The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the density-functional theory, are reformulated in terms of a particular many-body density, which is translational and Galilean invariant and therefore is relevant for self-bound systems. In a similar way that there is a unique relation between the one-body density and the external potential that gives rise to it, we demonstrate that there is a unique relation between that particular many-body density and a definite many-body potential. The energy is then a functional of this density, and its minimization leads to the ground-state energy of the system. As a proof of principle, the analogous of the Kohn-Sham equation is solved in the specific case of ${}^4\mathrm{He}$ atomic clusters, to put in evidence the advantages of this formulation in terms of physical insights.

A set of quantum states is said to be absolutely entangled when at least one state in the set remains entangled for any definition of subsystems, i.e., for any choice of the global reference frame. In this work we investigate the properties of absolutely entangled sets (AESs) of pure quantum states. For the case of a two-qubit system, we present a sufficient condition to detect an AES, and use it to construct families of $N$ states such that $N-3$ (the maximal possible number) remain entangled for any definition of subsystems. For a general bipartition $d=d_1{d}_2$, we prove that sets of $N>⌊(d_1+1)(d_2+1)/2⌋$ states are AESs with Haar measure 1. Then, we define AESs for multipartitions. We derive a general lower bound on the number of states in an AES for a given multipartition, and also construct explicit examples. In particular, we exhibit an AES with respect to any possible multipartitioning of the total system.

We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian unitary operations, and monotonicity under Gaussian channels. Furthermore, we find a quantitative relation between our measure and the previously proposed non-Gaussianity measures defined via quantum relative entropy and the quantum Hilbert-Schmidt distance. This allows us to estimate the non-Gaussianity measures readily by homodyne detection, which would otherwise require a full quantum-state tomography.

We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross–Pitaevskii equation. To determine the classical partition function thereof, we leverage the semi-analytical transfer integral operator (TIO) technique. The latter predicts a distribution of the observed wave-function amplitudes and yields two-point correlation functions providing insights into the emergent dynamics involving quantum droplets. We compare the ensuing TIO results with the probability distributions obtained at large times of the modulationally unstable dynamics as well as with the equilibrium properties of a suitably constructed Langevin dynamics. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions and which are found to coalesce at large evolution times. Our results from the distinct methodologies are in good agreement aside from the case of low temperatures in the special limit where the droplet widens. In this limit, the distribution acquires a pronounced bimodal character, exhibiting a deviation between the TIO solution and the Langevin dynamics.

The generation of Raman solitons in the mid-IR range in a multicore fiber with two zero-dispersion wavelengths is studied analytically and numerically. The estimate for the maximum shift of the Raman soliton wavelength depending on the parameters of the media dispersion, the frequency-dependent losses, and the nonlinearity decreasing is obtained, which is in good agreement with the results of numerical simulation. A realistic design of a 10-core fiber made of a pair of compatible glasses is proposed for the Raman shift of the wavelength of soliton pulses propagating in an out-of-phase mode. The nonlinear dynamics of a laser pulse, specified at the wavelength of $2.3\mu \mathrm{m}$, energy of 1.5 nJ, and duration of 100 fs, during propagation in a fiber with this design, is studied numerically. The generation of Raman solitons in the mid-IR range at wavelengths exceeding $4\mu \mathrm{m}$, as well as dispersion waves in the $5\text{−}\mu \mathrm{m}$ range, emitted by a soliton when approaching the second zero-dispersion wavelength, is demonstrated.

We theoretically analyze the collective dynamics of a thermal beam of atomic dipoles that couple to a single mode when traversing an optical cavity. For this setup we derive a semiclassical model and determine the onset of superradiant emission and its stability. We derive analytical expressions for the linewidth of the emitted light and compare them with numerical simulations. In addition, we find and predict two different superradiant phases; a steady-state superradiant phase and a multicomponent superradiant phase. In the latter case we observe sidebands in the frequency spectrum that can be calculated using a stability analysis of the amplitude mode of the collective dipole. We show that both superradiant phases are robust against free-space spontaneous emission and $T_2$ dephasing processes.

We show that a continuous-variable (CV) qudit can be constructed using quasiorthogonal cat states of a bosonic mode, when the phase encoded in each cat state is chosen appropriately. With the constructed CV qudit and the discrete-variable (DV) qudit encoded with Fock states, we propose an approach to generate the hybrid maximally entangled state of a CV qudit and a DV qudit by using two microwave cavities coupled to a superconducting flux qutrit. This proposal relies on the initial preparation of a superposition of Fock states of one cavity and the initial preparation of a cat state of the other cavity. After the initial state of each cavity is prepared, this proposal requires only two basic operations, i.e., the first operation employs the dispersive coupling of both cavities with the qutrit while the second operation uses the dispersive coupling of only one cavity with the qutrit. The entangled state production is deterministic and the operation time decreases as the dimensional size of each qudit increases. In addition, during the entire operation, the coupler qutrit remains in the ground state and thus decoherence from the qutrit is significantly reduced. As an example, we further discuss the experimental feasibility for generating the hybrid maximally entangled state of a DV qutrit and a CV qutrit based on circuit QED. This proposal is universal and can be extended to accomplish the same task, by using two microwave or optical cavities coupled to a natural or artificial three-level atom.

A Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for the Boltzmann machine learning to obtain a suitable probability distribution. The Boltzmann machine learning consists of calculating the gradient of the loss function given in terms of the thermal average, which is the most time-consuming procedure. Here, we propose a method to implement the Boltzmann machine learning by using noisy intermediate-scale quantum devices. We prepare an initial pure state that contains all possible computational basis states with the same amplitude, and we apply a variational imaginary time simulation. Readout of the state after the evolution in the computational basis approximates the probability distribution of the thermal equilibrium state that is used for the Boltzmann machine learning. We perform the numerical simulations of our scheme and confirm that the Boltzmann machine learning works well. Our scheme leads to a significant step toward an efficient machine learning using quantum hardware.

We investigate the orientation dependence of high-order harmonic generation (HHG) in graphene by solving the semiconductor Bloch equations. The tight-binding approximation including up to the third-nearest-neighbor atoms is used to model the graphene. Our simulations show that the orientation dependence of HHG shows different patterns for different harmonics. With increasing the laser intensity, these patterns become similar except for a double-peak structure shown in lower-order harmonics. The double-peak structure appears at high laser intensity due to the contribution of the harmonic perpendicular to the laser polarization direction. The harmonic yield is decomposed as the contributions of the nearest-neighbor interaction, the second-nearest-neighbor interaction, and the third-nearest-neighbor interaction. Our results show that the harmonic yields are mainly contributed by the nearest-neighbor interaction, but the third-nearest-neighbor interaction also plays an important role and modifies the orientation dependence.

The formation of quantum vortices in photodetachment by a sequence of left- and right-handed circularly polarized laser pulses in various configurations is analyzed using either the strong-field approximation or numerical solution of the time-dependent Schrödinger equation. Two types of pulse sequences are considered: reducible and irreducible. While the former can be decomposed into series of consecutive and identical (irreducible) subtrains of pulses, the latter cannot be decomposed in that way. As we show, the vortex pattern in the probability amplitude of photodetachment is fully determined by the irreducible pulse configuration. Additional repetitions of an irreducible train create, in the three-dimensional momentum space, nonvortex nodal surfaces, the position of which is estimated. The conditions for the experimental observation of quantum vortices are also determined.

Among different approaches to generate mirrorless lasing, resonant multiphoton pumping of gas constituents by deep-UV laser pulses exhibits so far the highest efficiency and produces measurable lasing energies, but the underlying mechanism was not yet fully settled. Here, we report lasing generation from atomic oxygen in a methane-air flame via femtosecond two-photon excitation. Temporal profiles of the lasing pulses were measured for varying concentrations of atomic oxygen, which shows that the peak intensity and time delay of the lasing pulse approximately scales as $N$ and $1/\sqrt{N}$, respectively, where $N$ represents the concentration. These scaling laws match well with the prediction of oscillatory superfluorescence (SF), indicating that the lasing we observed is essentially SF rather than amplified spontaneous emission. In addition, the quantum-beating effect was also observed in the time-resolved lasing pulse. A theoretical simulation based on nonadiabatic Maxwell-Bloch equations well reproduces the experimental observations of the temporal dynamics of the lasing pulses. These results on fundamentals should be beneficial for the better design and applications of lasing-based techniques.

We introduce a minimal set of physically motivated postulates that the Hamiltonian $H$ of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We found that these conditions are satisfied by infinitely many quantum Hamiltonians, which provide novel degrees of freedom for quantum enhanced protocols, In particular, the on-site energies, i.e., the diagonal elements of $H$, and the phases of the off-diagonal elements are unconstrained on the quantum side. The diagonal elements represent a potential-energy landscape for the quantum walk and may be controlled by the interaction with a classical scalar field, whereas, for regular lattices in generic dimension, the off-diagonal phases of $H$ may be tuned by the interaction with a classical gauge field residing on the edges, e.g., the electromagnetic vector potential for a charged walker.

Anisotropy parameters describing the angular dependence of the photoionization delay are defined. The formalism is applied to results obtained with the relativistic random phase approximation with exchange for photoionization delay from the outermost $s$-orbitals in selected rare-gas atoms. Any angular dependence in the Wigner delay is induced here by relativistic effects, while the measurable atomic delay exhibits such a dependence also in the nonrelativistic limit. The contributions to the anisotropy from the different sources are disentangled and discussed. For the heavier rare gases, it is shown that measurements of the delay for electrons ejected in specific angles, relative to, e.g., those ejected along the laser polarization, are directly related here to the Wigner delay. For a considerable range of angles, the contributions from the second photon largely get canceled when the results in different angles are compared, and this angle-relative atomic delay is then close to the corresponding Wigner delay.

The wave function of an electron interacting with a finite-range potential and an intense low-frequency laser pulse is analyzed within the adiabatic approximation. The closed analytic form for the wave function, which includes the rescattering corrections, is obtained with quasiclassical accuracy for an electron in both the initial bound and continuum states. We discuss the parametrizations of amplitudes of fundamental strong-field processes in terms of laser and binding-potential parameters. Based on the analytic results for the adiabatic wave functions, we develop the perturbation theory in an additional weak field. The modification of high-order harmonic generation amplitude caused by a weak extreme ultraviolet pulse is discussed in the first order of the perturbation theory.

Sensitivity limits are usually determined using the Cramér-Rao bound. Recently, this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits usually require the full measurement statistics, which can be challenging to access. In this work we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial-mode demultiplexing. For demultiplexing, our method is optimal, i.e., it saturates the quantum Cramér-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity, and the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cramér-Rao bound even in the presence of noise.

The quantum approximate optimization algorithm (QAOA) is the most studied gate-based variational quantum algorithm today. We train QAOA one layer at a time to maximize overlap with an $n$ qubit target state. Doing so we discovered that such training always saturates—called training saturation—at some depth $p^{*}$, meaning that past a certain depth, overlap cannot be improved by adding subsequent layers. We formulate necessary conditions for saturation. Numerically, we find layerwise QAOA reaches its maximum overlap at depth $p^{*}=n$ for the problem of state preparation. The addition of coherent dephasing errors to training removes saturation, recovering robustness to layerwise training. This study sheds new light on the performance limitations and prospects of QAOA.

We introduce a three-qubit waveguide-QED system to achieve a cavity-QED strong-coupling regime for a probe qubit embedded in atomlike mirrors, which was realized in recent experiments. We then extend this system into the deep non-Markovian regime and demonstrate the profound role that retardation plays on the dressed resonances, allowing one to significantly improve the polariton lifetimes (by several orders of magnitude), tune the resonances, as well as realize Fano-like resonances and simultaneous coupling to multiple cavity modes. Exact Green's function solutions are presented for the classical spectral resonances, and the full quantum dynamics are simulated using matrix product states, where we demonstrate additional control of the cavity-QED system using chiral probe qubits. We show example qubit dynamics with both one and two quantum excitations.

The value of residual phase noise, after phase compensation, is one of the key limitations of performance improvement for continuous-variable quantum key distribution using a local local oscillator (LLO CV-QKD) system, since it is the major excess noise. However, due to the nonideality of the realistic devices implemented in practice, for example, imperfect lasers, detectors, and unbalanced interferometers, the value of residual phase noise in the current system is still relatively large. Here, we develop a phase noise model to improve the phase noise tolerance of the LLO CV-QKD schemes. In our model, part of the phase-reference measurement noise associated with detection efficiency and electronic noise of Bob's detector as well as a real-time monitored phase-reference intensity at Bob's side is considered trusted because it can be locally calibrated by Bob. We show that using our phase noise model can significantly improve the secure key rate and transmission distance of the LLO CV-QKD system. We further conduct an experiment to substantiate the superiority of the phase noise model. Based on experimental data of a LLO CV-QKD system in the 25-km optical fiber channel, we demonstrate that the secure key rate under our phase noise model is approximately 40% higher than that under the conventional phase noise model.