A multiphoton collective phase is a multiphoton-scattering feature that cannot be reduced to a sequence of two-photon scattering events, and the three-photon “triad phase” is the smallest nontrivial example. Observing a higher-order collective phase is experimentally challenging, and only triad and four-photon tetrad collective phases have been observed. We introduce a scheme to make higher-order multiphoton collective-phase observations feasible by designing a sparse interferometer, which significantly reduces complexity compared with the current best scheme for observing a multiphoton collective phase. Specifically, our scheme reduces the optical depth from logarithmic to constant and reduces the number of beam splitters from $O(nlogn)$ to linear scaling with respect to the collective-phase order $n$. As constant depth reduces loss and dispersion to a fixed rate regardless of collective-phase order, a major obstacle to observing large-scale collective phases is removed.

When a ferromagnet is placed in contact with a superconductor owing to incompatible spin order, the Cooper pairs from the superconductor cannot survive more than 1 or 2 nm inside the ferromagnet. This is confirmed in the measurements of ferromagnetic nickel (Ni) nanowires contacted by superconducting niobium (Nb) leads. However, when a 3 nm thick copper oxide (CuO) buffer layer made by exposing an evaporated or a sputtered 3 nm Cu film to air is inserted between the Nb electrodes and the Ni wire, the spatial extent of the superconducting proximity range is dramatically increased from 2 to a few tens of nanometers. A scanning transmission electron microscope study confirms the formation of a 3 nm thick CuO layer when an evaporated Cu film is exposed to air. Magnetization measurements of such a 3 nm CuO film on a ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate and on $\mathrm{Nb}/\mathrm{Si}{\mathrm{O}}_2/\mathrm{Si}$ show clear evidence of ferromagnetism. One way to understand the long-range proximity effect in the Ni nanowire is that the CuO buffer layer with ferromagnetism facilitates the conversion of singlet superconductivity in Nb into triplet supercurrent along the Ni nanowires.

Biphotons, generated from a hot atomic vapor via the process of spontaneous four-wave mixing (SFWM), have the following merits: Stable and tunable frequencies as well as linewidth. Such merits are very useful in the application of long-distance quantum communication. However, the hot-atom SFWM biphoton sources previously had far lower values of generation rate per linewidth, i.e., spectral brightness, as compared with the sources of biphotons generated by the spontaneous parametric down-conversion process. Here we report a hot-atom SFWM source of biphotons with a linewidth of 960 kHz and a generation rate of $3.7\times {10}^5$ pairs/s. The high generation rate, together with the narrow linewidth, results in a spectral brightness of $3.8\times {10}^5$ pairs/s/MHz, which is 17 times the previous best result with atomic vapors and also better than all known results with all kinds of media. The all-co-propagating scheme together with a large optical depth (OD) of the atomic vapor is the key improvement, enabling the achieved spectral brightness to be about one quarter of the ultimate limit. Furthermore, this biphoton source had a signal-to-background ratio (SBR) of 2.7, which violated the Cauchy-Schwartz inequality for classical light by about 3.6-fold. Although an increasing spectral brightness usually leads to a decreasing SBR, our systematic study indicates that both of the present spectral brightness and SBR can be enhanced by further increasing the OD. This work demonstrates a significant advancement and provides useful knowledge in quantum technology using photons.

Friction-driven static electrification is familiar and fundamental in daily life, industry, and technology, but its basics have long been unknown and have continually perplexed scientists from ancient Greece to the modern high-tech era. Despite its simple manifestation, triboelectric charging is believed to be very complex because of the unresolvable interfacial interaction between two rubbing materials. Here, we reveal a simple physics of triboelectric charging and triboelectric series based on friction-originated thermoelectric charging effects at the interface, characterized by the material density ($\rho$), specific heat ($c$), thermal conductivity ($k$), and Seebeck coefficient ($S$) of each material. We demonstrate that energy dissipational heat at the interface induces temperature variations in the materials and thus develops electrostatic potentials that will initiate thermoelectric charging across the interface. We find that the trends and quantities of triboelectric charging for various polymers, metals, semiconductors, and even lightning clouds are simply governed by the triboelectric factor $\xi =S/\sqrt{\rho ck}$. The triboelectric figure of merit is expressed with the triboelectric power $K=\xi \sqrt{t/\pi },$ of which the difference can be maximized up to $1.2\mathrm{V}/\mathrm{W}·\mathrm{c}{\mathrm{m}}^{–2}$ at the friction time $t=$ 1 s. Our findings will bring significant opportunities for microscopic understanding and management of triboelectricity or static electrification.

Exceptional points (EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the asymptotic dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudochiral symmetry enforces $n\mathrm{th}$ order EPs to disperse with the $(n-1)\mathrm{th}$ root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their asymptotic dispersion relations.

We consider the effect of periodic conditional no-click measurements on a quantum system. What is the final state of such a driven system? When the system has some symmetry built into it, the final state is a dark state provided that the initial state overlaps with this nondetectable fragment of the Hilbert space. We find two classes of such states: generic dark states that are found also for nonperiodic measurements, and Floquet dark states that are directly controlled by the periodicity of the measurements and which do not rely on the underlying symmetry of the Hamiltonian. A different behavior is found in the absence of dark manifolds, where for specific periodicities of the measurements we find nontrivial oscillatory dynamics, controlled by the measurement rate. Finally, when the control parameters are tuned, the eigenvalues of the survival operator coalesce to zero, and then one finds exceptional points with a large degeneracy. The physical meaning of this special type of degeneracy is that the null measurement process becomes impossible, implying that detecting the state is guaranteed. We analyze these effects with a nonperturbative method based on a classical charge picture.

In many approximate approaches to fermionic quantum many-body systems, such as Hartree-Fock and density functional theory, solving a system of noninteracting fermions coupled to some effective potential is the computational bottleneck. In this paper, we demonstrate that this crucial computational step can be accelerated using recently developed methods for Gaussian fermionic matrix product states (GFMPS). As an example, we study the generalized Hartree-Fock method, which unifies Hartree-Fock and self-consistent BCS theory, applied to Hubbard models with an inhomogeneous potential. We demonstrate that for quasi-one-dimensional systems with local interactions, our approach scales approximately linearly in the length of the system while yielding a similar accuracy to standard approaches that scale cubically in the system size.

Topological superconductivity has attracted intensive interest for its ability to host the Majorana zero mode and its implementation in topological quantum computations. Based on first-principles calculations and the analysis of the effective Bogoliubov–de Gennes Hamiltonian, we demonstrate that $1T\text{−}\mathrm{Ti}{\mathrm{Te}}_2$ is a topological metal hosting topological surface states near the Fermi level, and it exhibits a normal-topological-normal superconducting phase transition as a function of the chemical potential. These results point to a new promising topological superconductor. Furthermore, our calculations also suggest that the transition metal intercalated $\mathrm{Ti}{\left({\mathrm{Se}}_{1-y}{\mathrm{Te}}_y\right)}_2$ is also a highly possible route to realize topological superconductivity and Majorana zero modes.

We introduce the quantum Gaussian process state, motivated via a statistical inference for the wave function supported by a data set of unentangled product states. We show that this condenses down to a compact and expressive parametric form, with a variational flexibility shown to be competitive or surpassing established alternatives. The connections of the state to its roots as a Bayesian inference machine as well as matrix product states, also allow for efficient deterministic training of global states from small training data with enhanced generalization, including on application to frustrated spin physics.

Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve intensity correlations between multiple detectors and may have the advantage over the traditional second-order interference effect exhibited in only one detector. We discuss various scenarios with unbalanced delays in different paths in fourth-order interference exhibited in coincidence between two detectors. We find, in some cases, interference effect persists even when the delays are much larger than the coherence time of the sources. We also extend the discussion to nonstationary pulsed fields, which need to consider the pulse shape and require a different treatment. These results will be useful in remote sensing applications.

This paper studies the interaction of laser-driven $\gamma$ photons and high-energy charged particles with high-Z targets through Monte Carlo simulations. The interacting particles are taken from particle-in-cell simulations of the interaction of a tightly focused ultra-intense laser pulse with a titanium target. Lead is chosen as the secondary high-Z target because of its high cross-section of the giant dipole resonance and electron-positron pair production. The results reveal an ultra-short, ultra-relativistic collimated positron population and their energy spectra, angular distribution, and temporal profile are found. We investigate the target thickness dependence of the resulting total numbers and total kinetic energies of various particle species emitted from the lead target irradiated with laser-generated $\gamma$ photons and charged particles separately. We plot the charts of residual high-Z nuclides generated by irradiation of the lead target. Because of the short pulse duration, the $\gamma$ photon, electron-positron, and neutron sources could find applications in material science, nuclear physics, laboratory astrophysics, and as injectors in laser-based accelerators of charged particles.

We investigate the in-field critical current density $J_{\text{c}}\left(B\right)$ of superconducting-normal-superconducting (SNS) Josephson junctions (JJs) and polycrystalline superconducting systems with grain boundaries modeled as Josephson-type planar defects, both analytically and through computational time-dependent Ginzburg-Landau (TDGL) simulations in two and three dimensions. For very narrow SNS JJs, we derive analytic expressions for $J_{\text{c}}\left(B\right)$ that are high-field solutions for $J_{\text{c}}\left(B\right)$ for JJs across the entire applied field range up to the effective upper critical field $B_{\text{c2}}^{*}$. They generalize the well-known (low-field) exponential junction thickness dependence for $J_{\text{c}}$ from de Gennes, often used in the Josephson relation. We then extend our analytic expressions to describe wider junctions using physical arguments, and we confirm their agreement with TDGL simulations. These results are then compared with the current densities found in superconductors optimized for high-field applications. They provide an explanation for the Kramer field dependence and inverse power-law grain size dependence widely found in many low-temperature superconductors, and the power-law field dependence $J_{\text{c}}\left(B\right)\sim B^{-0.6}$ found at intermediate fields in some high-temperature superconductors including powder-in-tube ${\text{Bi}}_2{\text{Sr}}_2{\text{Ca}}_2{\text{Cu}}_3{\text{O}}_x$ and $R{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_7$ tapes ($R=\text{rare}\text{earth}$). By reanalyzing critical current density data using the mathematical framework derived here and confirmed using TDGL, we enable an analysis of $J_{\text{c}}$ data that provides the local properties of grain boundaries in high-field superconductors and hence a deeper understanding of how grain boundaries influence $J_{\text{c}}$ in high magnetic fields.

The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid (QSL) with Majorana excitations, Chern number $\pm 4$ and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral QSL, an orbital magnetic-field effect and spin-orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. A large quantized low-temperature thermal Hall effect can be induced in our model of Mott insulating cuprates by the orbital effect of an applied magnetic field.

Open quantum and wave systems exhibit exotic degeneracies at exceptional points in parameter space that have attracted considerable attention in various fields of physics, including optics and photonics. One reason is the strong response of open systems at such degeneracies to external perturbations and excitations. We introduce two characteristics of exceptional points that quantify the response in terms of energy eigenvalues and eigenstates, intensity, and dynamics. The concept is verified for several physically relevant examples. This work provides a new perspective on the physics of exceptional points.

The geometric interpretation of (pseudo)spin-$1/2$ systems on the Bloch sphere has been appreciated across different areas ranging from condensed matter to quantum information and high-energy physics. Although similar notions for larger Hilbert spaces are established in mathematics, they have been so far less explored beyond the two-level case for practical usage in condensed matter settings, or have involved restrictions to sub manifolds within the full Hilbert space. We here employ a coherence vector description to theoretically characterize a general $N$-level system on the higher dimensional generalized Bloch (hyper)sphere by respecting the structure of the underlying $\mathrm{SU}\left(N\right)$ algebra and construct physically intuitive geometric pictures for topological concepts. Focusing on two spatial dimensions, we reveal a geometric interpretation for the Chern number in larger Hilbert spaces in terms of a nested structure comprising $N-1$ two-spheres. We demonstrate that for the $N$-level case, there is an exterior two-sphere that provides a useful characterization of the system, notably by playing a primary role in determining the Chern number. The external sphere can be directly measured in ultracold atoms via well-established band mapping techniques, thereby imparting knowledge of the topological nature of state. We also investigate how the time evolution of the coherence vector defined on the generalized Bloch hypersphere can be utilized to extract the full state vector in experiments, allowing us to develop a tomography scheme involving quenches for three-level systems. Our geometric description opens up another avenue for the interpretation of the topological classification and the dynamical illustration of multilevel systems, which in turn is anticipated to help in the design of new experimental probes.

In thermodynamically characterizing a mixture comprising a finite number of molecules, we consider two kinds of protocol for producing a mixture from a pure substance. The first is a single alchemical operation, whereas the second is a series of processes with feedback control in information thermodynamics and conventional mixing with semipermeable membranes. A comparison of the two numerically determined free-energy changes provides a combinatorial factor that indicates the indistinguishability of the molecules and an alternative Jarzynski equality. The comparison also uncovers a work relation for determining the mixing free energy without using semipermeable membranes. We demonstrate a numerical calculation of applying the work relation to a mixture of argon and krypton. The mixing free energy clearly shows the characteristics of liquid–vapor transition.

This paper considers physical systems described by hidden states and indirectly observed through repeated measurements corrupted by unmodeled nuisance parameters. A network-based representation learns to disentangle the coherent information (relative to the state) from the incoherent nuisance information (relative to the sensing). Instead of physical models, the representation uses symmetry and stochastic regularization to inform an autoencoder architecture called SymAE. It enables redatuming, i.e., creating virtual data instances where the nuisances are uniformized across measurements.