We investigate the formation of dark vector dissipative solitons in the presence of nonlinear polarization mode coupling in optical resonators subject to a coherent optical injection in the normal dispersion regime. This simple device is described by coupled Lugiato-Lefever equations. The stabilization of dark dissipative solitons is attributed to a front locking mechanism in the bistable regime as shown in a recent communication [B. Kostet et al., OSA Continuum 4, 1564 (2021)]. Here, we focus on a tristable homogeneous steady state regime. We show that two branches of dark dissipative solitons can coexist for a fixed value of the system parameters. These coexisting solutions possess different polarization states and different peak powers in the microresonator. We characterize their formation by drawing their bifurcation diagrams in regimes far from any modulational instability. It is shown that both branches of localized structures exhibit a heteroclinic collapsed snaking type of behavior. The coexistence of two vectorial branches of dark localized states is not possible without taking into account polarization degrees of freedom.

We examine the coupling process between the surface modes of a Su-Schrieffer-Heeger lattice both in the linear and the nonlinear regimes. We first develop a coupled-mode theory formalism for the modes of a finite lattice with zero boundary conditions. Our analysis relies on the closed-form expressions for the bulk and the surface eigenmodes of the system. The coupled-mode theory formalism is based on a decomposition of the supermodes into sublattice modes. In the case of the two zero sublattice surface modes, this leads to periodic oscillations between them without the involvement of the bulk modes. We analytically show that launching light only on the waveguide that is located at either edge of the array can be very effective in successfully exciting the respective surface mode. We extend our analysis, in the case of Kerr nonlinearity, and develop a simplified model that accounts only for the surface modes. By direct numerical simulations, we find that this model can very accurately capture the dynamics of the surface modes when the nonlinearity is small or moderate. On the other hand, in the case of strong nonlinearity, wave mixing leads to the quasiperiodic excitation of the bulk modes, or even to a chaotic behavior where all the modes of the systems are excited, and no prominent signature of the surface modes can be detected.

The photonic analog of an axioniclike system (or electronic topological insulator) is called an axionic photonic crystal. These materials are classified by three physical properties: permittivity $\epsilon$, permeability $\mu$, and the topological parameter $\theta$. As a particular case, crystals with periodic $\epsilon$ and $\mu$ are the so-called photonic crystals. In this paper, we employ a transfer-matrix treatment to study the propagation of light waves in an axionic photonic crystal composed of alternating building layers $A$ and $B$. We present numerical results for the photonic band structure as a function of the ratio between permittivities $R={\epsilon }_B/{\epsilon }_A$, layer thicknesses $X=d_B/d_A$, and topological parameters $\delta ={\pi }^2{({\theta }_A-{\theta }_B)}^2/{\alpha }^2$. Our numerical results reveal that the band-gap features (width, center position, upper and lower frequencies) depend on the three parameters $\epsilon$, $\mu$, and $\theta$, but with the dependence on $\theta$ being stronger. In particular, as far as the band-gap width is concerned, we find that $X$ and $R$ work against each other; that is, as $X$ increases, $R$ must decreases for a wide band-gap emergence and vice versa. More interesting, however, are the results for the topological parameter $\theta$. We show that the presence of $\theta$ produces a photonic band gap (PBG) which depends only on the $\delta$ term. The widening of this PBG is slightly asymmetrical and monotonic as a function of $\delta$. It was also found that $\delta$ has no influence on the center position of the PBG. Our results open possibilities for technological applications of axionic photonic crystals with regard to the controlling and confinement of the propagation of light.

The entanglement of optical angular position and orbital angular momentum has become one of the important degrees of freedom for quantum information science. Quantum control of the two conjugate variables may provide a gate to control the production of the entanglement. Here, we theoretically and experimentally show that by controlling the transverse spatial coherence of the pump beam, one can modulate the strength of the quantum correlations between the angular position and orbital angular momentum in down-converted photon pairs. By determining the relation of the Einstein, Podolsky, and Rosen correlations with the transverse spatial coherence of the pump, the boundary of the entanglement can be determined. Our work shows that the transverse spatial coherence of the pump can act as a switch to control the production of quantum entanglement both for discrete and continuous conjugate variables and may provide another platform for the quantum control research field.

In this paper we investigate the model of $N$ two-level atoms coupled to a squeezed vacuum inside a coherently driven cavity. By a linear stability analysis in the semiclassical description, we find that the optical tristability emerges in our system owing to the presence of the squeezed vacuum. Moreover, the transition among monostable, bistable, and tristable states can be realized by manipulating the squeezing phase or the squeezing strength of the squeezed vacuum. We also show the signatures of quantum tristability by using the $Q$ function and quantum trajectory methods for the situation of a single atom and low cavity photon number. Our paper offers a way to realize optical tristability in a two-level atomic system.

We study trajectories of collective spin states of an ensemble of spinors. The spinors considered here are either trapped ions in free space or atoms confined in a cavity, both systems of which are engineered through their interactions with light fields to obey an effective Dicke model. In an appropriate limit of the Dicke model, one obtains one-axis twisting dynamics of the collective spin and evolution after a finite time to a spin cat state or, in the long-time limit, the Dicke state ${|S,0\rangle }_x$, conditioned upon there being no photon emissions from the system (i.e., no quantum jumps). If there is a jump, however, the system evolves probabilistically into one of a finite number of entangled-state cycles, where the system then undergoes a persistent sequence of jumps between two Dicke-state superpositions in a rotated basis. The different cycles can be distinguished by the frequency at which jumps occur.

We study a system of a single qubit (or a few qubits) interacting with a soft-mode bosonic field. Considering an extended version of the Rabi model with both parity-conserving and parity-violating interactions, we disclose a complex arrangement of quantum phase transitions in the ground- and excited-state domains. An experimentally testable signature of some of these transitions is a dynamical stabilization of a fully factorized qubit-field state involving the field vacuum. It happens in the ultrastrong coupling regime where the superradiant field equilibrium is far from the vacuum state. The degree of stabilization varies abruptly with interaction parameters and increases with the softness of the field mode. We analyze semiclassical origins of these effects and show their connection to various forms of excited-state quantum phase transitions.

We analyze Lindblad-Gorini-Kossakowski-Sudarshan-type generators for selected periodically driven open quantum systems. All these generators can be obtained by temporal coarse-graining procedures, and we compare different coarse-graining schemes. Similarly to undriven systems, we find that a dynamically adapted coarse-graining time, effectively yielding non-Markovian dynamics by interpolating through a series of different but individually Markovian solutions, gives the best results among the different coarse-graining schemes, albeit at the highest computational cost.

We explore nonequilibrium quantum heat transport in nonlinear bosonic systems in the presence of a non-Kerr-type interaction governed by hyperparametric oscillation due to two-photon hopping between the two cavities. We estimate the thermodynamic response analytically by constructing the su(2) algebra of the nonlinear Hamiltonian and predict that the system exhibits a negative excitation mode. Consequently, this specific form of interaction enables the cooling of the system by inducing a ground-state transition when the number of particles increases, even though the interaction strength is small. We demonstrate a transition of the heat current numerically in the presence of symmetric coupling between the system and the bath and show long relaxation times in the cooling phase. We compare with the Kerr-type Bose-Hubbard form of interaction induced via cross-phase modulation, which does not exhibit any such transition. We further compute the nonequilibrium heat current in the presence of two baths at different temperatures and observe that the cooling effect for the non-Kerr-type interaction persists. Our findings may help in the manipulation of quantum states using the system's interactions to induce cooling.

The shortcut to adiabaticity (STA) is a powerful technique to speed up population transfer via quantum coherent control. This paper demonstrates that STA provides a fast, robust, and efficient population transfer compared to the stimulated Raman adiabatic passage. In the ideal situation of a closed system, STA is insensitive to the detunings and Rabi frequencies, and the undesired diabatic transitions could be eliminated by the auxiliary pulses, so the complete population transfer from the initial state to the target state in the designed adiabatic passage can be rapidly achieved against the inevitable amplitude noises of the interactions and systematic errors. When we consider the situation including the environment noises, spontaneous emission from the intermediate state $|2\rangle$ in STA can be sufficiently ignored in the cases of the dark-state evolution and quantum overdamping, since the state $|2\rangle$ is thoroughly separated from the three-state system. Moreover, the diabatic transitions induced by the spontaneous emission are also sufficiently suppressed in STA.

In the traditional quantum theory, one-dimensional quantum spin models possess a factorization surface where the ground states are fully separable and have vanishing bipartite as well as multipartite entanglement. We report that in the non-Hermitian counterpart of these models, these factorization surfaces either can predict the exceptional points where the unbroken-to-broken transition occurs or can guarantee the spectrum to be real, thereby suggesting a procedure to reveal the unbroken phase. We first analytically demonstrate it for the nearest-neighbor rotation-time- $\left(\mathcal{RT}\right)$ symmetric $XY$ model with uniform and alternating transverse magnetic fields, referred to as the $iATXY$ model. Exact diagonalization techniques are then employed to establish this fact for the $\mathcal{RT}$-symmetric $XYZ$ model with short- and long-range interactions as well as for the long-range $iATXY$ model. Moreover, we show that although the factorization surface prescribes the unbroken phase of the non-Hermitian model, the bipartite nearest-neighbor entanglement at the exceptional point is nonvanishing.

We discuss the local equilibration of closed systems using the relative purity, a paradigmatic information-theoretic distinguishability measure that finds applications ranging from quantum metrology to quantum speed limits. First we obtain an upper bound on the average size of the fluctuations on the relative purity: it depends on the effective dimension resembling the bound obtained with the trace distance. Second, we investigate the dynamics of relative purity and its rate of change as a probe of the speed of fluctuations around the equilibrium. In turn, such speed captures the notion of how fast some nonequilibrium state approaches the steady state under the local nonunitary dynamics, somehow giving the information of the quantum speed limit towards the equilibration. We show that the size of fluctuations depends on the quantum coherences of the initial state with respect to the eigenbasis of the Hamiltonian, also addressing the role played by the correlations between system and reservoir into the averaged speed. Finally, we have derived a family of lower bounds on the time of evolution between these states, thus obtaining an estimate for the equilibration time at the local level. These results could be of interest to the subjects of equilibration, quantum speed limits, and also quantum metrology.

This article investigates dissipative preparation of entangled nonequilibrium steady states (NESS). We construct a collision model where the open system consists of two qubits which are coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of qubits interacting with the open system. The model can be studied in different dynamical regimes: with and without environmental memory effects. We report that only a certain bath temperature range allows for entangled NESS. Furthermore, we obtain minimal and maximal critical values for the heat current through the system. Surprisingly, quantum memory effects play a crucial role in the long-time limit. First, memory effects broaden the parameter region where quantum correlated NESS may be dissipatively prepared and, second, they increase the attainable concurrence. Most remarkably, we find a heat current range that does not only allow, but even guarantees that the NESS is entangled. Thus, the heat current can witness entanglement of nonequilibrium steady states.

We present a set of techniques, based on the repeated arbitrary application of cp, cnot, and swap${}^{\alpha }$ (power-of-swap) quantum gate operations to an $n$-qubit quantum computer that can be used in its verification. We find isomorphisms between the groups generated by these gate operations and known groups and use techniques from representation theory to determine their invariant subspaces. For the cp operation, we find an isomorphism to the direct product of $n(n-1)/2$ cyclic groups of order 2, and determine $2^n$ one-dimensional invariant subspaces corresponding to the computational-basis vectors. For the cnot operation, we find an isomorphism to $GL(n,2)$, and determine two one-dimensional invariant subspaces and one $(2^n-2)$-dimensional invariant subspace. For the swap${}^{\alpha }$ operation we find a complex structure of invariant subspaces with varying dimensions and occurrences and present a recursive procedure to construct them. Using knowledge of these invariant subspaces, we propose a hardware verification scheme which tests the correct functioning of a quantum computer.

We report on a time-scaling technique to enhance the performances of quantum control protocols in non-Hermitian systems. The considered time scaling involves no extra couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum-state transfers in two- and three-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that with an appropriate driving the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit whereas reducing significantly the damping of the quantum-state norm.

We compute the conservative van der Waals forces between two atoms, one of which is initially excited, in the limit of identical atoms. Starting with the perturbative calculation of the interaction between two dissimilar atoms, we show that a time-dependent approach in the weak-interaction approximation is essential in considering the identical-atom limit in the perturbative regime. In this limit we find that, at leading order, the van der Waals forces are fully resonant and grow linearly in time, being different upon each atom. The resultant net force upon the two-atom system is related to the directionality of spontaneous emission, which results from the violation of parity symmetry. The strength of this force is much greater than that found in dissimilar atoms, raising the possibility of its experimental detection. In contrast to the usual stationary van der Waals forces, the time-dependent conservative forces cannot be written as the gradients of the expectation values of the interaction potentials, but as the expectation values of the gradients of the interaction potentials only.

We investigate the four-body proton-helium scattering problem using the two-center wave-packet convergent close-coupling approach. The approach uses a correlated two-electron wave function for the helium target. The continuum is discretized using wave-packet pseudostates. Calculations of ionization cross sections differential in the electron emission energy, in the emission angle, as well as in the scattered-projectile angle are performed in the intermediate energy region where coupling between various channels and electron-electron correlation effects are important. The results agree well with experimental data, where available. Moreover, our calculations reveal an interesting interplay between direct ionization and electron capture into the continuum. In particular, we demonstrate that the ionization cross section differential in the angle of the ejected electron is dominated by electron capture into the continuum for ejection into small angles, while ejection into large angles is purely due to direct ionization. It is concluded that the two-center wave-packet convergent close-coupling approach can provide accurate singly differential cross sections for ionization in proton-helium collisions. For comparison, a recently developed method that reduces the target to an effective single-electron system is also used. Somewhat unexpectedly, the results of the effective one-electron method exhibit a very good level of agreement with the full two-electron ones for all three singly differential cross sections. Therefore, we also conclude that, at least for the purpose of calculating the singly differential cross sections for single ionization of helium, an effective one-electron treatment of the target suffices.

We examine how nondestructive measurements generate spin squeezing in an atomic Bose-Einstein condensate confined in a double-well trap. The condensate in each well is monitored using coherent light beams in a Mach-Zehnder configuration that interacts with the atoms through a quantum nondemolition Hamiltonian. We solve the dynamics of the light-atom system using an exact wave-function approach, in the presence of dephasing noise, which allows us to examine arbitrary interaction times and a general initial state. We find that monitoring the condensate at zero detection current and with identical coherent light beams minimizes the backaction of the measurement on the atoms. In the weak atom-light interaction regime, we find the mean spin direction is relatively unaffected, while the variance of the spins is squeezed along the axis coupled to the light. Additionally, squeezing persists in the presence of tunneling and dephasing noise. For long atom-light interaction time, we equally show our methods can be used to prepare non-Gaussian correlated spin states.

An analytic formula for a certain type of a cylindrical beam, which might be called a $\gamma$ beam, has been derived directly from the paraxial equation and independently using the method of the Hankel transform formulated in our previous work [T. Radożycki, Opt. Laser Technol. 147, 107670 (2022)]. The fundamental properties of this beam are analyzed and the parameters characterizing the beam shape are identified. The connection with Gaussian and elegant Laguerre-Gauss beams is demonstrated. In the plane perpendicular to the propagation axis, this beam is shown to display an expanding ring of high-energy concentration. At large radial distances the spatial profile exhibits a power-law falloff. The phase of the wave is also studied in this paper. Close to the symmetry axis it is shown to be typical of modes that exhibit vortex character, such as Gaussian beams of $n\mathrm{th}$ order, but at large distances it reveals a peculiar behavior distinct from Gaussian-type beams.