We theoretically investigate one-dimensional (1D) $\mathrm{SU}(\kappa$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D $\mathrm{SU}(\kappa$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into a spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to $N=32$. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all $S_z$ manifolds included. In contrast to noninteracting multicomponent fermions, the momentum distributions are broadened due to strong interactions. As $\kappa$ increases, the momentum distributions are less broadened for fixed $N$, while they are more broadened for fixed number of particles per spin component. We then compare numerically calculated high-momentum tails with analytical predictions which are proportional to $1/p^4$, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable $\mathrm{SU}(\kappa$) spin symmetry in the spin-incoherent regime.

We experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. We first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, we observe localized edge states at the boundary of regions with different winding numbers. We also confirm the robustness of edge states against chiral-symmetry-preserving disorder.

We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects can only be observed in integrable or weakly chaotic settings. Similar features are present also in the postquench dynamics of some observables.

We investigate the Markovian and non-Markovian dynamics of Gaussian quantum channels, exploiting a recently introduced necessary and sufficient criterion and the ensuing measure of non-Markovianity based on the violation of the divisibility property of the dynamical map. We compare the paradigmatic instances of quantum Brownian motion (QBM) and pure damping channels, and for the former we find that the exact dynamical evolution is always non-Markovian in the finite-time as well as in the asymptotic regimes for any nonvanishing value of the non-Markovianity parameter. If one resorts to the rotating-wave approximated form of the QBM, that neglects the anomalous diffusion contribution to the system dynamics, we show that such an approximation fails to detect the non-Markovian nature of the dynamics. Finally, for the exact dynamics of the QBM in the asymptotic regime, we show that the quantifiers of non-Markovianity based on the distinguishability between quantum states fail to detect the non-Markovian nature of the dynamics.

In this paper, a conserved current for Klein–Gordon equation is derived. It is shown, for ($1+1$) dimensions, the first component of this current is non-negative and reduces to ${\left|\varphi \right|}^2$ in nonrelativistic limit. Therefore, it can be interpreted as the probability density of spinless particles. In addition, main issues pertaining to localization in relativistic quantum theory are discussed, with a demonstration on how this definition of probability density can overcome such obstacles. Our numerical study indicates that the probability density deviates significantly from ${\left|\varphi \right|}^2$ only when the uncertainty in momentum is greater than $m_{0}c$.

We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement setup after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before Alice's announcement. In the latter case, he can only postprocess his measurement outcome when Alice's extra information becomes available. We compare the optimal guessing probabilities in the two scenarios, and we prove that they are the same if and only if there exist compatible (i.e., jointly measurable) optimal measurements for all of Alice's state ensembles. When this is the case, postprocessing any of the corresponding joint measurements is Bob's optimal strategy in the postmeasurement information scenario. Furthermore, we establish a connection between discrimination with postmeasurement information and the standard state discrimination. By means of this connection and exploiting the presence of symmetries, we are able to compute the various guessing probabilities in many concrete examples.

Building upon the results of R. Augusiak et al. [Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting states is indeed genuine we then introduce criteria allowing us to decide it efficiently. The construction is then exploited to provide examples of multipartite states that are genuinely entangled but not genuinely nonlocal, giving further illustration for the inequivalence between entanglement and nonlocality in the multiparticle scenario. It is also shown how to construct genuinely entangled states which are unsteerable across certain bipartite cuts.

Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization. We introduce an NP-Hard problem called Max-Haf and show that Gaussian boson sampling (GBS) can be used to enhance any stochastic algorithm for this problem. These results are applied by enhancing the random search, simulated annealing, and greedy algorithms. With numerical simulations, we confirm that all algorithms are improved when employing GBS, and that a GBS-enhanced random search performs the best despite being the one with the simplest underlying classical routine.

It is well established that different electronic channels, in resonant inelastic x-ray scattering (RIXS), display different polarization dependences due to different orientations of their corresponding transition dipole moments in the molecular frame. However, this effect does not influence the vibrational progression in the Franck-Condon approximation. We have found that the transition dipole moments of core excitation and deexcitation experience ultrafast rotation during dissociation in the intermediate core-excited state. This rotation makes the vibrational progression in RIXS sensitive to the polarization of the x-ray photons. We study the water molecule, in which the effect is expressed in RIXS through the dissociative core-excited state where the vibrational scattering anisotropy is accompanied also by violation of parity selection rules for the vibrations.

By harnessing the quantum states of light for illumination, precise phase and absorption estimations can be achieved with precision beyond the standard quantum limit. Despite their significance for precision measurements, quantum states are fragile in noisy environments which leads to difficulties in revealing the quantum advantage. In this paper, we propose a scheme to improve optical absorption estimation precision by using the correlated photon pairs from spontaneous parametric down-conversion as the illumination. This scheme performs better than classical illumination when the loss is below a critical value. Experimentally, the scheme is demonstrated by a scanning transmission-type microscope that uses correlated photon illumination. As a result, the signal-to-noise ratio of a two-photon image shows a 1.36-fold enhancement over that of the single-photon image for single-layer graphene with a 0.98 transmittance. This enhancement factor will be larger when using a multimode squeezed state as the illumination.

We show that strong parametric driving of a quantum harmonic oscillator coupled to a thermal bath allows one to distinguish between different microscopic models for the oscillator-bath coupling. We consider a bath with an Ohmic spectral density and a model where the system-bath interaction can be tuned continuously between position and momentum coupling via the coupling angle $\alpha$. We derive a master equation for the reduced density operator of the oscillator in Born-Markov approximation and investigate its quasisteady state as a function of the driving parameters, the temperature of the bath and the coupling angle $\alpha$. We find that the driving introduces a strong dependence of the time-averaged variance of position and momentum on these parameters. In particular, we identify parameter regimes that maximize the $\alpha$ dependence and provide an intuitive explanation of our results.

The staggered quantum walk is a type of discrete-time quantum-walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered dynamics on a two-dimensional lattice composed of superconducting microwave resonators connected with tunable couplings. The naive generalization of the one-dimensional staggered dynamics generates two uncoupled one-dimensional quantum walks; thus more complex partitions need to be employed. However, by analyzing the coherence of the dynamics, we show that the quantumness of the evolution corresponding to two independent one-dimensional quantum walks can be elevated to the level of a single two-dimensional quantum walk, only by modifying the boundary conditions. In fact, by changing the lattice boundary conditions (or topology), we explore the walk on different surfaces such as a torus, a Klein bottle, a real projective plane, and a sphere. The coherence and the entropy reach different levels depending on the topology of the surface. We observe that the entropy captures similar information as coherence; thus we use it to explore the effects of boundaries on the dynamics of the continuous-time quantum walk and the classical random walk.

The apparent absence of meaningful assignments of electrons and indistinguishable nuclei to particular atoms in a chemical aggregate would seem to preclude the quantum-mechanical definition of atomic Hamiltonian operators within molecules and matter. The electronic energies of individual constituent atoms, as well as the interactions between them, are accordingly widely perceived as objectively undefined in molecular quantum theory, requiring additional auxiliary conditions to achieve quantitative specificity, giving rise to a plethora of individual preferences. Here we address the issue of assignments of electrons to atoms within molecules at the Born-Oppenheimer classical fixed-nuclei level of theory and provide thereby quantum-mechanical definitions of atomic operators and of the interactions between them. In the spirit of early work of Longuet-Higgins, a van der Waals subgroup of the full molecular electronic symmetric group is shown to facilitate assignments of electrons to particular atomic nuclei in a molecule. The orthonormal (Eisenschitz-London) outer products of atomic eigenstates that provide separable Hilbert space representations of this symmetric subgroup furthermore support totally antisymmetric solutions of the molecular Schrödinger equation. Self-adjoint atomic and atomic-interaction operators within a molecule defined in this way are seen to have universal Hermitian matrix representatives and physically significant expectation values in totally antisymmetric molecular eigenstates. Adiabatic Born-Oppenheimer molecular energies emerge naturally from the development in the form of sums of the energies of individual atomic constituents and of their atomic-pairwise interactions, in the absence of additional auxiliary conditions. A detailed and nuanced quantitative description of electronic structure and bonding is provided thereby which includes the interplay between atomic promotion and interaction energies, common representations of atomic-state hybridization and interatomic charge apportionment, potentially measurable multiatom entanglements upon coherent dissociations of molecules, and other attributes of the development revealed by selected illustrative calculations. These include applications to the ground and electronically excited states of diatomic and triatomic hydrogen molecules, which exhibit significant accommodation among the atomic promotion and interaction energies, as well as entanglements among atomic states, over the entire range of molecular geometries traversed in the course of two- and three-atom dissociations.

The optimization of quantum control for physical qubits relies on accurate noise characterization. Probing the spectral density $S\left(\omega \right)$ of semiclassical phase noise using a spin interacting with a continuous-wave (CW) resonant excitation field has recently gained attention. CW noise spectroscopy protocols have been based on the generalized Bloch equations (GBE) or the filter function formalism, assuming weak coupling to a Markovian bath. However, this standard protocol can substantially underestimate $S\left(\omega \right)$ at low frequencies when the CW pulse amplitude becomes comparable to $S\left(\omega \right)$. Here we derive the coherence decay function more generally by extending it to higher orders in the noise strength and discarding the Markov approximation. Numerical simulations show that this provides a more accurate description of the spin dynamics compared to a simple exponential decay, especially on short timescales. Exploiting these results, we devise a protocol that uses an experiment at a single CW pulse amplitude to extend the spectral range over which $S\left(\omega \right)$ can be reliably determined to $\omega =0$.

We study numerically the evolution of ultrashort pulses in passive uniform photonic-crystal fibers designed such that their nonlinear Kerr coefficient $\gamma$ varies considerably with wavelength. Such fibers exhibit a zero-nonlinearity wavelength in addition to the zero-dispersion wavelength. We show that soliton evolution is affected considerably by the relative locations of the zero-nonlinearity and zero-dispersion wavelengths with respect to the input wavelength. Among the features observed numerically are as follows: the enhancement or suppression of the Raman-induced redshift of fundamental solitons, amplification or suppression of a dispersive wave shed by the soliton, and the splitting of a fundamental soliton into two co-propagating solitons through a dispersive wave that forms a soliton in the normal-dispersion region because of a negative value of $\gamma$ in this region.

We derive a spatiotemporal equation describing nonlinear optical dynamics in Fabry-Perot (FP) cavities containing a Kerr medium. This equation is an extension of the equation that describes dynamics in Kerr-nonlinear ring resonators, referred to as the Lugiato-Lefever equation (LLE) due to its formulation by Lugiato and Lefever in 1987. We use the equation to study the generation and properties of Kerr frequency combs in FP resonators. The derivation of the equation starts from the set of Maxwell-Bloch equations that govern the dynamics of the forward and backward propagating envelopes of the electric field coupled to the atomic polarization and population difference variables in a FP cavity. The final equation is formulated in terms of an auxiliary field $\psi (z,t)$ that evolves over a slow time $t$ on the domain $-L\le z\le L$ with periodic boundary conditions, where $L$ is the cavity length. We describe how the forward and backward propagating field envelopes can be obtained after solving the equation for $\psi$. This formulation makes the comparison between the FP and ring geometries straightforward. The FP equation includes an additional nonlinear integral term relative to the LLE for the ring cavity, with the effect that the value of the detuning parameter $\alpha$ of the ring LLE is increased by an amount equal to twice the spatial average of ${\left|\psi \right|}^2$. This feature establishes a general connection between the stationary phenomena in the two geometries. For the FP-LLE, we discuss the linear stability analysis of the flat stationary solutions, analytic approximations of solitons, Turing patterns, and nonstationary patterns. We note that Turing patterns with different numbers of rolls may exist for the same values of the system parameters. We then discuss some implications of the nonlinear integral term in the FP-LLE for the kind of experiments that have been conducted in Kerr-nonlinear ring resonators.

We derive the full statistics of the product events in homodyne correlation measurements, involving a single mode signal, a local oscillator, a linear optical network, and two linear photodetectors. This is performed for the regime of high intensities impinging on the detectors. Our description incorporates earlier proposed homodyne correlation measurement schemes, such as the homodyne cross-correlation and homodyne intensity-correlation measurements. This analysis extends the amount of information retrieved from such types of measurements, since previously attention was paid only to the expectation value of the correlation statistics. As an example, we consider the correlation statistics of coherent, Gaussian, and Fock states. Moreover, nonclassical light is certified on the basis of the variance of the measurement outcome.

In the context of ultrafast quantum communication and random number generation, detection-timing jitter represents a strong limitation because it can introduce major time-tagging errors and affect the quality of time-correlated photon counting or quantum state engineering. Despite their importance in emerging photonic quantum technologies, no detector model including such effects has been developed so far. We propose here an operational theoretical model based on positive operator-valued measurements density formalism that is able to explicitly quantify the effect of timing jitter for a typical class of single-photon detector. We apply our model to some common experimental situations.