme to perform a readout of the properties of a quasiperiodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a one-dimensional quasiperiodic system with a potential given by the André-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single-particle eigenstates (SPEs). More specifically, we can use the non-Markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH models and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasiperiodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive, and no transport engendered by SPEs that are delocalized, critical, and localized respectively. In addition, the localization length of the SPEs can also be gleaned from the exponential decay of correlations at long times as a function of distance between qubits. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behavior and the scaling of the threshold time with qubit separation are governed by the fastest spreading states.

Partially parity-time-symmetric ($\mathrm{p}\mathcal{PT}$-symmetric) lattice solitons are explored in quadratic nonlinear media. The solution of the model a nonlinear Schrödinger (NLS) equation with coupling to a mean term and an additional external potential, is computed by modern numerical methods, and it is shown that $\mathrm{p}\mathcal{PT}$-symmetric lattice solitons can exist in quadratic nonlinear media. The study concentrates on effects generated by the variation of lattice depth and quadratic nonlinearity strength that specify characteristics of the model, and the stability of the model is examined comprehensively by the nonlinear evolution and linear stability spectra of the solitons. It is demonstrated that stable evolution of solitons in a quadratic nonlinear media is possible for self-focusing $\mathrm{p}\mathcal{PT}$-symmetric lattices. Moreover, it is observed that, for the defocusing case of the lattice, fundamental solitons decay into radiation modes, and the decay of these solitons can be delayed by a deeper potential.

Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that preshared entanglement between the sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of entanglement. Subsequently, the same authors derived a version of the so-called quantum Singleton bound that relates the parameters of the entanglement-assisted quantum-error-correcting codes proposed by them. We present an entanglement-assisted quantum communication scheme with parameters violating this bound in certain ranges. For a fixed transmission rate, our scheme allows one to correct a larger fraction of errors.

It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no cloning of quantum coherence. Here, in this article, we show that it is impossible to clone the coherence of an arbitrary quantum state. In particular, with an ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which coherence cloning will be possible for a given choice of machine. Furthermore, we find the maximum range of states whose coherence can be cloned perfectly. The impossibility proof also holds when we do not include machine states. Lastly, we generalize the impossibility of cloning of coherence in terms of dimension of the quantum state and coherence measure taken into consideration.

We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider the so-called constant-$\widehat{p}$ displaced states, which include mixtures of multimode coherent states arbitrarily displaced along a common axis. We first show that no global or local Gaussian transformations or generalized Gaussian measurements can lead to a better discrimination method than simple homodyne measurements applied to each mode separately and classical postprocessing of the results. This result is applied to binary state comparison problems. We show that homodyne measurements, separately performed on each mode, are the best Gaussian measurement for binary state comparison. We further compare the performance of the optimal Gaussian strategy for binary coherent states comparison with these of non-Gaussian strategies using photon detections.

An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $-\alpha cos\left(\theta \right)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the radial equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of the angular part of the Schrödinger equation and derive several useful approximations in the limit of large $\alpha$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the radial equation are given by Bessel functions, and we analyze their behavior in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.

A variational basis set motivated by mean-field theory is utilized to describe the Bose-Einstein condensate within the adiabatic hyperspherical coordinate framework. The simplest single-orbital variant of this treatment reproduces many of the ground-state properties predicted by the Gross-Pitaevskii equation. But a multiorbital improvement to the basis set yields a better representation of particle correlations and of the critical number where the condensate collapses for a negative two-body scattering length. The method also produces systematic deviations from Bogoliubov theory for the fundamental monopole excitation frequency.

This article aims to study the existence of stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian system when exposed to external fields. We investigate a non-Hermitian $\mathcal{PT}$-symmetric diamond chain network and its transport dynamics in two different situations, namely in a flat-band case and a non-flat-band case. The considered system does not support an unbroken-$\mathcal{PT}$ phase or completely real eigenspectra in any of the parametric regions in both the flat- and non-flat-band cases. In the flat-band case, up to a critical value of the gain-loss parameter, the bands are found to be gapless or inseparable, and for other values the bands are isolated. Considering the non-flat-band case, all the bands are found to be complex dispersive and are also isolated. In the case of a completely broken $\mathcal{PT}$ phase, we look at the possibility of having stable dynamics or Bloch oscillations upon the application of external fields like a synthetic electric field. In particular, when the complex bands are isolated, we point out that the Landau-Zener tunneling induced by the synthetic electric field can enable Bloch oscillations. The amplitude of these Bloch oscillations is large and persists for a long propagation distance, which reveals that super Bloch oscillations can be observed in the broken $\mathcal{PT}$ phase of the system. We also report the amplified Bloch oscillations, which pave the way toward controlling transport phenomena in non-Hermitian systems.