It is shown that the claim that the velocity of the electron never exceeds the speed of light is invalid. The velocity of the energy flow, as defined by the author, becomes even infinite at some points. We also show that the proof of the nonexistence of the lower limit on the size of the electron wave function can be obtained from simple dimensional arguments.

We propose a complete architecture for deterministic generation of entangled multiphoton states. Our approach utilizes periodic driving of a quantum-dot emitter and an efficient light-matter interface enabled by a photonic crystal waveguide. We assess the quality of the photonic states produced from a real system by including all intrinsic experimental imperfections. Importantly, the protocol is robust against the nuclear spin bath dynamics due to a naturally built-in refocusing method reminiscent to spin echo. We demonstrate the feasibility of producing Greenberger-Horne-Zeilinger and one-dimensional cluster states with fidelities and generation rates exceeding those achieved with conventional “fusion” methods in current state-of-the-art experiments. The proposed hardware constitutes a scalable and resource-efficient approach towards implementation of measurement-based quantum computing and quantum communication.

We theoretically study dynamical formation of a quantum droplet in a two-component Bose-Hubbard system with an external trap potential. Specifically, the superfluid in the central region surrounded by the Mott insulator with double filling forms a quantum droplet, which is self-bound thanks to the discontinuous nature of the quantum phase transition between the two phases. We show how to induce the characteristic behavior of the droplet through the control of the trap potential by using the time-dependent Gutzwiller simulations in a two-dimensional system. The static and dynamical properties of the droplet can be described qualitatively by the effective Ginzburg-Landau field theory with cubic-quintic nonlinearities where the attractive cubic nonlinearity emerges, although all the bare interparticle interactions are repulsive.

We study theoretically and numerically the optical analogs of the relativistic quantum electron-positron dynamic pair production (PP) and annihilation processes in a single binary waveguide array (BWA) consisting of a curved section located between two straight sections at the input and output. Both of these processes can be mimicked by the breakup of beams in the curved section, which plays the role of the external oscillating field. Thanks to our scheme, we are able to observe not only the PP, but also annihilation in a single BWA with a single input beam. Moreover, this scheme allows us to obtain the numerical results for PP and annihilation probabilities by directly simulating beam propagation in binary waveguide arrays, and then compare them to the theoretical results for the same discrete model. This kind of verification demonstrates the striking excellent agreement between them in wide ranges of all relevant parameters. We also show that under certain conditions the probabilities of these two processes based on the discrete model with binary waveguide arrays agree quite well with those based on the truly continuous Dirac equation in quantum field theory.

We consider computer-generated configurations of quantized vortices in planar superfluid Bose-Einstein condensates. We show that unsupervised machine-learning technology can successfully be used for classifying such vortex configurations to identify prominent vortex phases of matter. The machine-learning approach could thus be applied for automatically classifying large data sets of vortex configurations obtainable by experiments on two-dimensional quantum turbulence.

Particle beam scattering is a conventional technique for detecting the nature of matter. We studied the scattering problem of a cluster connected to multiple leads. We established the connection between the eigenstate of the topological scattering center and the transmission and reflection amplitudes for the resonant scattering process. We discovered that, as an application, this approach enables the detection of the edge state in the band gap for both Hermitian and non-Hermitian systems and the identification of the topology of a system. We investigated two types of Su-Schrieffer-Heeger chains as examples. In addition, we proposed a dynamic scheme through an evanescently coupled-waveguide array to detect the edge state on the basis of measured transmission intensity. Numerical simulation revealed that pattern visibility can be the signature of the edge states.

Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time-driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical nonadiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

The Leggett-Garg (LG) inequalities were introduced to test for the possible presence of macroscopic quantum coherence. Since such effects may be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and also to more general bound systems, using a single dichotomic variable $Q$ given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely, energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the LG inequalities at two, three, and four times can each be independently violated or satisfied. We also find that the violations persist, although are reduced, when the sign function defining $Q$ is smeared to reflect experimental imprecision. For higher-energy eigenstates, we find that LG violations diminish, showing the expected classicalization. With a $Q$ defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state. We also show that two-time LG violations in a Gaussian state are readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the approach, we repeat much of the LG analysis for the Morse potential, finding qualitatively similar physical results.

Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter, and nuclear physics. We propose an algorithm to implement imaginary time propagation on a quantum computer. Our algorithm is devised in the context of an efficient encoding into an optimized gate, drawing on the underlying characteristics of the quantum device of a unitary operation in an extended Hilbert space. However, we prove that for simple problems it can also be successfully applied to standard digital quantum machines. This work paves the way for porting quantum many-body methods based on imaginary-time propagation to near-term quantum devices, enabling the future quantum simulation of the ground states of a broad class of microscopic systems.

Noisy intermediate-scale quantum algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and $W$ states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this preknowledge, some errors can be detected during the evolution of the circuit, by filtering the states not obeying the pattern through postselection. In this paper, we present mid-circuit postselection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the quantum alternating operator ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and resetting are possible, but classical conditional operators are not.

Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In this quantum setting, it is essential to conceal the CSI measurement as well. A regularized formula is derived for the masking equivocation region, and a full characterization is established for a class of measurement channels.

We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued measure, and consider its limiting case when it can be used to construct a projection operator that collapses the state to a total spin projection state. We then analyze how a stroboscopic sequence of such projections made in the $x$ and $z$ basis evolves the initial wave function. Such a sequence of QND projections can enhance the entanglement between the atomic ensembles and makes the state converge towards a highly entangled state. We show several mathematical identities which greatly simplify the state evolution in the projection sequence and allow one to derive the exact state in a highly efficient manner. Our formalism does not use the Holstein-Primakoff approximation as is conventionally done, and treats the spins of the atomic gases in an exact way.

Optomechanical systems open new possibilities in fundamental research at the interface between quantum information and gravity. Recently, an ambitious experimental proposal was suggested by Bose et al. [S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim, and G. Milburn, Phys. Rev. Lett. 119, 240401 (2017)] to measure the entanglement between two optomechanical systems generated by their gravitational interaction. The scheme relied on witnessing entanglement between the two systems. Here we develop a general framework to study the quality of bipartite entanglement witnesses using fidelity witnesses. We then apply this framework to the gravitational entanglement proposal, optimizing for the detection of entanglement. We construct a witness consisting of only five nontrivial spin measurements, which we compare with other proposed witnesses. With postprocessing our witness can detect entanglement for any choice of phases in the setup, up to a set of measure zero, for a closed system. We also explore the effects of a simple dephasing channel on this witness.

The electric-field distribution in a single mode of a $\lambda /4$ superconducting coplanar waveguide (CPW) microwave resonator has been probed using beams of helium Rydberg atoms. In the experiments the atoms were prepared in the $1\mathrm{s}55\mathrm{s}{}^3{\mathrm{S}}_1$ Rydberg level by laser photoexcitation. They then traveled over the CPW resonator that was fabricated on a NbN superconducting chip operated at 3.8 K. The resonator was driven at its third-harmonic frequency, near resonant with the two-photon $1\mathrm{s}55\mathrm{s}{}^3{\mathrm{S}}_1\to 1\mathrm{s}56\mathrm{s}{}^3{\mathrm{S}}_1$ transition at ${\omega }_{55\mathrm{s},56\mathrm{s}}/2=2\pi \times 19.556499$ GHz. The coherence times of the atom–resonator-field interaction were determined at selected locations above the resonator by time-domain measurements of Rabi oscillations and found to be up to $0.8\mu \mathrm{s}$ for Rabi frequencies of $\sim 2\pi \times 3$ MHz. The coherence times of the atomic superposition states, generated following the interaction of the atoms with the microwave field in the resonator, were inferred from high-resolution cavity-enhanced Ramsey spectra to be $\sim 2.5\mu \mathrm{s}$. These Ramsey spectra also allowed the measurement of residual uncanceled dc electric fields of $26.6\pm 0.6$ mV/cm at the position of the atoms $\sim 300\mu \mathrm{m}$ above the surface of the superconducting chip. These results represent an essential step toward applications of hybrid systems, comprising Rydberg atoms coherently coupled to superconducting microwave circuits, in quantum optics and quantum information processing.

We consider an ensemble of atoms with $\mathrm{\Lambda }$-type level structure trapped in a single-mode cavity, and propose a geometric scheme of coherent manipulation of quantum states on the subspace of zero-energy states within the quantum Zeno subspace of the system. We find that the particular subspace inherits the decoherence-free nature of the quantum Zeno subspace and features a symmetry-protected degeneracy, fulfilling all the conditions for a universal scheme of arbitrary unitary operations on it.

We show that the average power output of a quantum battery based on a quantum interacting spin model, charged via a local magnetic field, can be enhanced with the increase of spin quantum number, thereby exhibiting dimensional advantage in quantum batteries. In particular, we demonstrate such increment in the power output when the initial state of the battery is prepared as the ground or canonical equilibrium state of the spin-$jXY$ model and the bilinear-biquadratic spin-$j$ Heisenberg chain (BBH) in presence of the transverse magnetic field and a weak value of interaction strength between the spins in the former model. Interestingly, we observe that in the case of the $XY$ model, a tradeoff relation exists between the range of interactions in which the power increases and the dimension, while for the BBH model, the improvements depend on the phase in which the initial state is prepared. Moreover, we exhibit that such dimensional advantages persist even when the battery Hamiltonian has some defects or when the initial battery state is prepared at finite temperature.

Benzene, a hexagonal molecule with formula ${\mathrm{C}}_6{\mathrm{H}}_6$, is one of the most important aromatic hydrocarbons. Its structure arises from the $s{p}^2$ hybridization from which three in-plane $\sigma$ bonds are formed. A fourth $\pi$ orbital perpendicular to the molecular plane combines with those arising from other carbon atoms to form $\pi$ bonds, very important to describe the electronic properties of benzene. Here this $\pi$ system is emulated with elastic waves. The design and characterization of an artificial mechanical benzene molecule, composed of six resonators connected through finite phononic crystals, are reported. The latter structures trap the vibrations in the resonators and couple them through evanescent waves to neighboring resonators, establishing a tight-binding regime for elastic waves. Our results show the appearance of a spectrum and wave amplitudes reminiscent of that of benzene. Finite element simulations and experimental data show excellent agreement with the Hückel model for benzene.

Temperature-dependent corrections to energy levels, including relativistic effects, for the positronium atom are discussed. The theoretical description of the thermal environment impact on atomic characteristics is carried out within the framework of rigorous relativistic quantum electrodynamics. As a result, the finite temperature corrections to the fine and hyperfine structure of positronium levels are evaluated. In addition, the annihilation rates of a positronium atom placed in an equilibrium thermal environment (blackbody radiation field) are studied. The numerical results are discussed throughout the paper in view of modern experiments.

Imaging surfaces using low-energy neutral atom scattering is a relatively recent development in the field of microscopy. In this paper, we demonstrate that this technique is sensitive enough to distinguish films as thin as a single monolayer from the underlying substrate. Using collimated beams of He and Kr atoms as an incident probe on ${\mathrm{MoS}}_2$ films grown on ${\mathrm{SiO}}_2/\mathrm{Si}$ substrates, we observe systematic changes in the scattered atom flux which allows us to map the thin ${\mathrm{MoS}}_2$ films. Measurements carried out by varying incidence energy using both He and Kr provides insights into the details of atom-surface collision dynamics and its role in contrast generation.

This work introduces and validates a model that explains an observed upper limitation of the emission of below-threshold harmonics generated by noble gases bound electrons in a restricted region of space. The model uses fundamental parameters from the gases and the laser beam, and correctly predicts an intensity threshold above which the harmonics yield cannot be increased by raising the laser power. This restraint is a consequence from the depletion of electrons due to laser-induced ionization, which exactly compensates the harmonics yield increase with the excitation power.