Quantum information distribution in a tripartite state plays a fundamental role in quantum information processes. Here we investigate how a bipartite unitary transformation $U_{AB}$ redistributes the quantum mutual information with the third party $C$ in a tripartite pure state ${|\psi \rangle }_{ABC}$ in a $d_A\times d_B\times d_C$-dimensional Hilbert space. In particular, we focus on finding out the optimal unitary transformation $U_{AB}^{*}$ that maximizes the quantum mutual entropy between party $A$ and party $C, I(A:C)=S\left({\rho }_A\right)-S\left({\rho }_B\right)+S\left({\rho }_C\right)$. We show that the mutual entropy $I(A:C)$ is upper bounded by $2S\left({\rho }_C\right)$ derived from the Araki-Lieb inequality. This upper bound can be realized via an optimal unitary transformation for any pure state with the rank $r_C$ of ${\rho }_C$ satisfying $r_C\le d_A$. For a generic pure state with $r_C>d_A$, the upper bound cannot be realized by any bipartite unitary transformation. To maximize the mutual entropy in the later case, we propose a fast numerical algorithm to produce an approximate optimal unitary transformation, where our optimization is transformed into a modified number partition problem. The validness of our algorithm is confirmed by its comparison with the results from the Adam algorithm for parameterized unitary transformations. Our approximate algorithm thus provides a practical protocol to implement redistribution of quantum mutual information for a tripartite quantum state with high dimensions.

A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups, and differential geometry and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally, we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.

We show that the simultaneous interaction of two single-photon fields with a single atom in the V configuration can, in principle, produce a conditional phase gate of arbitrarily high fidelity, for an appropriate choice of the interaction time, as long as the fields can be described by a single temporal mode (as in an optical cavity); this requires a “gated” interaction, where, e.g., dynamical coupling techniques could be used to get the fields in and out of the cavity, and a large detuning induced by a strong external field could be used to turn the atom-field interaction on and off at the right times. With these assumptions, our analysis shows that the largest gate fidelities are obtained for a cavity containing a single atom, and that adding more atoms, in effect, “dilutes” the system's nonlinearity. We also study how spontaneous emission losses into noncavity modes degrade the fidelity, and consider as well a couple of alternate atomic level schemes, namely, two- and five-level systems.

We explore the hypercomplex Kohn-Sham (HCKS) formalism and develop a third exact functional theory beyond the popular Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT), called 1-HCKS. The orbitals of hierarchical correlation introduced in 1-HCKS are interesting because their occupations are neither necessarily integers, as in KS-DFT, nor overly flexible, as in RDMFT; rather, they can capture strong correlation with fractional occupations, governed by stringent constraints. This feature allows 1-HCKS to combine the advantages of KS-DFT and RDMFT in dealing with dynamic correlation and strong correlation, while eliminating the issues of computational convergence and basis set dependence encountered in RDMFT. Thus, 1-HCKS is a promising alternative for implementing DFT beyond KS-DFT, especially for the treatment of strongly correlated systems.

Recent studies [e.g., Sci. Rep. 12, 11256 (2022)] on laser interaction (for a wavelength of 800 nm and intensity greater than ${10}^{16}\mathrm{W}/{\mathrm{cm}}^2$) with a deuterium nanocluster in an ambient magnetic field $B_0$ demonstrate that collisionless absorption of laser light occurs in two stages via anharmonic resonance and electron-cyclotron resonance (ECR) or relativistic ECR (RECR) processes. The auxiliary magnetic field $B_0$ enhances the coupling of the laser field to cluster electrons via improved frequency matching for ECR or RECR as well as phase matching for the prolonged duration of the 5-fs (FWHM) broadband pulse. As a result, the average absorbed energy per electron $\overline{\mathcal{E}}$ significantly jumps up approximately $36–70$ times its ponderomotive energy $U_{\mathrm{p}}$. In this paper we report the energy dispersion of these energetic electrons and their angular distribution in position and momentum space by performing hybrid particle-in-cell simulations. By simulating bigger clusters (radius $R_0\approx 3–4$ nm) at high intensities of approximately ${10}^{16}–{10}^{18}\mathrm{W}/{\mathrm{cm}}^2$, we find $\overline{\mathcal{E}}\approx 36U_{\mathrm{p}}–70U_{\mathrm{p}}$, which is similar to a small cluster $(R_0\approx 2$ nm), but total energy absorption increases almost linearly with increasing cluster size due to the greater number of available energy carriers. In all cases near ECR or RECR, electrons form a narrow conelike weakly relativistic gyrating beam (about $B_0$) within an angular spread $\mathrm{\Delta }\theta <5^{\circ }$, propagating far beyond $200R_0$ along $B_0$. This study may be relevant because an intense, weakly relativistic electron beam has wide applications, including the fast ignition technique for inertial confinement fusion, ultrashort-x-ray sources, and medical applications.

Electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) have many applications, especially for achieving slow light and fast light. EIT and EIA have been widely observed in both quantum and classical systems where two transition pathways could interference destructively or constructively. Multipathway interference has been a concern in recent works, however, due to the difficulty of precisely controlling the system parameters, the experimental study of multipathway interference is generally challenging. In this paper, we explore a coupled high-temperature-superconducting (HTS) resonator platform for implementing three-pathway electromagnetically induced transparency (TEIT) and absorption (TEIA). In our system, both resonant frequencies and linewidths (loss) of each resonator as well as their coupling strength can be precisely controlled, thus TEIT and TEIA can be implemented as a set. Our proposed method shows great potential for use in microwave signal processing in the future, such as slow wave, fast wave, and radio-frequency memory. Our results indicate the HTS resonator is an ideal platform for investigating versatile coherent phenomena.

Recent experiments have realized a twisted-bilayer-like optical potential for ultracold atoms, which in contrast to solid-state setups may allow for an arbitrary ratio between the inter- and intralayer couplings. For commensurate moiré twistings, a large-enough interlayer coupling results in particle transport dominated by channel formation. For incommensurate twistings, the interlayer coupling acts as an effective disorder strength. Whereas for weak couplings the whole spectrum remains ergodic, at a critical value part of the eigenspectrum transitions into multifractal states. A similar transition may be observed as well as a function of an energy bias between the two layers. Our theoretical study reveals atoms in a twisted-bilayer system of square optical lattices as an interesting platform for the study of ergodicity breaking and multifractality.

We report experimental and theoretical investigations of photon diffusion in a second-order-nonlinear disordered medium under conditions of strong nonlinearity. Experimentally, photons at the fundamental wavelength $\left(\lambda =1064\mathrm{nm}\right)$ are launched into the structure in the form of a cylindrical pellet, and the second-harmonic $\left(\lambda =532\mathrm{nm}\right)$ photons are temporally analyzed in transmission. For comparison, separate experiments are carried out with incident green light at $\lambda =532\mathrm{nm}$. We observe that the second-harmonic light peaks earlier compared to the incident green photons. Next, the sideways spatial scattering of the fundamental as well as second-harmonic photons is recorded. The spatial diffusion profiles of second-harmonic photons are seen to peak deeper inside the medium in comparison to both the fundamental and incident green photons. In order to give more physical insights into the experimental results, a theoretical model is derived from first principles. It is based on the coupling of transport equations. Solved numerically using a Monte Carlo algorithm and experimentally estimated transport parameters at both wavelengths, it shows excellent semiquantitative agreement with the experiments for both fundamental and second-harmonic light.

Bohmian mechanics has garnered significant attention as an interpretation of quantum theory since the paradigmatic experiments by [Kocsis et al., Science 332, 1170 (2011)] and [Mahler et al., Sci. Adv. 2, e1501466 (2016)], which inferred the average trajectories of photons in the nonrelativistic regime. These experiments were largely motivated by Wiseman's formulation of Bohmian mechanics, which grounded these trajectories in weak measurements. Recently, Wiseman's framework was extended to the relativistic regime by expressing the velocity field of single photons in terms of weak values of the photon energy and momentum. Here, we propose an operational, weak value-based definition for the Bohmian “local mass” of relativistic single particles. For relativistic wave functions satisfying the scalar Klein-Gordon equation, this mass coincides with the effective mass defined by de Broglie in his relativistic pilot-wave theory, a quantity closely connected with the quantum potential that is responsible for Bohmian trajectory self-bending and the anomalous photoelectric effect. We demonstrate the relationship between the photon trajectories and the mass in an interferometric setup.

The Margolus-Levitin (ML) bound says that for any time-independent Hamiltonian, the time needed to evolve from one quantum state to another is at least $\pi \alpha \left(\epsilon \right)/2\langle E-E_0\rangle$, where $\langle E-E_0\rangle$ is the expected energy of the system relative to the ground state of the Hamiltonian and $\alpha \left(\epsilon \right)$ is a function of the fidelity $\epsilon$ between the two states. For a long time, only an upper bound ${\alpha }_{>}\left(\epsilon \right)$ and a lower bound ${\alpha }_{<}\left(\epsilon \right)$ are known, although they agree up to at least seven significant figures. Recently, Hörnedal and Sönnerborn [arXiv:2301.10063] proved an analytical expression for $\alpha \left(\epsilon \right)$, a fully classified system whose evolution time saturates the ML bound, and gave this bound a symplectic-geometric interpretation. Here I solve the same problem through an elementary proof of the ML bound. By explicitly finding all the states that saturate the ML bound, I show that ${\alpha }_{>}\left(\epsilon \right)$ is indeed equal to ${\alpha }_{<}\left(\epsilon \right)$. More importantly, I point out a numerical stability issue in computing ${\alpha }_{>}\left(\epsilon \right)$ and report a simple way to evaluate it efficiently and accurately.

Understanding multipartite entanglement is a key goal in quantum information. Entanglement in pure states can be characterized by considering transformations under local operations assisted by classical communication (LOCC). However, it has been shown that, for $n\ge 5$ parties, multipartite pure states are generically isolated, i.e., they can be neither reached nor transformed under LOCC. Nonetheless, in any real laboratory, one never deterministically transforms a pure initial state exactly to a pure target state. Instead, one transforms a mixed state near the initial state to an ensemble that is on average close to the target state. This motivates studying approximate LOCC transformations. After reviewing in detail the known results in the bipartite case, we present the gaps that remain open in the multipartite case. While the analysis of the multipartite setting is much more technically involved due to the existence of different stochastic LOCC (SLOCC) classes, certain features simplify in the approximate setting. In particular, we show that it is sufficient to consider pure initial states, that it is sufficient to consider LOCC protocols with finitely many rounds of communication, and that approximate transformations can be approximated by ensemble transformations within an SLOCC class. Then we formally define a hierarchy of different forms of approximate transformations that are relevant from a physical point of view. Whereas this hierarchy collapses in the bipartite case, we show that this is not the case for the multipartite setting, which is fundamentally richer. To wit, we show that optimal multipartite approximate transformations are not generally deterministic, that ensemble transformations within an SLOCC class can achieve a higher fidelity than deterministic transformations within an SLOCC class, and that there are approximate transformations with no deterministic transformations nearby.

We present an alternative way of calculating the Keldysh amplitude, i.e., the length-gauge form of the ionization amplitude in the strong-field approximation. The amplitude is evaluated exactly by expanding it in Fourier components and partial waves. Comparisons of the semianalytic model predictions with results of ab initio numerical simulations of the time-dependent Schrödinger equation for the interaction of electrons in short-range potentials with intense laser light yield excellent agreement, for wavelengths from the single photon to the multiphoton to the tunneling regime. Specifically, for ionization from initial states with higher angular momentum quantum number, e.g., $p$ states, a significant improvement over predictions based on the popular saddle-point approximation is found. Furthermore, the current model rate allows for interpretation of the strong-field ionization process in terms of multiphoton absorption pathways and angular momentum selection rules.

We investigate the process of photon absorption by atoms or molecules shortly interacting with a laser beam in the dipole approximation. Assuming that the interaction time $\tau$ is much smaller than the lifetime of the corresponding excited state, we examine the absorption probability as a function of $\tau$. In addition, we incorporate Doppler broadening due to nonzero temperature of the atoms (molecules). It is demonstrated that in the case of a zero detuning and without Doppler broadening the absorption probability is quadratic in $\tau$. Once Doppler broadening is taken into account or the laser beam is off from the resonant frequency, the absorption probability becomes linear in $\tau$. Our findings are expected to be important for experimental studies in optical cells or cavities where atoms or molecules traverse continuous laser beams. The experimental prospects of searching for the electric dipole moment of the electron are discussed in detail.

We propose a method of generating and detecting spatially defined entanglement in exciton-polariton condensates at steady state. In our scheme we first create a spinor polariton condensate, such that steady-state squeezing is obtained under a one-axis twisting interaction. Then the condensate is split either physically or virtually, which results in entanglement generated between the two parts. A virtual split means that the condensate is not physically split, but its near-field image is divided into two parts, and the spin correlations are deduced from polarization measurements in each half. We theoretically model and examine the logarithmic negativity criterion and several correlation-based criteria to show that entanglement exists under experimentally achievable parameters.

The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov–de Gennes (BdG) equation throughout the Bardeen-Cooper-Schrieffer (BCS)–Bose-Einstein condensation (BEC) crossover. Consistent with the Poincaré-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided.

The derivation of determinant representations for the space-, time-, and temperature-dependent correlation functions of the impenetrable Gaudin-Yang model in the presence of a trapping potential is presented. These representations are valid in both equilibrium and nonequilibrium scenarios like the ones initiated by a sudden change of the confinement potential. In the equal-time case our results are shown to be equivalent to a multicomponent generalization of Lenard's formula from which Painlevé transcendent representations for the correlators can be obtained in the case of harmonic trapping and Dirichlet and Neumann boundary conditions. For a system in the quantum Newton's cradle setup the determinant representations allow for an exact numerical investigation of the dynamics and even hydrodynamization, which is outside the reach of generalized hydrodynamics or other approximate methods. In the case of a sudden change in the trap's frequency, we predict a many-body bounce effect, not present in the evolution of the density profile, which causes a nontrivial periodic narrowing of the momentum distribution with amplitude depending on the statistics of the particles.

We study the impact of distinguishability and mixedness, two fundamental properties of quantum states, on quantum interference. We show that these can influence the interference of multiple particles in different ways, leading to effects that cannot be observed in the interference of two particles alone. This is demonstrated experimentally by interfering three independent photons in pure and mixed states and observing their different multiphoton interference, despite exhibiting the same two-photon Hong-Ou-Mandel interference. In addition to its fundamental relevance, our observation has important implications for quantum technologies relying on photon interference.

A hybrid system established by the direct interaction between a magnon mode and a superconducting transmon qubit is used to realize a high-degree blockade for magnon. It is a fundamental way toward quantum manipulation at the level of a single magnon and preparation of single magnon sources. Through weakly driving the magnon and probing the qubit, our magnon-blockade proposal can be optimized when the transversal coupling strength between the magnon and qubit is equivalent to the detuning of the qubit and the probing field or that of the magnon and the driving field. Under this condition, the equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ can be analytically minimized when the probing intensity is about three times the driving intensity. Moreover, the magnon blockade could be further enhanced by proper driving intensity and system decay rate, whose magnitudes outrange the current systems of cavity QED and cavity optomechanics. In particular, the correlation function achieves $g^{\left(2\right)}\left(0\right)\sim {10}^{-7}$, about two orders lower than that for the photon blockade in cavity optomechanics. Also, we discuss the effects on $g^{\left(2\right)}\left(0\right)$ from thermal noise and the extra longitudinal interaction between the magnon and qubit. Our optimized conditions for blockade are found to persist in these nonideal situations.