A quantum optical model for high-order harmonic generation is presented in which both the exciting field and the high-order harmonic modes are quantized, while the target material appears only via parameters. As a consequence, the model is independent of the excited material system to a large extent and allows us to focus on the properties of the electromagnetic fields. Technically, the Hamiltonian known for parametric down-conversion is adopted, where photons in the $n\mathrm{th}$ harmonic mode are created during the annihilation of $n$ photons from the fundamental mode. In our treatment, initially, the fundamental mode is in a coherent state corresponding to large photon numbers, while the high-order harmonic modes are in vacuum state. Due to the interaction, the latter modes get populated while the fundamental one loses photons. Analytical approximations are presented for the time evolution that are verified by numerically exact calculations. For multimode, finite-bandwidth excitation, the time dependence of the high-order harmonic radiation is also given.

Quantum networks based on quantum key distribution ensure the security which is guaranteed by the fundamental laws of quantum physics between multiple parties. The discrete-modulation (DM) continuous-variable quantum key distribution (CV-QKD) protocols have the characteristics of simple implementation and compatibility with classical digital communication, making them very suitable for deployment in large-scale communication networks. However, the actual communication network has a huge communication capacity and a large number of units. To solve this problem, we propose a multiple-quadrature-amplitude-modulation (MQAM) DM protocol with a numerical method and complete the security analysis of the DM protocol in a downstream-access network situation. By introducing an extra dimension of signal modulation, the high-order modulated MQAM protocol greatly improves the number of supported units and the key rate of each unit. We give the results of a 16 quadrature amplitude modulation CV-QKD protocol in a downstream-access network which achieves 64 supported network units even in the case of high excess noise, which shows the application prospects of high-order discrete-modulation CV-QKD in network security.

We investigate the quantum phase transition in the anisotropic Dicke model through an examination of the quantum geometric tensor of the ground state. In this analysis, two distinct classical limits exhibit their unique anisotropic characteristics. The classical spin limit demonstrates a preference for the rotating-wave coupling, whereas the classical oscillator limit exhibits symmetry in the coupling strength of the bias. The anisotropic features of the classical spin limit persist at finite scales. Furthermore, we observe that the interplay among the anisotropic ratio, spin length, and frequency ratio can collectively enhance the critical behaviors. This critical enhancement without a trade-off between these factors provides a flexible method for quantum precision measurement.

Quantum control techniques are employed to perform quantum algorithms inspired by the adiabatic quantum computing protocols in the presence of noise. First, we analyze the entanglement protocol for two qubits. In this case, we find that this protocol is very robust against noise. The reason behind this fact is related to the chosen Hamiltonians, where the ground state of the initial Hamiltonian is not affected by the noise. The optimal control solution, in this case, is to leave the system in its ground state and apply a fast pulse to entangle the qubits at the end of the time evolution. Second, we probe a system composed of three qubits, where the goal is to teleport the first qubit to the third qubit. In this case, the ground state of the system does not share the same robustness against noise as in the case of the entanglement protocol. To circumvent this problem, we propose the inclusion of a local control field that can drive the system to an intermediate state, which is more robust against noise in comparison to other states. The target state is also achieved by a fast pulse close to the final time. We find that this approach provides a significant gain and promises to improve the realization of quantum computing in the so-called noisy intermediate-scale quantum devices.

Atoms confined in a three-dimensional dissipative optical lattice oscillate inside potential wells, occasionally hopping to adjacent wells, thereby diffusing in all directions. Illumination by a weak probe beam modulates the lattice, yielding propagating atomic density waves, referred to as Brillouin modes, which travel perpendicular to the direction of travel of the probe. The probe is made incident at a small angle relative to a lattice symmetry axis, yielding a driving potential perturbation whose spatial period is not a multiple of the period of the underlying optical potential, thus enabling exploration of the regime of space quasiperiodic drive. A theory, based on the Fourier decomposition of the current into its atomic density wave contributions, reveals that, unlike the previously studied time quasiperiodic case, wherein a lattice driven by two incommensurate frequencies may exhibit abrupt suppression in directed current as the driving transitions from quasiperiodic to periodic, a spatial-quasiperiodically driven lattice exhibits no such abrupt response. Further, detailed modeling of spatial-quasiperiodically driven lattices reveals that directed propagation occurs not only as a consequence of velocity matching between the propagating modulation and the average velocity of the atom oscillating inside a well, as was previously reported in the literature, but also as a distinct consequence of another mechanism, namely, frequency matching between the modulation frequency and the oscillation frequencies. A systematic measurement of the transmitted probe spectra as a function of off-axis probe angle is presented, which is consistent with the velocity- and frequency-matching predictions from the detailed model.

We study the initiation of primary comb generation in surface nanoscale axial photonic (SNAP) microcavities within the framework of modulation instability theory. In such cylindrical microcavities, the whispering gallery modes exhibit different effective volumes as well as varying overlap integrals with the excitation field, which poses a challenge to the process of nonlinear mode generation. We derive the threshold power for the nonlinear generation and find it considerably diverse for modes with different sideband numbers. We also suggest special dispersion control, effectively reducing the threshold and simplifying the generation in cylindrical cavities.

Simultaneous ground-state cooling of two levitated nanoparticles is a crucial prerequisite for investigation of macroscopic quantum effects such as quantum entanglement and quantum correlation involving translational motion of particles. Here we consider a coupled cavity-levitated-particle system and present a detailed derivation of its Hamiltonian. We find that the $y$-direction motions of the two particles are decoupled from the cavity field and both the $x$- and $z$-direction motions, and that the $z$-direction motions can be further decoupled from the cavity field and the $x$-direction motions by choosing proper locations of the particles. We study the simultaneous cooling of these mechanical modes in both the three-mode and five-mode cavity-levitated optomechanical models. It is found that there exists a dark-mode effect when the two tweezers have the same powers, which suppress the simultaneous ground-state cooling. Nevertheless, the simultaneous ground-state cooling of these modes can be realized by breaking the dark-mode effect under proper parameters. Our system provides a versatile platform to study quantum effects and applications in cavity-levitated optomechanical systems.

We measure and model the combined relaxation of a qubit coupled to a discrete two-level system (TLS) environment, also known as the central spin model. If the TLSs are much longer-lived than the qubit, nonexponential relaxation and non-Poissonian quantum jumps can be observed. In the limit of large numbers of TLSs, the relaxation is likely to follow a power law, which we confirm with measurements on a superconducting fluxonium qubit. Moreover, the observed relaxation and quantum jump statistics are described by the Solomon equations, for which we present a derivation starting from the general Lindblad equation for an arbitrary number of TLSs. We also show how to reproduce the non-Poissonian quantum jump statistics using a diffusive stochastic Schrödinger equation. The fact that the measured quantum jump statistics can be reproduced by the Solomon equations, which ignore the quantum measurement back action, hints at a quantum-to-classical transition.

We investigate the dynamics of ergotropy in open systems under Markovian and non-Markovian evolutions. In this scenario, we begin by formulating the ergotropy of an arbitrary qubit state in terms of energy and coherence. Thus we determine the conditions for ergotropy freezing and ergotropy sudden death as a consequence of the system-bath interaction. In order to use ergotropy as a resource for energy extraction in the form of work in an open-system scenario, we adopt the entropy-based formulation of quantum thermodynamics. In this approach, the work gains an additional environment-induced component, which may be present even for constant Hamiltonians. We then establish an analytical relationship between the environment-induced work and ergotropy, providing an interpretation of environment-induced work in terms of variation of ergotropy. In particular, energy transfer by environment-induced work can be performed up to a limit, which is governed by the energy cost to transit between the initial and final passive states of the quantum dynamics. We illustrate these results for qubit states evolving under nondissipative and dissipative quantum processes.

Using a general-order ab initio many-body Green's function method, we numerically illustrate several pathological behaviors of the Feynman-Dyson diagrammatic perturbation expansion of one-particle many-body Green's functions as electron Feynman propagators. (i) The perturbation expansion of the frequency-dependent self-energy is not convergent at the exact self-energy in many frequency domains. (ii) An odd-perturbation-order self-energy has a qualitatively wrong shape and, as a result, many roots of the corresponding Dyson equation are nonphysical in that the poles may be complex or residues can exceed unity or be negative. (iii) A higher even-order self-energy consists of vertical lines at many frequencies, predicting numerous phantom poles with zero residues. (iv) Infinite partial resummations of diagrams by vertex or edge renormalization tend to exacerbate these pathologies. (v) The nonconvergence is caused by the nonanalyticity of the rational-function form of the exact Green's function at many frequencies, where the radius of convergence of its Taylor expansion is zero. This is consistent with the fact that (vi) Padé approximants (power-series expansions of a rational function) can largely restore the correct shape and poles of the Green's function. Nevertheless, not only does the nonconvergence render higher-order Feynman-Dyson diagrammatic perturbation theory useless for many lower-lying ionization or higher-lying electron-attachment states but it also calls into question the validity of its combined use with the Ansätze requiring the knowledge of all poles and residues. Such Ansätze include the Galitskii-Migdal identity, the self-consistent Green's function methods, and some models of the algebraic diagrammatic construction.

Fluctuations can challenge the possibility of improving work extraction from quantum correlations. This uncertainty in the work extraction process can be addressed by resorting to the expected utility hypothesis, which can provide an optimal method for work extraction. We study a bipartite quantum system and examine the role of quantum correlations in a daemonic work extraction performed by certain local operations and classical communication. Specifically, we demonstrate and explain how, depending on the so-called absolute risk aversion, a non-neutral risk agent, influenced by fluctuations, views quantum correlations differently from a neutral risk agent that is affected solely by the average work.

The generation of squeezed Fock states by the one or more photon subtraction from a two-mode entangled Gaussian (TMEG) state is theoretically addressed. We showed that an arbitrary order Fock state can be generated this way and we obtained a condition that should be imposed on the parameters of the TMEG state to guarantee such a generation. We called the regime, in which this condition is satisfied, the universal solution regime. We showed that, for the first squeezed Fock state, the above condition is redundant such that the generation of the first squeezed Fock state is still possible by a one-photon subtraction from an arbitrary TMEG state. At the same time, the maximum generation probability of the first squeezed Fock state generation corresponds to the universal solution regime. We applied the above results to the description of generation of the squeezed Fock states using a beam splitter and a controlled-Z operation. We have estimated the parameters of such setups and input squeezed states, which are necessary to obtain squeezed Fock states with the maximum probability.

A mapping is made between fermion exchange and excluded volume in the quantum-classical isomorphism using polymer self-consistent field theory. Apart from exchange, quantum particles are known to be exactly representable in classical statistical mechanics as ring polymers, with contours that are parametrized by the inverse thermal energy, often called the imaginary time. Evidence in support of a previously used approximation for fermion exchange in ring polymer self-consistent field theory is given, specifically, that the use of all-contour interactions in the mean field picture instead of equal imaginary time interactions is justified based on the symmetry of ring polymers. It is also shown that the removal of forbidden thermal trajectories, both those that violate excluded volume directly and those that represent topologically inaccessible microstates, is equivalent to antisymmetric exchange. The electron density of the beryllium atom is calculated with ring polymer self-consistent field theory ignoring classical correlations, and very good agreement is found with Hartree-Fock theory which also neglects Coulomb correlations. The total binding energies agree to within less than $6\%$, which, while still far from chemical accuracy, is remarkable given that the field theory equations are derived from first principles with zero free parameters. The discrepancy between self-consistent field theory and Hartree-Fock theory is attributed to classical Coulomb self-interactions which are included in Hartree-Fock theory but not in self-consistent field theory. A potential method to improve the agreement by more accurately representing electron-electron self-interactions in self-consistent field theory is discussed, as are the implications for quantum foundations of the quantum-classical mapping between fermion exchange and thermal trajectory excluded volume.

In this paper we study the dispersive readout of a driven three-level atom weakly interacting with a passive cavity that couples to an active cavity. The system excluding the three-level atom exhibits a parity-time ($\mathcal{P}\mathcal{T}$) symmetric phase transition at the exceptional point (EP), which originates from the balance between dissipation of the passive cavity and gain of the active cavity. The perturbation to the passive cavity induced by the three-level atom can be amplified near the EP, where the eigenvalues of the effective Hamiltonian have significant differences when the three-level atom is in the excited, metastable, and ground states, respectively. Applying the modified Laplace transformation and input-output theory near the EP, we can realize the dispersive readout of the three-level atom weakly interacting with coupled cavities, which can be characterized through the different distributions of the transmission spectrum of the passive cavity and the ratio of the active cavity excitation number to the input photon number corresponding to the different levels of the three-level atom. Moreover, we generalize the dispersive readout method to the non-Markovian regime, which is in good agreement with that obtained by the Markovian approximation. We find that the non-Markovian effects of the environment backacting on the system dynamics can lead to the enhancement of the dispersive readout for the three-level atom, which is revealed by the excitation backflow generated in the interaction between the passive cavity and environment. The dispersive readout proposed is conducive to understanding the influences of $\mathcal{P}\mathcal{T}$ symmetry and the non-Markovian effect on dispersive readout, which offers the possibility of an alternative field of possible applications for quantum information and quantum communication.

The photoassociation (PA) of a rubidium dimer in a dark magneto-optical trap (MOT) is studied using atom-cavity collective strong coupling. This allows nondestructive detection of the molecule formation process as well as rapid and repeated interrogation of the atom-molecule system. The vacuum Rabi splitting (VRS) measurements from the bright MOT are carefully calibrated against equivalent measurements with fluorescence. Further loading rates in the dark MOT are determined using VRS. This method provides a reliable, fast, and nondestructive detection scheme for detecting the PA using the free atoms coupled to a cavity when the atoms are in a nonfluorescing state.

We present a theory of cascade emission from an array of $N$ fixed, “three-level” atoms. The total angular momentum of the ground state of each atom is $J=0$, that of the intermediate state is $J=1$, and that of the upper state is $J=0$. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of $N$ atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.

Absorption and gain processes are fundamental to any light-matter interaction and a precise measurement of these parameters is important for various scientific and technological applications. Quantum probes, specifically the squeezed states, have proved very successful, particularly in the applications that deal with phase shift and force measurements. In this paper, we focus on improving the sensitivity of the estimation of the photon-loss coefficient of a weakly absorbing medium as well as the estimation of the gain parameter using a two-mode bright squeezed state. The generation of this state combines the advantage of a coherent beam for its large photon number with the quantum properties of the two-mode squeezing operation in an optical parametric amplifier. We present two measurement schemes: balanced photodetection and time-reversed metrology, both utilizing two-mode bright squeezed light. The maximum quantum advantage we can achieve using two-mode bright squeezed light is 3.7 times for the absorption parameter $\alpha =0.05$ and 8.4 times for $\alpha =0.01$ as compared to using only the coherent state. Similarly, the maximum quantum advantage for the estimation of optical gain is found around 2.95 times for the gain coefficient $G=1.05$ and around 6.35 times for $G=1.01$. We discuss the significance of using one measurement scheme over the other under different squeezing conditions. We compare our results with the Cramér-Rao bound for a two-mode bright squeezed state to assess the quality of the proposed methodologies.

Much recent work has been devoted to the study of information scrambling in quantum systems. In this paper, we study the long-time properties of the algebraic out-of-time-order-correlator (“$\mathcal{A}\text{−}\mathrm{OTOC}$”) and derive an analytical expression for its long-time average under the nonresonance condition. The $\mathcal{A}\text{−}\mathrm{OTOC}$ quantifies quantum scrambling with respect to degrees of freedom described by an operator subalgebra $\mathcal{A}$, which is associated with a partitioning of the corresponding system into a generalized tensor product structure. Recently, the short-time growth of the $\mathcal{A}\text{−}\mathrm{OTOC}$ was proposed as a criterion to determine which partition arises naturally from the system's unitary dynamics. In this paper, we extend this program to the long-time regime where the long-time average of the $\mathcal{A}\text{−}\mathrm{OTOC}$ serves as the metric of subsystem emergence. Under this framework, natural system partitions are characterized by the tendency to minimally scramble information over long timescales. We consider several physical examples, ranging from quantum many-body systems and stabilizer codes to quantum reference frames, and perform the minimization of the $\mathcal{A}\text{−}\mathrm{OTOC}$ long-time average both analytically and numerically over relevant families of algebras. For simple cases subject to the nonresonant condition, minimal $\mathcal{A}\text{−}\mathrm{OTOC}$ long-time average is shown to be related to minimal entanglement of the Hamiltonian eigenstates across the emergent system partition. Finally, we conjecture and provide evidence for a general structure of the algebra that minimizes the average for nonresonant Hamiltonians.