The fields of precision timekeeping and spectroscopy increasingly rely on optical-frequency-comb interferometry. However, comb-based measurements are not described by existing quantum theory because they exhibit both large mode mismatch and finite-strength local oscillators. To establish this quantum theory, we derive measurement operators for homodyne detection with arbitrary mode overlap. These operators are a combination of quadrature and intensity-like measurements, which inform a filter that maximizes the quadrature-measurement signal-to-noise ratio. Furthermore, these operators establish a foundation to extend frequency-comb interferometry to a wide range of scenarios, including metrology with nonclassical states of light.

In this work, a parity-time $\left(\mathcal{PT}\right)$-symmetric system is investigated based on superconducting circuits, which allows the tunability of atom-atom coupling using superconducting qubits. The calculation results demonstrate that the interaction between artificial atoms significantly impacts the transmission spectrum and the conditions of the phase transition in the system. When introducing a weak probe signal into the $\mathcal{PT}$-symmetric system, several findings are observed. (1) The symmetry and intensity of both the linear and nonlinear outputs can be fine-tuned by adjusting the coupling strength between artificial atoms or manipulating the gauge-invariant phase in the system. (2) Nonreciprocal transmission can be achieved by driving different cavity modes. (3) The exceptional point (EP) of the $\mathcal{PT}$ phase transition can be adjusted within a certain range by modifying the gauge-invariant phase or adjusting the coupling strength in the system. One feasible experimental setup is also described and analyzed based on existing experimental techniques. These findings may inspire further research into modulating quantum phase transitions based on superconducting circuits.

We investigate a broad class of nonclassical states, composed of superposed squeezed and displaced number states. The phase-space structure is analyzed, keeping in mind the Heisenberg limited sensitivity in parameter estimation. Appropriate squeezing and displacement parameters are identified, wherein the state fidelity in comparison to the metrologically sensitive compass state is more than $99\%$. Also, the equal variance in small shift measurements, for the proposed and compass state, shows identical behavior of the average photon number. In metrological application, the number variance of the compass state, which is small for low coherent amplitude, suggests its potential to estimate damping parameters. Finally, we present the theoretical models corresponding to their preparation.

We address the problem of the fundamental limitations of information extraction from the environment in open quantum systems. We derive a model-independent, hybrid quantum-classical solution of open dynamics in the recoilless limit, which includes environmental degrees of freedom. Specifying to the celebrated Caldeira-Leggett model of hot thermal environments, ubiquitous in everyday situations, we reveal the existence of a new lengthscale, called the distinguishability length, different from the well-known thermal de Broglie wavelength that governs the decoherence. Interestingly, a new integral kernel, called quantum Fisher information kernel, appears in the analysis. It complements the well-known dissipation and noise kernels and satisfies disturbance-information gain type of relations, similar to the famous fluctuation-dissipation relation. Our results complement the existing treatments of the Caldeira-Legget model from a non-standard and highly nontrivial perspective of information dynamics in the environment. This leads to a full picture of how the open evolution looks like from both the system and the environment points of view, as well as sets limits on the precision of indirect observations.

We show that a single polynomial entanglement measure is enough to verify equivalence between generic $n$-qubit states under stochastic local operations with classical communication (SLOCC). SLOCC operations may be represented geometrically by Möbius transformations on the roots of the entanglement measure on the Bloch sphere. Moreover, we show how the roots of the three-tangle measure classify four-qubit generic states, and propose a method to obtain the normal form of a four-qubit state, which bypasses the possibly infinite iterative procedure.

The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multilevel amplitude damping channels. We investigate some of the information capacities of the simplest member of the multilevel amplitude damping channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.

We numerically investigate a hybrid trapping architecture for two-dimensional (2D) ion crystals using static electrode voltages and optical cavity fields for in-plane and out-of-plane confinements, respectively. By studying the stability of 2D crystals against 2D-3D structural phase transitions, we identify the necessary trapping parameters for ytterbium ions. Multiple equilibrium configurations for 2D crystals are possible, and we analyze their stability by estimating potential barriers between them. We find that scattering to antitrapping states limits the trapping lifetime, which is consistent with recent experiments employing other optical trapping architectures. These 2D ion crystals offer an excellent platform for quantum simulation of frustrated spin systems, benefiting from their 2D triangular lattice structure and phonon-mediated spin-spin interactions. Quantum information processing with tens of ions is feasible in this scheme with current technologies.

The conventional certification method for quantum teleportation protocols relies on surpassing the highest achievable classical average fidelity between target and teleported states. Our paper highlights the limitations of this approach: inconsistent conclusions can be obtained when considering different distance measures in the quantum state space, leading to contradictory interpretations. In particular, this behavior is manifested when modeling a very common noisy experimental scenario, in which the resource state takes the form of a Werner state generated by the influence of a depolarizing channel acting on the Bell state resource. Two additional noise models, based on amplitude-damping channels, are also analyzed. Our paper, therefore, stresses the necessity of new certification methods for quantum teleportation.

We present a comprehensive mathematical model and experimental measurements for the evolution of a trapped-particle ensemble driven by collisions with a room-temperature background vapor. The model accommodates any trap geometry, confining potential, initial trapped distribution, and other experimental details; it only depends on the probability distribution function $P_t\left(E\right)$ for the collision-induced energy transfer to the trapped ensemble. We describe how to find $P_t\left(E\right)$ using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a ${}^{87}\mathrm{Rb}$ ensemble energy evolution exposed to a room-temperature background gas of Ar by means of a single parameter fit for the total collision rate $\mathrm{\Gamma }$. We extracted a collision rate of $\mathrm{\Gamma }=0.649\left(2\right){\text{s}}^{-1}$. We further refine our analysis by using monotonic Gaussian process regression to smooth the experimental data, which extracts a collision rate of $\mathrm{\Gamma }=0.646\left(1\right){\text{s}}^{-1}$. This is compared to a value of 0.67(1) ${\text{s}}^{-1}$ found by the commonly used method of zero-trap depth extrapolation, a 3.5% correction that is a result of our model fully taking ensemble loss and heating into account. Finally, we report a fivefold increase in the precision of our collision rate extraction from the experimental data and a tenfold increase in the precision of our collision rate extraction from the smoothed experimental data.

By means of analytical calculations based on first-order perturbation theory within the electric dipole, laser, and rotating wave approximations, we investigate the linear (in intensity) process of one-photon single ionization of the hydrogen atom by two synchronous crossed linearly chirped pulses in the configuration where one pulse is linearly polarized along the propagation direction of another circularly polarized pulse. We show that transform limited or identically chirped pulses create a monopole (horseshoelike) pattern in the photoelectron momentum distribution, whereas a single-arm reversible spiral resembling the patterns of a snake biting its own tail (Ouroboros patterns) emerges when these pulses are differently chirped. This self-splitting spiral is controlled by varying the amount and sign of chirp, the pulse duration, the helicity, and the ellipticity of the second pulse. We show that the use of an elliptically polarized second pulse can destroy the Ouroboros spirals when the ellipticity is less than 0.4. Our results are valid for any $S$-state atoms, as illustrated here for the hydrogen atom as well as the helium atom.

We perform a systematic comparison between photoelectron momentum distributions computed with the rescattered quantum-orbit strong-field approximation (RQSFA) and the Coulomb quantum-orbit strong-field approximation (CQSFA). We exclude direct, hybrid, and multiply scattered CQSFA trajectories and focus on the contributions of trajectories that undergo a single act of rescattering. For this orbit subset, one may establish a one-to-one correspondence between the RQSFA and CQSFA contributions for backscattered and forward-scattered trajectory pairs. We assess the influence of the Coulomb potential on the ionization and rescattering times of specific trajectory pairs, kinematic constraints determined by rescattering, and quantum interference between specific pairs of trajectories. We analyze how the Coulomb potential alters their ionization and return times, and their interference in photoelectron momentum distributions. We show that Coulomb effects are not significant for high or medium photoelectron energies and shorter orbits, while for lower momentum ranges or longer electron excursion times in the continuum, the residual Coulomb potential is more important. We also assess the agreement of both theories for different field parameters and show that it improves with the increase of the wavelength.

Systems of interacting bosons in double-well potentials, modeled by two-site Bose-Hubbard models, are of significant theoretical and experimental interest and attracted intensive studies in contexts ranging from many-body physics and quantum dynamics to the onset of quantum chaos. In this work we systematically study a kicked two-site Bose-Hubbard model (Bose-Hubbard dimer) with the on-site potential difference being periodically modulated. Our model can be equivalently represented as a kicked Lipkin-Meshkov-Glick model and thus displays different dynamical behaviors from the kicked-top model. By analyzing spectral statistics of Floquet operator, we unveil that the system undergoes a transition from regularity to chaos with increasing the interaction strength. Then based on semiclassical approximation and the analysis of Rényi entropy of coherent states in the basis of Floquet operator eigenstates, we reveal the local chaotic features of our model, which indicate the existence of integrable islands even in the deep chaotic regime. The semiclassical analysis also suggests that the system in chaotic regime may display different dynamical behavior depending on the choice of initial states. Finally, we demonstrate that dynamical signatures of chaos can be manifested by studying dynamical evolution of local operators and out-of-time-order correlation function as well as the entanglement entropy. Our numerical results exhibit the richness of dynamics of the kicked Bose-Hubbard dimer in both regular and chaotic regimes as the initial states are chosen as coherent spin states located in different locations of phase space.

We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte Carlo simulations. We show that when the intrawell repulsion is as strong as the on-site repulsion, a dimerized Mott-insulator phase appears at the tip of the dimerized density-wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane-insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.

Stability domains (i.e., pump frequency detuning range) of a single dark soliton (or platicon) and dark breather in high-$Q$ Kerr optical microresonators with normal group velocity dispersion is studied for a wide range of pump amplitudes within the framework of the Lugiato-Lefever model. The effect of the significant fragmentation of the stability domains at high pump intensities is revealed. The existence of stable drifting dark solitons (platicons) is demonstrated above the threshold pump amplitude value. Properties of drifting solitons are investigated.

Magnon blockade is an effective physical mechanism to generate a single magnon, which is of great importance in quantum information processing. We present a scheme to realize the unconventional magnon blockade effect by using Kerr nonlinearity in a cavity electromagnonic system. Under weak driving conditions, we give the optimal parameter conditions for magnon antibunching through analytical calculations, which are in good agreement with numerical results. Furthermore, we find that Kerr nonlinearity is necessary to create magnon blockade. In particular, unconventional magnon blockade can be achieved in both weak nonlinearity and weak coupling regimes. The present scheme indicates a method for generating unconventional magnon blockade effect and provides a feasible and flexible platform for the realization of a single-magnon source with high purity.

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time invariance of the law of evolution. In both quantum and classical mechanics, Hamiltonian mechanics demands a precise relationship between time evolution and observable energy, albeit using slightly different terminology. We distill basic conditions satisfied in both quantum and classical mechanics, including canonical coordinate symmetries and inner product invariance. We express these conditions in the framework of generalized probabilistic theories, which includes generalizing the definition of energy eigenstates in terms of time-invariant properties of the Hamiltonian system. By postulating these conditions to hold, we derive a unified Hamiltonian system model. This unified framework describes quantum and classical mechanics in a consistent language, facilitating their comparison. We moreover discuss alternative theories: an equation of motion given by a mixture of commutation relations, an information-restricted version of quantum theory, and Spekken's toy theory. The findings give a deeper understanding of the Hamiltonian in quantum and classical theories and point to several potential research topics.