By numerically solving the three-dimensional time-dependent Schrödinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{−}2p$ transition. Due to the Rabi oscillations between the $1s$ and $2p$ states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.

We investigate the stationary vortex solutions in two-dimensional Rashba spin-orbit-coupled spin-1 Bose-Einstein condensates. By introducing the generalized momentum operator, the linear version of the system can be solved exactly and its solutions are a set of the Bessel vortices. Based on the linear version solutions, the stationary vortex solutions of the full nonlinear system are constructed and determined entirely by the variational approximation. The results show that the variational results are in good agreement with the numerical ones. By means of the variational results, the vortex ground-state phase transition between the stationary vortex solutions, the stability, and the unit Bloch vector textures are discussed in detail. The results have the potential to be realized in experiment.

Nonlinear spectroscopies can disentangle spectra that are congested due to inhomogeneous broadening. In conjunction with theoretical calculations, attosecond extreme ultraviolet (XUV) four-wave-mixing (FWM) spectroscopy is utilized here to probe the dynamics of autoionizing inner valence excited Rydberg states of the polyatomic molecule, ${\mathrm{CO}}_2$. This tabletop nonlinear technique employs a short attosecond XUV pulse train and two noncollinear, few-cycle near-infrared pulses to generate background-free XUV wave-mixing signals. FWM emission is observed from the $n=5\text{–}7$ states of the Henning sharp $nd{\sigma }_g$ Rydberg series that converges to the ionic $\tilde{B}{}^2\mathrm{\Sigma }_u^{+}$ state. However, these transient emission signals decay with lifetimes of 33 $\pm$ 6, 53 $\pm$ 2, and 94 $\pm$ 2 fs, respectively, which calculations show are consistent with the lifetimes of the short-lived $n=6\text{–}8$ members of the $ns{\sigma }_g$ character Henning diffuse Rydberg series. The oscillator strengths of transitions between states involved in all possible resonant FWM processes are calculated, verifying that the nonlinear spectra are dominated by pathways described by an initial excitation to the diffuse $ns{\sigma }_g$ Rydberg series and emission from the sharp $nd{\sigma }_g$ Rydberg series. The results substantiate not only that attosecond XUV FWM spectroscopy produces rigorous and meaningful measurements of ultrafast dynamics in polyatomic systems, but also that nonlinear spectroscopic techniques are versatile tools to selectively probe dynamics that are otherwise difficult to access.

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications, in particular in optics and photonics. However, the experimental realization is notoriously difficult. Recently, Zhong et al. [Q. Zhong, J. Kou, Ş. K. Özdemir, and R. El-Ganainy, Phys. Rev. Lett. 125, 203602 (2020)] have introduced a robust construction where a unidirectional coupling of two subsystems having exceptional points of the same order leads generically to a single exceptional point of twice the order. Here, we investigate this scheme in a different manner by exploiting the nilpotency of the traceless part of the involved Hamiltonians. We generalize the scheme and derive a simple formula for the spectral response strength of the composite system hosting a higher-order exceptional point. Its relation to the spectral response strengths of the subsystems is discussed. Moreover, we investigate nongeneric perturbations. The results are illustrated with an example.

We study the classical and quantum Fisher information of the interaction coupling in the Lieb-Liniger model. Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey interferometry. Here we investigate the case that a Hamiltonian parameter to be estimated is imprinted on eigenstates of that Hamiltonian and thus is not necessarily encoded by a unitary operator. We take advantage of the fact that the Lieb-Liniger model is exactly soluble for both periodic and hard-wall boundary conditions. For the latter case, we provide a derivation of the explicit expression for the norm of the Lieb-Liniger wave function. The Fisher information is determined for various small numbers of particles, for both ground state and excited states of type I and type II in the Lieb-Liniger terminology. We discuss the dependence of the Fisher information on interaction strength and system size, to further evaluate the metrological aspects of the model. Particularly noteworthy is the fact that the Fisher information displays a maximum when we vary the system size, indicating that the distinguishability of the wave functions is largest when the Lieb-Liniger parameter is at the crossover between Bose-Einstein condensate and Tonks-Girardeau limits. The saturability of this Fisher information by employing standard absorption imaging as the measurement method is assessed by a specific modeling of the latter.

We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in the sense that every entangled subspace is shown to be so at some finite level of the hierarchy. It straightforwardly generalizes to the case of higher Schmidt rank, as well as the multipartite cases of completely and genuinely entangled subspaces. These hierarchies work extremely well in practice even in very large quantum systems, as they can be implemented via elementary linear algebra techniques rather than the semidefinite programming techniques that are required by previously known hierarchies.

The $\mathrm{Lu}\mathrm{O}{\mathrm{H}}^{+}$ cation is a promising system to search for manifestations of time reversal and spatial parity violation effects. Such effects in $\mathrm{Lu}\mathrm{O}{\mathrm{H}}^{+}$ induced by the electron electric dipole moment $e\mathrm{EDM}$ and the scalar-pseudoscalar interaction of the nucleus with electrons, characterized by $k_s$ constant, in $\mathrm{Lu}\mathrm{O}{\mathrm{H}}^{+}$ are studied. The enhancement factors, polarization in the external electric field, hyperfine interaction, and rovibrational structure are calculated. The study is required for the experiment preparation and extraction of the $e\mathrm{EDM}$ and $k_s$ values from experimental data.

In this work we propose and theoretically characterize optical isolators consisting of an all-dielectric and nonmagnetic resonator featuring an intensity-dependent refractive index and a strong coherent field propagating in a single direction. Such devices can be straightforwardly realized in state-of-the-art integrated photonics platforms. The mechanism underlying optical isolation is based on the breaking of optical reciprocity induced by the asymmetric action of four-wave mixing processes coupling a strong propagating pump field with copropagating signal and idler modes but not with reverse-propagating ones. Taking advantage of a close analogy with fluids of light, our proposed isolation mechanism is physically understood in terms of the Bogoliubov dispersion of collective excitations on top of the strong pump beam. A few most relevant setups realizing our proposal are specifically investigated, such as a coherently illuminated passive ring resonator and unidirectionally lasing ring or Taiji resonators.

Higher-order topological insulators have triggered a great deal of interest because they exhibit nontrivial bulk topology on lower-dimensional boundaries such as corners and hinges. While such interesting phases have been investigated in a plethora of systems by tuning staggered tunneling strength or manipulating existing topological phases, here we show that a higher-order topological phase can be driven solely by mirror-symmetric on-site potentials. We start with a chain model, and we show that it has nonzero edge states due to the lack of internal symmetries such as chiral and particle-hole symmetries. We then generalize the model to two dimensions, and we demonstrate the emergence of topological corner modes. These corner modes are an intrinsic manifestation of nontrivial bulk band topology protected by mirror symmetry, and thus they are robust against symmetry-preserved perturbations. Our model only requires the tuning of on-site energies, and it provides a realistic platform for studying a class of higher-order topological insulators using state-of-the-art experiment techniques.

The photonic Bose-Einstein condensate is a recently observed collective ground state of a coupled light-matter system. We describe this quantum state based on macroscopic quantum electrodynamics in dispersing and absorbing environments. To model the coupled photon-dye dynamics, we derive a master equation using a nested-open-quantum-systems approach yielding all parameters essential to describe the condensation process. This approach allows us to describe photon condensates of arbitrary shapes because all geometry-dependent decay constants can be expressed in terms of the Green's tensor. In particular, we obtain the cavity mode absorption and emission rates of the dye molecules.

The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. Although there were proposals to refer von Neumann entropy as the thermodynamic entropy, it has its own limitations. The observational entropy has been developed as a generalization of Boltzmann entropy, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this paper, we study the behavior of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-André (AA) model. We find that for the typical midspectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, whereas in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase in the observational entropy followed by the quantum quench is logarithmic in time in the delocalized phase as well as at the transition point, whereas in the localized phase it oscillates. Finally, we also venture the self-dual property of the AA model using momentum space coarse graining.

We study an open quantum spin chain of arbitrary length with nearest neighbor $XX$ interactions of strength $g$, immersed in an external constant magnetic field $\mathrm{\Delta }$ along the $z$ direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio $r\equiv g/\mathrm{\Delta }$. By increasing $r$, some of the chain Bohr transition frequencies become negative; when this occurs, both the generator of the dissipative time evolution and its stationary states behave discontinuously. As a consequence, the asymptotic spin and heat flows also exhibit discontinuities, but in a different way: while source terms in the spin flow continuity equation show jumps, the heat flow instead is continuous but with discontinuous first derivatives with respect to $r$. These two behaviors might be experimentally accessible; in particular, they could discriminate between the global and the local approaches to open quantum spin chains. Indeed, the latter one, which neglects interspin interactions in the derivation of the master equation, does not show any kind of discontinuous behavior.

The uncertainty principle, which demonstrates the intrinsic uncertainty of nature from an information-theory perspective, is at the heart of quantum information theory. In the realm of quantum information theory, Shannon entropy is used to depict the uncertainty relation in general. A tighter lower bound for uncertainty relations facilitates more accurate predictions of measurement outcomes and more robust quantum information processing. Interestingly, the tripartite entropic uncertainty relation (EUR) can be further optimized. Renes et al. proposed a tripartite EUR [J. M. Renes and J.-C. Boileau, Phys. Rev. Lett. 103, 020402 (2009)], and subsequently, Ming et al. strengthened its lower bound in [F. Ming, D. Wang, X.-G. Fan, W.-N. Shi, L. Ye, and J.-L. Chen, Phys. Rev. A 102, 012206 (2020)]. Specifically, we derive a tighter lower bound of the tripartite EUR using the Holevo quantity. Furthermore, we generalize the tripartite EUR, that is, the generalized entropic uncertainty relation for multiple measurements in multipartite systems. As illustrations, we provide several typical examples to show that our bound is tight and outperforms the previous bound. Furthermore, our findings pave the way for using the tighter bound for the quantum secret key rate in quantum key distribution protocols and are essential for quantum precision measurements in the framework of genuine multipartite systems. By providing a close peek at the nature of uncertainty, our results may find broad applications in the security analysis of quantum cryptography.

The shot noise in coherent control of a quantum system sets an ultimate precision limit in measurement and information processing. It is caused by the fundamental quantum fluctuation of the photon number of a coherent control field and thus is inevitable. By strongly coupling a two-level system to a quantum vacuum field, we propose an effective $N$-type four-level system. In such a configuration, the coupling of a conventional $N$-type system to a coherent control field is replaced by the quantum vacuum field. As a result, we can achieve a shot-noise-suppressing quantum nonlinearity, due to the vanishing fluctuation of photon number of the quantum vacuum field. The resulting photon blockade effect is only subject to the contribution from the probe field. Thus, it becomes shot-noise suppressing. Our work shows an advantage of a quantum vacuum protocol over a coherent-field protocol in manipulation of quantum systems and presents an opportunity to exploit the quantum vacuum field as a powerful tool in quantum information processing.

We propose an alternative form for the quantum master equation in the theory of open quantum systems. This alternative formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper times. In the Born-Markov approximation, we consider a quantum massless scalar field coupled with two-level systems. Starting from a separable state, we show the emergence of entanglement harvesting. For different proper accelerations we also verify the entanglement sudden death.

Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these parameters, and a full reconstruction is not needed. A paradigmatic example is a scenario in which one aims at determining all the reduced states only up to a given size. Overlapping tomography provides constructions to address this problem with a number of product measurements much smaller than what is obtained when performing independent tomography of each reduced state. There are, however, many relevant physical systems with a natural notion of locality where one is mostly interested in the reduced states of neighboring particles. In this work, we study this form of local overlapping tomography. First of all, we show that, contrary to its full version, the number of product-measurement settings needed for local overlapping tomography does not grow with system size. Then, we present strategies for qubit and fermionic systems in selected lattice geometries. The developed methods find a natural application in the estimation of many-body systems prepared in current quantum simulators or quantum computing devices, where interactions are often local.

Open quantum systems are a topic of intense theoretical research. The use of master equations to model a system's evolution subject to an interaction with an external environment is one of the most successful theoretical paradigms. General experimental tools to study different open system realizations have been limited, and so it is highly desirable to develop experimental tools which emulate diverse master equation dynamics and give a way to test open systems theories. In this paper we demonstrate a systematic method for engineering specific system-environment interactions and emulating master equations of a particular form using classical stochastic noise in a superconducting transmon qubit. We also demonstrate that non-Markovian noise can be used as a resource to extend the coherence of a quantum system and counteract the adversarial effects of Markovian environments.

The effect of thermal shape fluctuations on the recurrent fluorescence of boron-cluster cations, ${\mathrm{B}}_N{}^{+}$ $(N=9–14)$, has been investigated numerically, with a special emphasis on ${\mathrm{B}}_{13}{}^{+}$. For this cluster, the electronic structures of the ground state and the four lowest electronically excited states were calculated using time-dependent density-functional theory and sampled on molecular dynamics trajectories of the cluster calculated at an experimentally relevant excitation energy. The sampled optical transition matrix elements for ${\mathrm{B}}_{13}{}^{+}$ allowed us to construct its emission spectrum from the thermally populated electronically excited states. The spectrum was found to be broad, reaching down to at least 0.85 eV. This contrasts strongly with the static picture, where the lowest electronic transition happens at 2.3 eV. The low-lying electronic excitations produce a strong increase in the rates of recurrent fluorescence, calculated to peak at $4.6\times {10}^4{\mathrm{s}}^{-1}$, with a time average of $8\times {10}^3{\mathrm{s}}^{-1}$. The average value is one order of magnitude higher than the static result, approaching the measured radiation rate. Similar results were found for the other cluster sizes. The results indicate that the effect makes a significant contribution to the radiative cooling, even given the exploratory nature of the study. Furthermore, the radiationless crossing between the ground-state and first-electronic-excited-state surfaces of ${\mathrm{B}}_{13}{}^{+}$ was calculated, found to be very fast compared to experimental timescales, justifying the thermal population assumption.

We investigate the harmonic response of neon atoms to mid-IR laser fields ($2000–3000$ nm) using a single active electron (SAE) model and the fully ab initio all-electron $R$ matrix with time dependence (RMT) method. The laser peak intensity and wavelength are varied to find suitable parameters for high-harmonic imaging in the water window. Comparison of the SAE and RMT results shows qualitative agreement between them as well as parameters such as the cutoff frequency predicted by the classical three-step model. However, there are significant differences in the details, particularly in the predicted conversion efficiency. These details indicate the possible importance of multielectron effects, as well as a strong sensitivity of quantitative predictions on specific aspects of the numerical model.