Mobility edges (MEs) are critical boundaries in disordered quantum systems that separate localized from extended states, significantly affecting transport properties and phase transitions. Although MEs are well-understood in single-photon systems, their manifestation in many-body contexts remains an active area of research. In this work, we investigate a one-dimensional Bose-Hubbard chain with a quasiperiodic potential modulating photon-photon interactions, effectively creating a mosaic lattice. We identify MEs for doublon states (i.e, bound photon pairs resulting from strong interactions) within the two-photon subspace. Our analytical solutions and numerical simulations confirm the existence of these MEs, extending single-photon MEs theories to the two-photon regime. Additionally, we analyze the dynamics of two emitters coupled to the waveguide, enabling the emission of supercorrelated photon pairs into the waveguide. Our findings reveal that coupling to extended states results in Markovian dynamics, characterized by exponentially supercorrelated decay, while coupling to localized states gives rise to non-Markovian dynamics, marked by suppressed decay and persistent oscillations. Here, a transition from Markovian to non-Markovian behavior occurs around the MEs of the doublons. Finally, we propose a feasible experimental implementation using superconducting circuits, providing a platform to observe the interplay between interactions and disorder in quantum systems.

We introduce a quasi-phase-matched technique in quadratic nonlinear crystals, constructing an artificial gauge field by changing the inclination angle of stripes, which is realized by the positive- and negative-polarization directions of nonlinear susceptibility along the crystal. Unlike the artificial gauge field constructed through linear coupling in other settings, the gauge field in this system is realized by nonlinear coupling. We demonstrate that this gauge field can generate stable chiral solitons with chiral energy flow rotating around the solitons. In contrast to conventional chiral currents generated with the same species or frequency, the chiral currents in the present system are formed by mutual coupling between fundamental-frequency and second-harmonic components. We derive the semianalytical solution for the chiral energy flow in this system. It is found that an optimal inclination angle that can maximize the chiral energy flow under different parameters exists, and this optimal inclination shows a positive correlation with the power and detuning. The mobility and collisions of the chiral solitons are also discussed. The results show that chiral solitons move in response to kicking and undergo fully elastic collisions with each other. In addition, the possibility of experimentally generating chiral solitons and chiral currents is outlined.

We theoretically investigate the superradiant phase transition (SPT) in the two-photon Dicke-Stark model, which incorporates both Rabi and Stark coupling. By introducing a Stark coupling term, we significantly reduce the critical Rabi coupling strength required to achieve the SPT, enabling it to occur even in non-ultrastrong-coupling regimes. Using mean-field theory, we derive the conditions for the SPT and show that it exhibits a second-order phase transition. Surprisingly, we demonstrate that the transition point can be widely tuned by the Stark coupling strength. The signatures of these Stark-tunable SPT points manifest through atomic pseudospin mean values. When quantum fluctuations are included, the spin-squeezing distributions also reveal the effects of Stark-tunable SPT points. In addition, we propose an experimentally feasible realization using an ion-trap system driven by three lasers. Our scheme enables optical switching between normal and superradiant phases through pump field intensity modulation, where the Stark coupling coefficient serves as the optically tunable parameter. Our results offer an alternative approach to engineer the SPT, extending superradiance-based quantum technologies beyond the ultrastrong-coupling regime.

We present a numerical method to simulate a system of multiple emitters coupled to a noninteracting bath in any parameter regime. Our method relies on a Block Lanczos transformation that maps the whole system onto a strip geometry whose width is given by the number of emitters. Utilizing the spatial symmetries of the problem and identifying the relevant range of energies of the bath, we achieve a more efficient simulation, which we perform using tensor network techniques. As a demonstration, we study the collective emission from multiple emitters coupled to a square lattice of bosons and observe how the departure from Markovianity as coupling strength and emitter number is increased prevents collective radiation. We also simulate the dynamic preparation of an excitation in a bound state from a multiexcitation initial state. Our work opens possibilities for the systematic exploration of non-Markovian effects in the dynamics and equilibrium properties of multiemitter systems. Furthermore, it can easily be extended to other setups, including finite bath temperature or impurities coupled to fermionic environments.

The generation and manipulation of multipartite entanglement and Einstein-Podolsky-Rosen (EPR) steering in macroscopic systems not only play a fundamental role in exploring the nature of quantum mechanics, but are also at the core of current developments of various nascent quantum technologies. Here we report a theoretical method using squeezing-phase-controlled quantum noise flows to selectively generate and manipulate quantum entanglement and asymmetric EPR steering in a nonlinear ${\chi }^{\left(2\right)}$ whispering-gallery-mode (WGM) optomechanical resonator. We show that by pumping the ${\chi }^{\left(2\right)}$ nonlinear medium with two-photon optical fields and broadband squeezed lights, a pair of counterpropagating squeezed optical modes could be introduced to the WGM resonator, each coupled with an independent squeezed vacuum reservoir. This configuration could enable squeezing-phase-controlled light-reservoir interaction for each squeezed optical mode, providing a flexible tool for tailoring asymmetric optical noise flows in the counterpropagating modes. Based on this unique feature, it is found that with the injection of asymmetric noise flows, the generation of various types of bipartite and tripartite entanglement become phase-dependent, and thus they can be produced in an asymmetric way. More excitingly, it is also found that by further properly adjusting the squeezing parameters, the overall asymmetry of EPR steering can also be stepwise driven from a no-way regime, to a one-way regime, to a two-way regime. These findings, holding promise for preparing rich types of entangled quantum resources with asymmetric features, may have potential applications in the area of secure quantum information processing such as quantum secure direct communication and one-way quantum computing.

In the search for quantum advantage in real-world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA) is particularly well adapted for such a “warm start” approach and can be combined with the powerful classical Goemans-Williamson (GW) algorithms based on semidefinite programing. Nonetheless, the best way to leverage the power of the QAOA remains an open question. Here we propose a general model that describes a class of QAOA variants and use it to explore routes to quantum advantages in a canonical optimization problem, MaxCut. For these algorithms we derive analytic expectation values of the cost Hamiltonian for the MaxCut problem in the level-1 case. Using these analytic results we obtain reliable averages over many instances for fairly large numbers of qubits. We find that the warm start adaptive-bias QAOA (WS-ab-QAOA) initialized by the GW algorithm outperforms previously proposed warm start variants on problems with 40 to 180 qubits. To assess whether a quantum advantage exists with this algorithm, we did numerical simulations with up to 1000 qubits to see whether the level-1 WS-ab-QAOA can improve the GW solution for three-regular graphs. In fact the improvement in the 1000-qubit case even in level 1 can only be matched by the GW algorithm after about ${10}^{5.5}$ random projections performed after the semidefinite program stage. Thus this work gives numerical evidence that the final stage of optimization after an efficient classical algorithm has produced an approximate solution may be a place where quantum advantages can be realized.

Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges in modern science. Boson sampling seems to be a very promising platform in this regard, but to be confident of attaining the advantage regime, one must provide evidence of operating with the correct boson sampling distribution, and not with any of the distributions that admit efficient classical simulation. This problem is often called the validation problem, and it poses a major challenge to demonstrating unambiguous quantum advantage. In this work, using the recently proposed wave-function network approach, we study the sample space filling behavior with increasing the number of collected samples. We show that this allows for black-box data to exclude several undesired hypotheses, especially the distinguishable particles sampling. At this point, reference values corresponding to the true distribution are still required for the presented approach to be considered a complete validation protocol. Nevertheless, we show that it can instead be used for simple and efficient validation against a trusted sampling device. We also study the scaling of our approach with system size and under imperfections such as losses. These results highlight the potential of sample space filling analysis for addressing the validation problem.

We explore the feasibility of gate-based hybrid quantum computing using both discrete (qubit) and continuous (qumode) variables on trapped-ion platforms. Trapped-ion systems have demonstrated record one- and two-qubit gate fidelities and long qubit coherence times, while qumodes, which can be represented by the collective vibrational modes of the ion chain, have remained relatively unexplored for their use in computing. Using numerical simulations, we show that high-fidelity hybrid gates and measurement operations can be achieved for existing trapped-ion quantum platforms. As an exemplary application, we consider quantum simulations of the Jaynes-Cummings-Hubbard model, which is given by a one-dimensional chain of interacting spin and boson degrees of freedom. Using classical simulations, we study its real-time evolution and develop a suitable variational quantum algorithm for ground-state preparation. Our results should motivate further studies of hybrid quantum computing in this context, which may lead to direct applications in condensed-matter and fundamental particle and nuclear physics.

We use saturated absorption spectroscopy to study neutral ${}^9\mathrm{Be}$ atoms produced in a dc discharge lamp. Previous measurements of the $2s2p{}^{1}P^o$ state energy were limited in precision due to overlapping hyperfine structure. In this work, we apply a 400 G magnetic field, which splits the magnetic sublevels creating a spectral feature near the center-of-gravity energy of the state. We determine the transition frequency from the ground state to be $1276080105.5\left(1.2\right)\mathrm{MHz}$, corresponding to a center-of-gravity energy of $42565.45058\left(4\right){\text{cm}}^{-1}$. This result is a factor of 30 more precise than the previous best measurement and constitutes the most precise determination of an excited-state energy in a four-electron system to date. As theoretical methods advance, this result will enable stringent tests of quantum electrodynamics in four-electron systems.

The reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method is a leading technique for time-resolved investigation of photoionization processes. Interpretation of RABBITT spectra is limited to a lowest-order description, while new variants of the technique necessitate higher intensity infrared fields where this description breaks down. Here, we present an extension of RABBITT theory which can account for higher-order processes (RABBITT-HOP), and demonstrate RABBITT-HOP's ability to predict and describe higher-order processes through ab initio simulation of a RABBITT experiment targeting the high-lying $1snp$ Rydberg series of helium. We demonstrate that the signature line shape imparted by the resonances in the $2\omega$ phase of the lowest sideband can also be observed in the $2\omega$ phase of the next mainband, as well as in the $4\omega$ phases of the next sideband and mainband—each with additional phase shifts predicted under RABBITT-HOP. Repeating this analysis for a range of infrared intensities, we determine the lower limits of intensities required for these higher-order processes to become observable and upper limits beyond which nonperturbative effects begin to dominate. This new theoretical framework forms a much-needed basis for accurate interpretation of RABBITT spectra in experiments involving more intense fields, and paves the way for the development of new RABBITT-like techniques which take advantage of this new understanding of how atomic resonance effects may be propagated beyond their nearest sideband.

Recently, a local and imperfect chirality of the resonant eigenmode at the exceptional point (EP) has been reported in the optical whispering gallery microcavity system perturbed by two strong nanoscatterers [Phys. Rev. A 108, L041501 (2023)]. Here we discover a local perfect chirality of the resonant eigenmode away from the EP in the parameter space of the strongly perturbed microcavity system. By considering the multiple scattering process of the azimuthally propagating modes (APMs) at the nanoscatterers with a first-principles-based model, the local perfect chirality is predicted to result from the unidirectional reflectionlessness, i.e., the reflection-zero ($R$-zero) of the APMs at the two nanoscatterers. Numerical results and model predictions consistently show that the structural parameters of the $R$-zero typically deviate from those of the EP, which means that the pair of split resonant eigenmodes at the $R$-zero have different complex resonance frequencies and electromagnetic fields. In general, only one of the pair of split eigenmodes exhibits a local perfect chirality within the local azimuthal range divided by the two nanoscatterers. With the decrease of the two nanoscatterers' sizes or their relative azimuthal angle, the $R$-zero tends to coincide with the EP.

We propose powering a quantum clock with the nonthermal resources offered by the stationary state of an integrable quantum spin chain, driven out of equilibrium by a sudden quench. We describe the dynamics of the clock as a “biased random walk.” The bias level is directly related to the negativity of the steady-state response function. Using experimentally relevant examples of quantum spin chains, we suggest that crossing a phase transition point is crucial for the clock's operation. The coupling takes place through a global observable and, in this case, the battery lifespan is found to be extensive in its size.

Quantum network nonlocality plays a crucial role in long-distance quantum communication, and nonlocality sharing via sequential measurements provides a novel perspective for large-scale quantum network applications. In this paper, we investigate network nonlocality sharing in the two-forked tree-shaped network. For the two-input $n$-layer $(n\ge 2)$ scenario, the number of sequential observers in existing schemes is constrained by the layer $n$ and the number of sequential sides. Here we achieve unbounded sharing of network nonlocality for arbitrary $n$ by introducing sharpness parameters into Bell state measurements and allowing sequential observers to perform measurements with different sharpness parameters. An unbounded number of independent observers on each of the $m(m=1,\cdots ,2^{n-2})$ sequential sides can simultaneously share non-$(2^n-2)$-locality by violating the two-input $(2^n-2)$-local inequality with all other nonsequential observers. Furthermore, we extend the two-input scenario to a generalized $d$-input $(d\ge 2)$ case, investigating how the input number $d$ affects network nonlocality sharing. A general model for sequential measurement scenarios in $d$-input two-forked $n$-layer tree-shaped networks is established. Using the simplest case $(n=3)$ as an example, we investigate non-six-locality sharing based on the $d$-input six-local inequality and establish the relationship between the number of sequential observers, the number of sequential sides, and the input $d$. Based on the results, we conjecture that the two-input configuration is optimal for nonlocality sharing in two-forked tree-shaped networks.

The fermionic partial transpose introduced by Shapourian et al. [Phys. Rev. B 95, 165101 (2017)] has received widespread attention. A fundamental application of the partial transpose lies in the construction of entanglement witnesses. However, it is a notable characteristic that the fermionic partial transpose does not preserve Hermiticity. Instead, the fermionic partial transpose of a fermionic state yields a pseudo-Hermitian operator with respect to the local parity operators. This suggests that the suitable version of entanglement witness criterion for fermions is pseudo-Hermitian. Inspired by this, we systematically investigate whether the pseudo-Hermitian operators with respect to the local parity operators can serve as valid entanglement witnesses for fermions. These contents encompass completeness, comparison, intersection, and optimal conditions. Our answer is positive. We have provided some reasons why such pseudo-Hermitian operators are more suitable as entanglement witnesses than the Hermitian ones. As a byproduct, we observe that pseudo-Hermitian witnesses can reveal more information about entanglement contained in fermionic states.

The inherent limitations of physical processes prevent the copying of arbitrary quantum states. Furthermore, even if we only aim to clone two distinct quantum states, it remains impossible unless they are mutually orthogonal. To overcome this limitation, we propose a virtual-cloning protocol that bypasses the restrictions imposed by the quantum no-cloning theorem. Specifically, we begin by outlining the general framework for virtual cloning and deriving a necessary and sufficient criterion for the existence of a virtual operation capable of simultaneously cloning a set of states. Subsequently, through an analysis of the simulation cost of the virtual-cloning process, we demonstrate that the problem of identifying an optimal virtual-cloning protocol can be cast as a semidefinite programming problem. Finally, we establish a connection between virtual cloning and state discrimination, from which universal bounds on the optimal cloning cost are derived.

We consider entanglement-assisted private communication over a classical-quantum multiple-access channel with two senders and a single receiver. We initially determine the capacity region where senders and receiver share unlimited entanglement resources. In this setting, each sender performs an encoding measurement on their share of the entangled state to transmit a measurement outcome via the classical-quantum multiple-access channel. Meanwhile, the receiver applies a decoding operation to both the channel's output state and their share of the entangled state. We further derive the private capacity. Moreover, we consider the capacity region and private capacity when entanglement is shared between only the two senders. This corresponds to a quantum extension of the classical multiple-access channel with entanglement. Significantly, we show that the capacity region when both senders share entanglement with the receiver is strictly larger than when only the two senders share the entanglement.

We have studied the ionization and fragmentation of ${\mathrm{SO}}_2$ molecular target in collision with a 1 MeV proton beam using the technique of recoil ion momentum spectroscopy. Two- and three-body fragmentation channels were observed in the Coulomb break-up of ${\mathrm{SO}}_2^{2+}$ molecular ions. Kinetic-energy-release distributions were measured and compared with the available experimental and theoretical data. Dissociation pathways for three-body fragmentation of a ${\mathrm{SO}}_2^{2+}$ ion resulting in (${\mathrm{S}}^{+}+{\mathrm{O}}^{+}$ $+$ O) and (S $+$ ${\mathrm{O}}^{+}+{\mathrm{O}}^{+}$) were studied in detail using Dalitz plots and Newton diagrams. We also obtained the three-dimensional momentum distribution of all fragment particles, including the neutral atom. Correlated angular distributions of the particle momenta were used to infer the geometry of the molecular ion during the fragmentation process.

An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, $E^0/N_v\lesssim -4$, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent $z$ in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for $E^0/N_v\gtrsim -4$, to a value which depends explicitly on the initial conditions for $E^0/N_v\lesssim -5$.