Entropic uncertainty relation (EUR) formulates the restriction of the inherent uncertainty of quantum mechanics from an information-theoretic perspective. A tighter lower bound for uncertainty relations can provide information-theoretic security to quantum communication protocols. Recently, a generalized EUR (GEUR) for the measurement of multiple observables in arbitrary many-body systems has been formulated. Here, we experimentally test this GEUR using a four-photon entangled state with a controllable decoherence channel and show that for the tripartite scenario, the GEUR improves the entropic bound from Renes and Boileau's famous results. As an application, we further demonstrate an improvement of the secure key rate in quantum key distribution from the GEUR. Our results extend the test of EURs into multipartite regimes and may find applications in practical quantum cryptography tasks.

We investigate the spontaneous parity-time ($\mathcal{PT}$)-symmetry breaking and spectral properties of a $\mathcal{PT}$-symmetric quantum kicked rotor under resonance conditions. At resonance, the QKR reduces to a finite-dimensional system. In the localized regime, we find that increasing the non-Hermitian parameter always induces a transition from a phase where the states exhibit $\mathcal{PT}$ symmetry to one where $\mathcal{PT}$ symmetry is spontaneously broken. In contrast, in the delocalized regime, the existence of such a transition depends on whether the reduced system is $\mathcal{PT}$ symmetric. If the reduced system is not $\mathcal{PT}$ symmetric, $\mathcal{PT}$ symmetry remains in the broken phase regardless of the non-Hermitian parameter. We further analyze the spectral statistics of the system in the delocalized regime. For real energy spectra, the level-spacing distribution transitions from Wigner-Dyson statistics, associated with the Gaussian orthogonal ensemble, to Poisson statistics as the non-Hermitian parameter increases, with the intermediate regime well described by the Brody distribution. For complex spectra, the level-spacing ratios and distributions are governed by time-reversal symmetry. The spectral statistics align with predictions for non-Hermitian random matrix ensembles in classes ${\mathrm{AI}}^{†}$ and $\mathrm{A}$, depending on the presence or absence of time-reversal symmetry. Our results provide insights into the spectral characteristics of non-Hermitian quantum chaotic systems and their connection to $\mathcal{PT}$ symmetry.

With the help of nonrelativistic quantum electrodynamics (NRQED) method, relativistic and QED corrections to the dipole polarizabilities for a large set of states of ${}^4\mathrm{He}$ are calculated by using the correlated $B$-spline basis functions, in which the interelectronic coordinate $r_{12}$ is explicitly included. The numerical calculations began with solving the Schrödinger equation for the case of infinite or finite mass of a nucleus. Then, we summed the matrix elements of the effective operators involving all intermediate states to obtain relativistic and QED corrections to polarizabilities by using perturbation theory. Present computational uncertainties are mainly due to neglected nonradiation contributions in the ${\alpha }^4$-order QED effect. Results for the $1{}^{1}S_0$ state are in good agreement with available data, previous relativistic configuration interaction results for the $2{}^{3}S_1$ state are amended, and a three orders of magnitude improvement in precision for the $3{}^{3}S_1$ state is achieved. Especially, we report better than 0.2 ppm numerical results of dipole polarizabilities for other singlet and triplet $S$ states with the principal quantum number up to 7, which were not available before, thereby allowing for potential direct comparisons with experimental results in the future. This capability of achieving calculations for both low-lying and highly-excited states reaffirms the high precision and broad applicability of the correlated $B$-spline basis functions.

We investigate the role of relativity in photoionization of hydrogenlike ions by a laser pulse. For hydrogen, the wavelengths of the laser resides in the weakly ultraviolet region. For higher nuclear charges, the laser parameters are scaled in a manner which renders the time-dependent Schrödinger equation in the electric dipole approximation independent of nuclear charge. The ionization potentials of these highly charged ions are strongly modified by relativistic effects. In an earlier work by Ivanova et al. [Phys. Rev. A 98, 063402 (2018)], it is demonstrated how this explains most of the relativistic correction to the ionization probability. Here we investigate to what extent remaining discrepancies can be attributed to relativistic effects stemming from the strong external field. To this end, we solve semirelativistic formulations of both the Schrödinger and the Dirac equations; the former accounts for increased inertia due to the external laser field, while the latter features a nonrelativistic interaction term.

We investigate the phase-induced susceptibilities for both components of the probe vector beam (PVB) within an atomic system. The atoms are prepared in a nondegenerate four-level configuration. The transitions are coupled by a $\pi$ polarized control field and two orthogonally polarized components of a PVB. We show that the linear susceptibility of the medium depends on the phase shift between the control field and PVB, characterizing loss or gain in the system. Additionally, the phase shift causes polarization rotation in the vector beams (VBs) as they propagate. We further study the effect of nonlinearity on the VB propagation through the medium for a couple of Rayleigh lengths. The self-focusing and defocusing phenomena are observed for radial, azimuthal, and spiral VBs. The special chain-like self-focusing and defocusing leads to the formation of consecutive smaller spot sizes with moderate gain. Therefore, the mechanism of control of susceptibility and self-focusing may hold promise for applications such as transitioning from an absorber to an amplifier, high-resolution microscopy, and optical trap systems.

Atoms coupled to cavities provide an exciting playground for the study of fundamental interactions of atoms mediated through a common channel. Many of the applications of cavity QED and cold-atom experiments more broadly, suffer from limitations caused by the transient nature of an atomic loading cycle. The development of continuous operation schemes is necessary to push these systems to the next level of performance. Here we present a machine designed to produce a continuous flux of collimated atoms that traverse an optical cavity. The atom-light interaction is enhanced by a fast-decaying cavity optimal for studying phenomena where atomic properties dominate. We demonstrate the transition to a collective strong-coupling regime heralded by a normal-mode splitting. We observe a second phase with a binary normal-mode splitting born from an offset in the mean velocity of the atoms. Inverting the atomic ensemble in the collective strong-coupling regime, we measure continuous optical gain. This work sets the stage for studying threshold conditions for continuous collective phenomena, such as continuous superradiant lasing.

The superradiant phase transition (SRT) is prohibited in the standard isotropic Dicke model by the no-go theorem, which is induced by the $A^2$ term. Within the Dicke model framework, we demonstrate that SRTs can occur at both zero and finite temperatures by independently tuning the rotating-wave and counter-rotating atom-cavity couplings and/or introducing nonlinear Stark coupling terms, thereby overcoming the no-go theorem. The phase transitions in the anisotropic Dicke-Stark model belong to the same universality class as the original Dicke model. We believe that we have proposed a feasible scheme for observing SRTs in future solid-state experiments.

We analyze the dynamics of a quantum particle on a force-free surface of a cube. Employing the methods of group theory, we divide the solutions of the stationary Schrödinger equation (the modes) into classes based on irreducible representations of the symmetry group of the cube and for each class we reduce the problem to finding the modes on a square with special boundary conditions. We analyze the properties of the resulting modes, present them visually, and discuss the possibility of quantum state revivals on the cube.

In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred to as quantum Cramér-Rao bound (QCRB), and to construct an optimal estimator that achieves QCRB. This paper studies the amplitude estimation in the presence of depolarizing noise with unknown intensity. The main difficulty in this problem is that the optimal measurement depends on both the unknown quantum state and the amplitude we aim to estimate. To deal with these issues, we utilize the variational quantum circuits to approximate the (unknown) optimal measurement basis combined with the two-step adaptive estimation strategy which was proposed in the quantum estimation theory. We numerically show that the proposed method can nearly attain the QCRB.

We propose a toy model of ion-atom hybrid quantum system for quantum computing. We show that when two atomic qubits in two largely separated optical tweezers interact with a single trapped ion through Rydberg excitation of the atoms, there exists an ion-mediated atom-atom interaction which exceeds the direct interatomic interaction at large separation. We employ this mediated interaction to demonstrate a two-qubit control phase-gate operation with 97% fidelity by addressing the individual atomic qubits with lasers.

For an unstable anion, when using a diffuse basis set, the self-consistent field (SCF) solution often leads to a minimum energy solution with an additional electron in the most diffuse orbital present in the basis set. Eventually, it converges to a neutral molecule and a free electron with increase in the diffuse functions. Consequently, any post-SCF calculations using this solution do not yield meaningful physical results. This paper introduces the use of modified parametric equation of motion (PEM) in combination with nuclear charge stabilization to obtain a desirable SCF solution for an unstable anion. The SCF solution for an anion at a higher nuclear charge is used as the starting point, where the anion is bound. The modified PEM is then carried out until the additional nuclear charge reaches zero, ultimately producing the SCF solution for the unstable anion. The key to achieving meaningful SCF solutions for temporary anions lies in maintaining a fixed occupation number for the orbital corresponding to the singly occupied molecular orbital throughout the PEM calculation. The solution obtained using the modified PEM is checked for being self-consistent-field solution, confirming the accuracy of the method. To account for electron correlation, MP2 calculations are carried out for anionic species.

The collision of a high-energy electron beam with a laser pulse may be used to study radiation reaction and nonlinear Compton scattering among many other processes in strong-field quantum electrodynamics. Predictions from simulation and theory for these interactions rely on a number of approximations and assumptions that have not been experimentally tested. Here, experimentally measurable signatures are identified that might be able to distinguish between radiation reaction models, i.e., classical or quantum, or between the local constant field and local monochromatic approximations used to calculate the properties of the nonlinear Compton process. These signatures are considered through Monte Carlo simulations of various experimental conditions that are relevant to today's laser facilities. Potential detection schemes for measuring the signatures are proposed. We find that single-photon counting of keV photons to resolve harmonics and scintillator-based detection of MeV photons may allow us to validate nonlinear Compton scattering models and radiation reaction models respectively. This will require electron beams with divergence angles less than 2 mrad and less than $20\%$ energy spread.

The third quantization (3rd Q) for bosons provides the exact steady-state solution of the Lindblad equation with quadratic Hamiltonians. By decomposing the interaction of the Bose-Hubbard model (BHM) according to Hartree approximation, we present a self-consistent formalism for solving the open-system bosonic Lindblad equation with weak interactions in the steady state. The 3rd Q with Hartree approximation takes into account the infinite Fock space of bosons, while its demand of resource scales polynomially with the system size. We examine the method by analyzing three examples of the BHM, including the uniform chain, interaction-induced diode effect, and Su-Schrieffer-Heeger Hubbard model. When compared with the simulations with capped boson numbers for small systems, the 3rd Q with Hartree approximation captures the qualitative behavior and suggests an upper bound of the steady-state value. Finite-size scaling confirms the results from the 3rd Q with Hartree approximation converging towards the thermodynamic limit. Thus, the manageable method allows us to characterize and predict large-system behavior of quantum transport in interacting bosonic systems relevant to cold-atom experiments.

We consider the free-propagation geometry of a light beam (or fluid of light) in a multimode waveguide. As a result of the effective photon-photon interactions, the photon fluid thermalizes to an equilibrium state during its conservative propagation. In this configuration, Rayleigh-Jeans (RJ) thermalization and condensation of classical light waves have been recently observed experimentally in graded index multimode optical fibers characterized by a two-dimensional parabolic trapping potential. As is well known, the properties of RJ condensation differ substantially from those of Bose-Einstein (BE) condensation: The condensate fraction decreases quadratically with the temperature for BE condensation, while it decreases linearly for RJ condensation. Furthermore, for quantum particles the heat capacity tends to zero at low temperatures and it takes a constant value in the classical particle limit at high temperatures. This is in contrast with classical RJ waves, where the specific heat takes a constant value at low temperatures and tends to vanish above the condensation transition in the normal (uncondensed) state. Here we reconcile the thermodynamic properties of BE and RJ condensation: By introducing a frequency cutoff inherent to light propagation in a waveguide, we derive generalized expressions of the thermodynamic properties that include the RJ and BE limits as particular cases. We extend the approach to encompass negative temperatures. In contrast to positive temperatures, the specific heat does not display a singular behavior at negative temperatures, reflecting the noncritical nature of the transition to a macroscopic population of the highest-energy level. Our work contributes to understanding the quantum-to-classical crossover in the equilibrium properties of light, within a versatile experimental platform based on nonlinear optical propagation in multimode waveguides.

We model squeezed state generation in a lossy optical cavity in the presence of a thermal bath using the Lindblad master equation. We show that in the undepleted-pump approximation, the exact solution is a squeezed thermal state, where thermal photons arise both from loss and from the thermal bath. We derive a closed-form solution for the evolution of the quadrature uncertainty arising from pulsed degenerate spontaneous parametric down conversion in the cavity under the parametric oscillation threshold. We apply this solution under different pump conditions and show in detail how the thermal environment reduces quadrature squeezing as well as the second-order coherence function.

This paper reports the spontaneous emergence of a photon current in a class of spin-cavity systems, where an assemble of quantum emitters interact with distinct photon modes confined in tunneling-coupled cavities. Specifically, with necessary symmetry breaking, photons in a superradiant phase afforded by coherent photon-emitter interaction spontaneously flow from a cavity with a lower resonance frequency to a different cavity with a higher resonance frequency. Theoretical analysis reveals that counterrotating terms in the system Hamiltonian and cavity dissipation are the key to alter spin-cavity coherence, which then makes it possible to extract photons from and later return photons to the surroundings through the cavities. The interplay between photon loss and emitter coherence hence sustains a counterintuitive steady current of photons between cavities without an external pumping field directly exciting the cavity modes.

This paper delves into the crucial aspects of pointer-induced quantum decoherence and the transition between von Neumann's projective strong measurement and Aharonov's weak measurement. Both phenomena significantly impact the dynamical understanding of quantum measurement processes. Specifically, we focus on the interplay between quantum decoherence and the transition from weak to strong measurement by deducing and comparing the quantum decoherence and weak-to-strong measurement transition factors within a general model and using the well-known Stern-Gerlach experiment as an illustrative example. Our findings reveal that both phenomena can be effectively characterized by a universal factor intricately linked to the coupling between the measured system and the pointer. The analysis presented in our current work can clarify the mechanism behind the relations of pointer-induced quantum decoherence to the weak measurement and weak-to-strong measurement transition.

Efficiently learning an unknown Hamiltonian given access to its dynamics is a problem of interest for quantum metrology, many-body physics, and machine learning. A fundamental question is whether learning can be performed at the Heisenberg limit, where the Hamiltonian evolution time scales inversely with the error $\varepsilon$ in the reconstructed parameters. The Heisenberg limit has previously been shown to be achievable for certain classes of qubit and bosonic Hamiltonians. Most recently, a Heisenberg-limited learning algorithm was proposed for a simplified class of fermionic Hubbard Hamiltonians restricted to real hopping amplitudes and zero chemical potential at all sites, along with on-site interactions. In this work, we provide an algorithm to learn a more general class of fermionic Hubbard Hamiltonians at the Heisenberg limit, allowing complex hopping amplitudes and nonzero chemical potentials in addition to the on-site interactions, thereby including several models of physical interest. The required evolution time across all experiments in our protocol is $O\left(1/\varepsilon \right)$ and the number of experiments required to learn all the Hamiltonian parameters is $O\left[\text{polylog}\right(1/\varepsilon \left)\right]$, independent of system size as long as each fermionic mode interacts with $O\left(1\right)$ other modes. Unlike prior algorithms for bosonic and fermionic Hamiltonians, to obey fermionic parity superselection constraints in our more general setting, our protocol utilizes $O\left(N\right)$ ancillary fermionic modes, where $N$ is the system size. Each experiment involves preparing fermionic Gaussian states, interleaving time evolution with fermionic linear optics unitaries, and performing local occupation number measurements on the fermionic modes. The protocol is robust to a constant amount of state preparation and measurement error.