Low-frequency classical $1/f$ noise and quantum noise from low-temperature phonon modes are ubiquitous across various experimental platforms, and are usually considered a hindrance for quantum technological applications. Here we show that the simultaneous action of classical $1/f$ noise and a low-temperature phonon bath on a nonlinear oscillator can result in the generation of nonclassical antibunched radiation without the need for any additional drive. The $1/f$ noise itself provides the source of energy for generation of photons, while the phonon bath prevents heating up to infinite temperature and takes the nonlinear oscillator to a noise-averaged nonequilibrium steady state. The photon current in this nonequilibrium steady state may be detected by a standard wide-band detector. For sufficient nonlinearity and frequency dependence of the effective noise spectrum, the detected radiation can be antibunched. This opens the possibility to turn two of the most ubiquitous intrinsic noises in experimental platforms from a hindrance to a resource. It shows that wasteful heat from unavoidable noises can be converted into useful radiation. These results are based on the Redfield equation, which provides a rigorously derived general approach to treat any type of weak noise in a quantum system, specified only via the noise spectral function, as we discuss in detail.

The concept of coherent states of single photons is generalized to the scenario wherein the fundamental building blocks are entangled two-photon states rather than single-photon states. To provide a concrete discussion, the case of photonic dimers (two-photon bound states) is explored. The coherent states of photonic dimers are defined. The correlation functions are calculated and expressed in terms of series expansion which is suitable for computational investigations. The quadrature properties and the squeezing effects are computed and compared with the experimental results at suitable regimes. Finally, the statistical properties of the coherent states of photonic dimers in the BEC and BCS limits are investigated. The correlation functions are shown to exhibit a BEC-BCS crossover behavior when the two-photon pairing correlations (i.e., the size of photonic dimers) are comparable to the average spacing between the dimer pairs.

Non-Hermitian Hamiltonians with nonreciprocal coupling can achieve amplification of initial states without external gain due to a kind of inherent source. We discuss the source and its effect on time evolution in terms of complex eigenenergies and nonorthogonal eigenstates. Demonstrating two extreme cases of Hamiltonians, namely one having complex eigenenergies with orthogonal eigenstates and one having real eigenenergies with nonorthogonal eigenstates, we elucidate the differences between the amplifications from complex eigenenergies and from nonorthogonal eigenstates.

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their theoretical limit and offer little room for further enhancement. However, with the advent of quantum computers and the need for quantum algorithms that can perform multiplication on quantum hardware, a new paradigm emerges. In this paper, inspired by the convolution theorem and quantum amplitude amplification paradigm we propose a quantum algorithm for integer multiplication with time complexity of $O\left(\sqrt{n}{log}^{2}n\right)$ which outperforms the best-known classical algorithm, the Harvey algorithm with time complexity of $O(nlogn)$. Unlike the Harvey algorithm, our algorithm does not have the restriction of being applicable solely to extremely large numbers, making it a versatile choice for a wide range of integer multiplication tasks. The paper also reviews the history and development of classical multiplication algorithms and motivates us to explore how quantum resources can provide new perspectives and possibilities for this fundamental problem.

Using the Dirac equation, we study corrections to electron binding energies and hyperfine splittings of atomic hydrogen and hydrogenlike ions due to finite-nuclear-size (FNS) effects, relativistic QED radiative corrections, and nuclear recoil corrections. Three models for the charge distribution and the magnetic moment distribution within the nucleus are considered. Calculations are carried for light atoms (H, He, and K) and heavy atoms (Rb, Cs, Pb, Bi, U). The FNS corrections to the ground-state energy are shown to be smaller than the electron-nucleus reduced mass corrections, and comparable to the relativistic QED radiative corrections for the light nuclei, but much larger than both these corrections for heavy nuclei. Comparison is made with an experiment on the $1s\text{−}2s$ transition frequency for hydrogen. FNS corrections to the ground-state hyperfine splitting are comparable in size to the relativistic QED radiative corrections for light nuclei, but are larger for heavy nuclei.

Topological nontrivial bands can be realized via Rydberg-dressed neutral atoms. We propose a two-dimensional hard-core boson model with a topological flat band on a honeycomb array, where the particle hopping is realized via van der Waals interactions that exchange the Rydberg states of two interacting atoms, while nonzero phases associated with hopping arises from the transfer of laser phase to the wave functions of Rydberg atoms. Using exactly diagonalization and infinite density matrix renormalization group simulation, we find in the system a fractional Chern insulator phase with a Chern number $C=1/2$, which can persist in the presence of weak many-body interactions. These reveal that neutral-atom arrays can emulate fractional Chern insulators. Finally, we also study the proposed two-dimensional hard-core boson model under different theoretical parameter settings; the results further support that the generated nonzero phases associated with hopping amplitudes can produce a stable fractional Chern insulator state theoretically.

We study the formation and evolution of the electron wave packets in the process of strong-field ionization of various atomic targets. Our study is based on reformulating the problem in terms of conditional amplitudes, i.e., the amplitudes describing outcomes of measurements of different observables provided that the electron is found in the ionized state after the end of the pulse. By choosing the electron coordinate as such an observable, we are able to unambiguously define the notion of the ionized wave packets and study their formation and spread. We show that the evolution of the ionized wave packets obtained in this way closely follows the classical trajectories at the initial stages of evolution providing an ab initio quantum mechanical confirmation of the basic premises of the classical Monte Carlo calculations approach. At the later stages of evolution, the picture becomes more complicated due to the wave packets' spread and due to interference of wave packets originating from different field maxima. Our approach also allows us to obtain information about the coordinate and velocity electron distributions at the tunnel exit.

We derive a compact analytical solution of the $n\mathrm{th}$-order equal-time correlation functions by using scattering matrix ($S$ matrix) under a weak coherent state input. Our solution applies to any dissipative quantum system that respects the U(1) symmetry. We further extend our analytical solution into two categories depending on whether the input and output channels are identical. The first category provides a different path for studying cross-correlation and multiple-drive cases, while the second category is instrumental in studying waveguide quantum electrodynamics systems. Our analytical solution allows for easy investigation of the statistical properties of multiple photons even in complex systems. Furthermore, we have developed a user-friendly open-source library in Python known as the quantum correlation solver, and this tool provides a convenient means to study various dissipative quantum systems that satisfy the above-mentioned criteria. Our study enables using $S$ matrix to study the photonic correlation and advance the possibilities for exploring complex systems.

Quantum illumination uses quantum correlations to provide an enhanced detection of an object in the presence of background noise. This advantage has been shown to exist even if one uses nonoptimal direct measurements on the two correlated modes. Here we present a protocol that mimics the behavior of quantum illumination, but does not use correlated or entangled modes. Instead, the protocol uses coherent (or phase-randomized coherent) pulses with randomly chosen intensities. The intensities are drawn from a distribution such that the average state looks thermal. Under appropriate conditions, the mimic protocol can perform similarly to quantum illumination schemes that use direct measurements. This holds even for a reflectance as low as ${10}^{-7}$. We also present an analytic condition which allows one to determine the sets of parameters in which each protocol works best.

Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be assumed to be finite without loss of generality, a numerical tool for finding explicit local models that reproduce a given statistical behavior was developed. The numerical procedure was then validated using families of statistical behaviors for which the network-local boundary is known, in the bilocal scenario. Furthermore, the critical visibility for three notable distributions mixed with a uniform random noise is investigated in the triangle network without inputs. We provide conjectures for the critical visibilities of the Greenberger-Horne-Zeilinger and W distributions (which are roots of fourth degree polynomials), as well as a lower bound estimate of the critical visibility of the elegant joint measurement distribution.

We present a detailed derivation of the QED effects of order ${\alpha }^{7}m$ to the hyperfine structure (hfs) of the ${}^3\mathrm{S}$ states of heliumlike ions and perform numerical calculations for ${}^6\mathrm{Li}^{+}$ and ${}^7\mathrm{Li}^{+}$. By comparing the theoretical point-nucleus results with the measured hfs of ${\mathrm{Li}}^{+}$, we determine the nuclear-structure contribution parametrized in terms of the effective Zemach radius. Using the experimental hfs results for ${\mathrm{Li}}^{+}$, we obtain accurate predictions for the hfs of ${}^6\mathrm{Li}^{2+}$ and ${}^6\mathrm{Li}^{2+}$, for which no experimental data is available so far. By examining the normalized differences of the hfs of ${\mathrm{Li}}^{+}$ and Li and of the corresponding isotope-shift differences, we test the consistency of the hfs measurements in ${}^{6,7}\mathrm{Li}^{+}$ and ${}^{6,7}\mathrm{Li}$.

The Hartree-Fock exchange energy expression, the Dirac exchange functional, and other exchange functionals of the electron density are extended to fermions of arbitrary spin quantum number $s$. The explicit $s$ dependence of the exchange energy provides illuminating insights into the meaning of exchange interactions, spin-scaling relations, and the self-interaction error. In particular, the spin-scaling relation for exchange functionals proves to be a special case of conversion between spin-unpolarized forms of the same functional appropriate for $s=0$ and for $s>0$. A rigorous definition of the many-particle self-interaction error suitable for one-orbital systems is formulated and interpreted as a set of exact constraints for exchange density-functional approximations.

Above-threshold ionization (ATI) by femtosecond laser pulses centered at 515 nm is studied for a gas mixture containing the van der Waals complex $\mathrm{Ar}\text{−}{\mathrm{H}}_2\mathrm{O}$. By detecting photoions and photoelectrons in coincidence, the ATI spectra for Ar, ${\mathrm{Ar}}_2,{\mathrm{H}}_2\mathrm{O}$, and Ar-${\mathrm{H}}_2\mathrm{O}$ are discerned and measured simultaneously. Using an intensity-scanning technique, we observe the red shift of the ATI spectra as a function of the laser intensity. The intensity-dependent shift of the ATI peak positions observed for $\mathrm{Ar}\text{−}{\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$ match but significantly differ from the ones measured for Ar and ${\mathrm{Ar}}_2$. This indicates that the photoelectron is emitted from the ${\mathrm{H}}_2\mathrm{O}$ site of the complex and the vertical ionization potential of $\mathrm{Ar}\text{−}{\mathrm{H}}_2\mathrm{O}$ is determined as $(12.4\pm 0.1)\mathrm{eV}$. For rescattered electrons, however, an enhancement of high-order ATI is observed for $\mathrm{Ar}\text{−}{\mathrm{H}}_2\mathrm{O}$, as compared to ${\mathrm{H}}_2\mathrm{O}$, suggesting that the relatively large Ar atom acts as a scattering center, which influences the ionization dynamics.

We investigate both analytically and numerically the scattering of one-dimensional quantum droplets by a Pöschl-Teller reflectionless potential well, confirming that there is a sharp transition between full reflection and full transmission at a certain critical incident speed for both small droplets and large flat-top droplets. We observe sharp differences between small quantum droplet scattering and large quantum droplet scattering. The scattering of small quantum droplets is similar to that of solitons, where a spatially symmetric trapped mode is formed at the critical speed, whereas for large quantum droplets a spatially asymmetric trapped mode is formed. Additionally, a nonmonotonic dependence of the critical speed on the atom number is identified: On the small-droplet side, the critical speed increases with the atom number, while in the flat-top regime, the critical speed decreases with increasing atom number. Strikingly, the scattering excites internal modes below the particle-emission threshold, preventing the quantum droplets from emitting radiation upon interaction with the potential. Analysis of the small-amplitude excitation spectrum shows that as the number of particles increases, it becomes increasingly difficult to emit particles out of the droplet during scattering, while radiation from solitons cannot be completely avoided. Finally, we study the collision of two quantum droplets at the reflectionless potential, revealing the role of the $\pi$-phase difference generator played by the reflectionless potential.

Nonseparability in classical and quantum states of light gives rise to the notions of classical (local) and quantum (nonlocal) entanglement, usually defined as global features of the fields and states. Here we use concurrence as a measure of this nonseparability and show that it can be spatially resolved, revealing regions of maximum nonseparability and regions with no nonseparability. We use the topical examples of vectorial structured light and its quantum analog, a hybrid spatial mode and polarization entangled states, to test the approach on both local and nonlocal forms of entanglement. Our work has wide reaching implications, for instance, in understanding the spatial dependence of coherence and polarization in vectorial light, as well as in quantum entangled states for imaging, where spatial correlations are vital.

We experimentally explore single-shot state identification using long alphabets of states and employing different modulation schemes. We use time-resolved quantum measurement and Bayesian inference to identify the input state and demonstrate the advantage of this single-shot measurement over classical state identification. For each single-shot measurement, we estimate the confidence of state identification based on the quantum measurement and demonstrate the physical significance of confidence estimates. Particularly, we show that a set of confidence values correctly represents the probabilities of successful state identification for a given experimental outcome. We investigate the alphabets of coherent states with different modulations and show that confidence estimates yield the reliability of each act of measurement independently of the modulation used.

We study the quantum dynamics of filling an empty lattice of size $L$ by connecting it locally with an equilibrium thermal bath that injects noninteracting bosons or fermions. We adopt four different approaches, namely, (i) direct exact numerics, (ii) Redfield equation, (iii) Lindblad equation, and (iv) quantum Langevin equation, which are unique in their ways for solving the time dynamics and the steady state. In this simple setup we investigate open quantum dynamics and subsequent approach to thermalization. The quantities of interest that we consider are the spatial density profile and the total number of bosons and fermions in the lattice. The spatial spread is ballistic in nature and the local occupation eventually settles down owing to equilibration. The ballistic spread of local density admits a universal scaling form. We show that this universality is only seen when the condition of detailed balance is satisfied by the baths. The difference between bosons and fermions shows up in the early time growth rate and the saturation values of the profile. The techniques developed here are applicable to systems in arbitrary dimensions and for arbitrary geometries.