Doped strontium titanate ${\mathrm{SrTiO}}_3$ (STO) is one of the most dilute superconductors known today. The fact that superconductivity occurs at very low carrier concentrations is one of the two reasons that the pairing mechanism is not yet understood, the other being the role played by the proximity to a ferroelectric instability. In undoped STO, ferroelectric order can in fact be stabilized by substituting ${}^{16}\mathrm{O}$ with its heavier isotope ${}^{18}\mathrm{O}$. Here, we explore the superconducting properties of doped and isotope-substituted $\mathrm{SrTi}{{(}^{18}{\mathrm{O}}_y^{16}{\mathrm{O}}_{1-y})}_{3-\delta }$ for $0\le y\le 0.81$ and carrier concentrations between $6\times {10}^{17}$ and $2\times {10}^{20}{\mathrm{cm}}^{-3}$ ($\delta <0.02$). We show that the superconducting $T_c$ increases when the ${}^{18}\mathrm{O}$ concentration is increased. For carrier concentrations around $5\times {10}^{19}{\mathrm{cm}}^{-3}$ this $T_c$ increase amounts to almost a factor 3, with $T_c$ as high as 580 mK for $y=0.74$. When approaching $\mathrm{SrTi}{}^{18}\mathrm{O}_3$ the maximum $T_c$ occurs at much smaller carrier densities than for pure $\mathrm{SrTi}{}^{16}\mathrm{O}_3$. Our observations agree qualitatively with a scenario where superconducting pairing is mediated by fluctuations of the ferroelectric soft mode.

We present a quantum circuit with measurements and postselection that exhibits a panoply of space- and/or time-ordered phases from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are incommensurate with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently nonequilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.

X-ray free-electron lasers (XFELs), with pulse durations of a few tens of femtoseconds or shorter, are cutting-edge instruments capable of observing structure and dynamics at the atomic scale. Temporal diagnostics are challenging but of fundamental importance for XFEL performance and experiments. In this paper, we demonstrate a method to characterize on a single-shot basis the temporal profile of both the electron beam and the XFEL radiation with femtosecond resolution. The approach consists in streaking the electron beam after the undulator using the wakefields of a corrugated structure. Its merits are arrival time stability and cost-effectiveness. Our method allows access to self-synchronized femtosecond diagnostics to any XFEL facility at low cost.

In quantum mechanics, physical states are represented by rays in Hilbert space $\mathcal{H}$, which is a vector space imbued by an inner product $\langle |\rangle$, whose physical meaning arises as the overlap $\langle \varphi |\psi \rangle$ for $|\psi \rangle$ a pure state (description of preparation) and $\langle \varphi |$ a projective measurement. However, current quantum theory does not formally address the consequences of a changing inner product during the interval between preparation and measurement. We establish a theoretical framework for such a changing inner product, which we show is consistent with standard quantum mechanics. Furthermore, we show that this change is described by a quantum operation, which is tomographically observable, and we elucidate how our result is strongly related to the exploding topic of PT-symmetric quantum mechanics. We explain how to realize experimentally a changing inner product for a qubit in terms of a qutrit protocol with a unitary channel.

Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with their environments in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of the bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. We further discuss a simple scenario where the present theory fits better with the common intuition about system entropy and heat.

We present a paradigm in the field of cavity QED by bringing out remarkable features associated with the avoided crossing of the dressed-state levels of the Jaynes-Cummings model. We demonstrate how the parametric couplings, realized by a second order nonlinearity in the cavity, can turn the crossing of dressed states into avoided crossings. We show how one can generate coherence between the avoided crossing of dressed states. Such coherences result, for example, in quantum beats in the excitation probability of the qubit. The quality of quantum beats can be considerably improved by adiabatically turning on the parametric interaction. We show how these avoided crossings can be used to generate superpositions of even or odd Fock states with the remarkable property of equal weights for the states in superposition. The fidelity of generation is more than 95%. In addition, we show strong entanglement between the cavity field and the qubit with the concurrence parameter exceeding 90%.

In ultra- and deep-strong cavity quantum electrodynamics (QED) systems, many intriguing phenomena that do not conserve the excitation number are expected to occur. In this paper, we theoretically analyze the optical response of an ultrastrong cavity-QED system in which an atom is coupled to the first and third harmonic modes of a cavity, and report the possibility of deterministic three-photon down-conversion of itinerant photons upon reflection at the cavity. In the conventional parametric down-conversion, a strong input field is needed because of the smallness of the transition matrix elements of the higher-order processes. However, if we use an atom-cavity system in an unprecedentedly strong-coupling region, even a weak field in the linear-response regime is sufficient to cause this rare event involving the fourth-order transitions.

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore, a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desirable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics. We solve this system analytically in the long-wavelength limit for an arbitrary number of noninteracting electrons, and we demonstrate that the electron-photon ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic ${\mathbf{A}}^2$ term is omitted. Further, by performing linear response we show that the cavity field induces plasmon-polariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas. Last, we show how the matter-modified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the light-matter system. Several of the presented findings should be experimentally accessible.

We employ various quantum-mechanical approaches for studying the impact of electric fields on both nonretarded and retarded noncovalent interactions between atoms or molecules. To this end, we apply perturbative and nonperturbative methods within the frameworks of quantum mechanics as well as quantum electrodynamics. In addition, to provide a transparent physical picture of the different types of resulting interactions, we employ a stochastic electrodynamic approach based on the zero-point fluctuating field. Atomic response properties are described via harmonic Drude oscillators—an efficient model system that permits an analytical solution and has been convincingly shown to yield accurate results when modeling nonretarded intermolecular interactions. The obtained intermolecular energy contributions are classified as field-induced electrostatics, field-induced polarization, and dispersion interactions. The interplay between these three types of interactions enables the manipulation of molecular dimer conformations by applying transversal or longitudinal electric fields along the intermolecular axis. Our framework based on the combination of four different theoretical approaches paves the way toward a systematic description and improved understanding of molecular interactions when molecules are subject to both external and vacuum fields.

Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the logical Hadamard, phase $\left(Z^{1/2}\right)$, and $T$ $\left(Z^{1/4}\right)$ gates which are essential for building up arbitrary logical gates are not implemented natively without using state distillation or lattice dislocations, to the best of our knowledge. In particular, state distillation generally consumes many ancillary logical qubits; thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all logical Clifford gates generated by the cnot, Hadamard, and phase gates can be implemented natively in a fault-tolerant manner, although the $T$ gate still requires state distillation to be fault-tolerant. The error thresholds of MBQC via CCCSs for logical-$Z$ errors are calculated to be 2.7%–2.8%, which are comparable to the values for RTCSs, assuming a simple error model where physical qubits have nontrivial errors independently with the same probability. We analyze and compare the resource overheads of both the schemes. In particular, we show that the number of physical qubits required for implementing a phase gate with CCCSs is at least about 26 times smaller than with RTCSs using state distillation, for the same code distance.

The high-fidelity storage, distribution, and processing of quantum information prefers qubits with different physical properties. Thus hybrid quantum gates interfacing different types of qubits are essential for the realization of complex quantum network structures. A Rydberg-atom-based physical quantum controlled-Z (CZ) gate is proposed to hybridly process the polarization-encoded single-photon optical qubit and the “Schrödinger cat” microwave qubit. The degradation of the fidelity under the influence of various noise channels, such as microwave cavity loss, spontaneous emission of atom states, and nonadiabaticity effect, etc., has been analyzed through detailed theoretical analysis by deriving the input-output relation of qubit fields. The feasibility and the challenges of the protocol within current technology are also discussed by analyzing the possible experimental parameter settings. Our work opens prospects for future large-scale quantum architecture based on hybrid quantum modules.

Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on $m$-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.

In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints. This problem is central to quantitative finance. After a detailed introduction to the problem, we implement a number of quantum and quantum-inspired algorithms on different hardware platforms to solve its discrete formulation using real data from daily prices over 8 years of 52 assets, and do a detailed comparison of the obtained Sharpe ratios, profits, and computing times. In particular, we implement classical solvers (Gekko, exhaustive), D-wave hybrid quantum annealing, two different approaches based on variational quantum eigensolvers on IBM-Q (one of them brand-new and tailored to the problem), and for the first time in this context also a quantum-inspired optimizer based on tensor networks. In order to fit the data into each specific hardware platform, we also consider doing a preprocessing based on clustering of assets. From our comparison, we conclude that D-wave hybrid and tensor networks are able to handle the largest systems, where we do calculations up to 1272 fully-connected qubits for demonstrative purposes. Finally, we also discuss how to mathematically implement other possible real-life constraints, as well as several ideas to further improve the performance of the studied methods.

In this paper, we analytically and numerically study the sideband interaction dynamics of the driven quantum Rabi model (QRM). We focus in particular on the conditions when the external transverse drive fields induce first-order sideband interactions. Inducing sideband interactions between two different systems is an essential technique for various physical models, including the QRM. However, despite its importance, a precise analytical study has not been reported yet that successfully explains the sideband interaction rates in a driven QRM applicable for all system parameter configurations. In our paper, we analytically derive the sideband interaction rates based on second-order perturbation theory, not relying on the rotating wave approximation (RWA). Our formula are valid for all ranges of drive frequencies and system's parameters. Our analytical derived formula agrees well with the numerical results in a regime of moderate drive amplitudes. Interestingly, we have found a nontrivial longitudinal drive effect derived from the transverse drive Hamiltonian. This accounts for significant corrections to the sideband interaction rates that are expected without considering the derived longitudinal effect. Using this approach, one can precisely estimate the sideband interaction rates in the QRM not confining themselves within specific parameter regimes for moderate drive amplitudes. This provides important contributions for quantitatively understanding experiments described by the driven QRM.

Orthorhombic ${\mathrm{PbMnBO}}_4$ is a rare example of an insulating ferromagnet in which the magnetic properties, in particular the strong magnetic anisotropy, are determined by the ${\mathrm{Mn}}^{3+}$ Jahn-Teller ion. Here, we report on the detailed investigation of magnetic excitations in the subterahertz and terahertz frequency ranges, as well as lattice excitations in the terahertz range. Using polarized azimuthally resolved Raman spectroscopy, four branches of magnetic excitations were observed and assigned to one acoustic and three optical one-magnon modes. The coupling between ferromagnetic ordering at $T_C=31\mathrm{K}$ and the Jahn-Teller distortions of $\left[{\mathrm{MnO}}_6\right]$ octahedra due to the spin-phonon interaction was directly observed for some specific phonon modes involved in these distortions. A spin-wave Hamiltonian was developed that allowed us to determine a unique set of exchange and effective anisotropy parameters. The intensity ratio of the anti-Stokes to Stokes acoustic magnon peaks is found to be anomalous and directly indicates the involvement of the magneto-optical parameters in the magnetic Raman scattering process.

An important problem in quantum information is the practical demonstration of nonclassical long-range order on quantum computers. One of the best known examples of a quantum system with nonclassical long-range order is a superconductor. Here we achieve Cooper-like pairing of qubits on a quantum computer, which can be interpreted as superconducting or superfluid states via a Jordan-Wigner mapping. We rigorously confirm the quantum long-range order by measuring the large $O\left(N\right)$ eigenvalue of the two-electron reduced density matrix. The demonstration of maximal quantum long-range order is an important step toward more complex modeling of phenomena with significant quantum long-range order on quantum computers such as superconductivity and superfluidity.

We study dynamical quantum phase transitions (DQPTs) in the extended Bose-Hubbard model after a sudden quench of the nearest-neighbor interaction strength. Using the time-dependent density matrix renormalization group, we demonstrate that interaction-driven DQPTs can appear after quenches between two topologically trivial insulating phases—a phenomenon that has so far only been studied between gapped and gapless phases. These DQPTs occur when the interaction strength crosses a certain threshold value that does not coincide with the equilibrium phase boundaries, which is in contrast to quenches that involve a change of topology. In order to elucidate the nonequilibrium excitations during the time evolution, we define a new set of string and parity order parameters. We find a close connection between DQPTs and these newly defined order parameters for both types of quenches. In the interaction-driven case, the order parameter exhibits a singularity at the time of the DQPT only when the quench parameter is close to the threshold value. Finally, the timescales of DQPTs are scrutinized and different kinds of power laws are revealed for the topological and interaction-driven cases.

The semiclassical equations of motion are widely used to describe carrier transport in conducting materials. Nevertheless, the substantial challenge of incorporating disorder systematically into the semiclassical model persists, leading to quantitative inaccuracies and occasionally erroneous predictions for the expectation values of physical observables. To address this issue, in this paper we provide a general prescription for reformulating the semiclassical equations of motion for carriers in disordered conductors by taking the quantum mechanical density matrix as the starting point. We focus on the case when only external electric fields are present, without magnetic fields, and the disorder potential is spin independent. The density matrix approach allows averaging over impurity configurations, and the trace of the velocity operator with the disorder-averaged density matrix can be reinterpreted as the semiclassical velocity weighted by the Boltzmann distribution function. Through this rationale the well-known intrinsic group and anomalous velocities are trivially recovered, while we demonstrate the existence of an extrinsic velocity, namely, a disorder correction to the semiclassical velocity of Bloch electrons, mediated by the interband matrix elements of the Berry connection. A similar correction is present in the nonequilibrium expectation value of the spin operator, contributing to spin-orbit torques. To obtain agreement with diagrammatic approaches, the scattering term in the Boltzmann equation must be corrected to first order in the applied electric field, and the Boltzmann equation itself must be solved up to subleading order in the disorder potential. Our prescription ensures that all vertex corrections present in diagrammatic treatments are taken into account, and to illustrate this, we discuss model cases in topological insulators, including the anomalous Hall effect as well as spin-orbit torques.

A substantial energy gap of charge excitations induced by strong correlations is the characteristic feature of Mott insulators. We study how the Mott gap is affected by long-range antiferromagnetic order. Our key finding is that the Mott gap is increased by the magnetic ordering: A magnetic blue shift (MBS) occurs. Thus the effect is proportional to the exchange coupling in the leading order in the Hubbard model. In systems with additional localized spins the double-exchange mechanism induces an additional contribution to the MBS which is proportional to the hopping in the leading order. The coupling between spin and charge degrees of freedom bears the potential to enable spin-to-charge conversion in Mott systems on extreme time scales determined by hopping and exchange only, since a spin-orbit-mediated transfer of angular momentum is not involved in the process. In view of spintronic and magnonic applications, it is highly promising to observe that several entire classes of compounds show exchange and double-exchange effects. Exemplarily, we show that the magnetic contribution to the band-gap blue shift observed in the optical conductivity of $\alpha$-MnTe is correctly interpreted as the MBS of a Mott gap.