By placing an atom into a cavity, the electromagnetic mode structure of the cavity is modified. In cavity QED, one manifestation of this phenomenon is the appearance of a gauge-dependent diamagnetic term, known as the $A^2$ contribution. Although in atomic cavity QED, the resulting modification in the eigenmodes is negligible, in recent superconducting circuit realizations, such corrections can be observable and may have qualitative implications. We revisit the canonical quantization procedure of a circuit-QED system consisting of a single superconducting transmon qubit coupled to a multimode superconducting microwave resonator. A complete derivation of the quantum Hamiltonian of an open circuit-QED system consisting of a transmon qubit coupled to a leaky transmission line cavity is presented. We introduce a complete set of modes that properly conserves the current in the entire structure and present a sum rule for the dipole transition matrix elements of a multilevel transmon qubit coupled to a multimode cavity. Finally, an effective multimode Rabi model is derived with coefficients that are given in terms of circuit parameters.

We investigate Landau-Zener processes modeled by a two-level quantum system, with its finite bias energy varied in time and in the presence of a single broadened cavity mode at zero temperature. By applying the hierarchy equation method to the Landau-Zener problem, we computationally study the survival fidelity of adiabatic states without Born, Markov, rotating-wave, or other perturbative approximations. With this treatment it also becomes possible to investigate cases with very strong system-bath coupling. Different from a previous study of infinite-time Landau-Zener processes, the fidelity of the time-evolving state as compared with instantaneous adiabatic states shows nonmonotonic dependence on the system-bath coupling and on the sweep rate of the bias. We then consider the effect of applying a counterdiabatic driving field, which is found to be useful in improving the fidelity only for sufficiently short Landau-Zener processes. Numerically exact results show that different counterdiabatic driving fields can have very different robustness against environment effects. Lastly, using a case study, we discuss the possibility of introducing a dynamical decoupling field in order to eliminate the decoherence effect of the environment and, at the same time, to retain the positive role of a counterdiabatic field. Our work indicates that finite-time Landau-Zener processes with counterdiabatic driving offer a fruitful testbed to understand controlled adiabatic processes in open systems.

The existence of higher-order entanglement in the stimulated and spontaneous Raman processes is established using the perturbative solutions of the Heisenberg equations of motion for various field modes that are obtained using the Sen-Mandal technique and a fully quantum mechanical Hamiltonian that describes the stimulated and spontaneous Raman processes. Specifically, the perturbative Sen-Mandal solutions are exploited here to show the signature of the higher-order two-mode and multimode entanglement. In some special cases, we have also observed higher-order entanglement in the partially spontaneous Raman processes. Further, it is shown that the depth of the nonclassicality indicators (parameters) can be manipulated by the specific choice of coupling constants, and it is observed that the depth of nonclassicality parameters increases with the order.

We construct an entanglement witness for many-qubit systems, based on symmetric two-body correlations with two measurement settings. This witness is able to detect the entanglement of some Dicke states for any number of particles and such detection exhibits some robustness against white noise and thermal noise under the Lipkin-Meshkov-Glick Hamiltonian. In addition, it detects the entanglement of spin-squeezed states, with a detection strength that approaches the maximal value for sufficiently large numbers of particles. As spin-squeezed states can be experimentally generated, the properties of the witness with respect to these states may be amenable to experimental investigation. We show that while the witness is unable to detect Greenberger-Horne-Zeilinger (GHZ) states, it is instead able to detect superpositions of Dicke states with GHZ states.

Relativistic two-photon decay rates of the $2s_{1/2}$ and $2p_{1/2}$ states towards the $1s_{1/2}$ ground state of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. Highly accurate values are obtained by a simple calculation involving different meshes for the initial, final, and intermediate wave functions and for the calculation of matrix elements. The accuracy of the results with a Coulomb potential is improved by several orders of magnitude in comparison with benchmark values from the literature. The general requirement of gauge invariance is also successfully tested, down to rounding errors. The method provides high accuracies for two-photon decay rates of a particle in other potentials and is applied to a hydrogen atom embedded in a Debye plasma simulated by a Yukawa potential.

The local spin dynamics of the electron is studied from the viewpoint of the electric dipole moment (EDM) of the electron in the framework of the quantum field theory. The improvements of the computational accuracy of the effective electric field $\left({\mathcal{E}}_{\mathrm{eff}}\right)$ for the EDM and the understanding of spin precession are important for the experimental determination of the upper bound of the EDM. Calculations of ${\mathcal{E}}_{\mathrm{eff}}$ in YbF $\left({}^2{\mathrm{\Sigma }}_{1/2}\right)$, BaF $\left({}^2{\mathrm{\Sigma }}_{1/2}\right)$, ThO $\left({}^3{\mathrm{\Delta }}_1\right)$, and ${\mathrm{HF}}^{+} \left({}^2{\mathrm{\Pi }}_{1/2}\right)$ are performed on the basis of the restricted active space configuration interaction approach by using the four-component relativistic electronic structure calculation. The spin precession is also discussed from the viewpoint of local spin torque dynamics. We show that a contribution to the torque density for the spin is brought into by the EDM. Distributions of the local spin angular momentum density and torque densities induced by external fields in the above molecules are calculated and a property related with large ${\mathcal{E}}_{\mathrm{eff}}$ is discussed.

We present fully differential cross-section ratios for electron-impact ionization of helium without excitation and with simultaneous excitation of the residual ion. The results are obtained from a nonperturbative close-coupling formalism, with the resulting equations being solved by a $B$-spline $R$-matrix-with-pseudostates approach. Very encouraging agreement is obtained with directly measured cross-section ratios for ionization leaving the residual ${\mathrm{He}}^{+}$ ion in either the $1s$ ground state or the $n=3(3s+3p+3d)$ excited states.

We demonstrate the observation of quasiperiodic revivals out to 27 ps in an impulsively aligned asymmetric-top molecule, sulfur dioxide $\left({\mathrm{SO}}_2\right)$, at high sample temperature and density (295 K, 0.5 bar). We find that the asymmetric top exhibits a strong correlation between population alignment and population lifetime $\left(r=0.97\right)$, in accordance with the trend observed in linear molecules. We use a linear birefringence measurement fit to a full quantum simulation of the asymmetric rotor and are able to separately measure both the population $\left({\mathrm{T}}_1\right)$ and coherence $\left({\mathrm{T}}_2\right)$ lifetimes of the rotational wave packet. Additionally, we observe a high rate of elastic decoherence $\left({\mathrm{T}}_2^{*}=9.6\mathrm{ps}\right)$ and attribute this to long-range interactions mediated by the permanent dipole of the ${\mathrm{SO}}_2$ molecule. We propose the use of birefringence measurements to study intermolecular interactions in a coherent ensemble, as a step toward using field-free alignment to investigate reaction dynamics and dissipative processes.

Using a time-dependent density-functional-theory (TDDFT) method, we calculated the high-harmonic generation (HHG) spectra of ${\mathrm{N}}_2$ in 800- and 1300-nm intense lasers. The calculations reproduce the experimentally observed minimum near 40 eV and the shift of the minimum due to interference of different molecular orbitals. They also support the proposed shape resonance near 30 eV. The TDDFT method allows us to analyze the involvement of different electronic configurations in the HHG process. We identified a significant role of Rydberg states and autoionizing states in enhancing HHG. This finding is consistent with studies of photoelectron spectra in a similar energy range. Moreover, we discover a significant contribution of the $2{\sigma }_g$ orbital above 40 eV, demonstrating the complexity of electronic structure information contained in molecular HHG. At high energy not only the HOMO and HOMO-1 are important, as suggested by earlier studies, but the HOMO-3 contributes substantially as well.

The exact velocity-gauge minimal-coupling Hamiltonian describing the laser-matter interaction is transformed into another form by means of a series of gauge transformations. The Hamiltonian corresponding to this point of view is valid for an arbitrary time- and space-dependent laser field, also known as a nondipole field. In effect, the Hamiltonian represents a generalization of the original velocity-gauge minimal-coupling Hamiltonian in the sense that the particle's (classical) velocity in the laser propagation direction is also explicitly accounted for by a new operator term. Imposing the so-called long-wavelength approximation (LWA) on the field, i.e., assuming the laser wavelength being much larger than the extent of the atomic system, the spatial dependence of the field can be neglected and the interaction Hamiltonian reduces to a simpler form. Nevertheless, the resulting LWA Hamiltonian includes the effect of the magnetic-field component of the laser, which is in clear contrast with the usual dipole approximation Hamiltonian derived by imposing the LWA directly on the initial velocity-gauge minimal-coupling Hamiltonian. As such, the weak-field condition necessary to justify neglecting the magnetic field, and the LWA condition, can be considered independently in this formalism, making it an attractive alternative for a broad range of applications in strong-field physics. We demonstrate that, from a numerical perspective, this form of the light-matter interaction is advantageous compared to its standard velocity-gauge counterpart as it gives rise to faster convergence properties when describing ionization dynamics in superintense fields beyond the dipole approximation.

We investigate the specific heat at constant volume $C_V$ in the Bardeen-Cooper-Schrieffer–Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\mathrm{c}}$. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gtrsim T_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a ${}^6\text{Li}$ unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.

We calculate how correlations in a Bose lattice gas grow during a finite-speed ramp from the Mott to the superfluid regime. We use an interacting doublon-holon model, applying a mean-field approach for implementing hard-core constraints between these degrees of freedom. Our solutions are valid in any dimension and agree with experimental results and with density matrix renormalization group calculations in one dimension. We find that the final energy density of the system drops quickly with increased ramp time for ramps shorter than one hopping time, $J{\tau }_{\text{ramp}}\lesssim 1$. For longer ramps, the final energy density depends only weakly on ramp speed. We calculate the effects of inelastic light scattering during such ramps.

We study the concavity of the dispersion relation $q\mapsto {\omega }_{\mathbf{q}}$ of the bosonic excitations of a three-dimensional spin-$\frac{1}{2}$ unpolarized Fermi gas in the random-phase approximation. In the limit of small wave numbers $q$, we obtain analytically the spectrum up to order 5 in $q$. In the neighborhood of $q=0$, a change in concavity between the convex Bose-Einstein condensation limit and the concave BCS limit takes place at $\mathrm{\Delta }/\mu \simeq 0.869 \left(1/k_{F}a\simeq -0.144\right)$, where $a$ is the scattering length between opposite spin fermions, $k_F$ is the Fermi wave number and $\mathrm{\Delta }$ the gap according to BCS theory, and $\mu$ is the chemical potential. At that point the branch is concave due to a negative fifth-order term. Our results are supplemented by a numerical study that shows the border between the zone of the $(q,\mathrm{\Delta })$ plane where $q\mapsto {\omega }_{\mathbf{q}}$ is concave and the zone where it is convex.

Unlike the Coulomb potential that acts between all semiconductor carriers, the potential commonly used for BCS superconductors and cold-atom gases acts between different fermion species only, these species differing by their spin or hyperfine index. The coboson formalism we develop here evidences that such composite bosons interact through fermion exchange only, thus rendering the structure of the Shiva diagrams that visualize their many-body effects far simpler. A separable potential is used to obtain analytical results for the $N$-coboson normalization factor and the $N$-coboson ground-state energy within the Born approximation, in terms of the Born dimer-dimer scattering length. This formalism opens the route toward approaching complex many-body effects, such as Bose-Einstein condensation, through a different perspective.

We show that a trapped-ion chain interacting with an optical spin-dependent force shows strong frustration effects due to the interplay between long range interactions and the dressing by optical phases. We consider a strong spin-phonon coupling regime and predict a quantum phase diagram with different competing magnetic and structural orders. In a highly frustrated region, the system shows enhanced quantum fluctuations and entanglement, which are characteristic of spin-liquid phases. We propose and describe within a mean-field approach a quantum annealing process to induce a quasiadiabatic evolution towards the ground state.

The Stokes-Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations with Kleinman symmetry. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, the relations between components of nonlinear susceptibility tensor and Mueller matrix are explicitly provided. The approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.

We propose that a pulsed quantum optomechanical system can be applied to the problem of quantum parameter estimation, which targets yielding a higher precision of parameter estimation utilizing quantum resources than using classical methods. Concentrating mainly on the quantum Fisher information with respect to the mechanical frequency, we find that the corresponding precision of parameter estimation for the mechanical frequency can be enhanced by applying applicable optical resonant pulsed driving to the cavity of the optomechanical system. Further investigation shows that the mechanical squeezing resulting from the optical pulsed driving is the quantum resource used in optimal quantum estimation of the frequency.

We study all-optical switches operating on a single four-level atom with the $N$-type transition configuration in a two-mode nanofiber cavity with a significant length (on the order of 20 mm) and a moderate finesse (on the order of 300) under the electromagnetically induced transparency (EIT) conditions. In our model, the gate and probe fields are the quantum nanofiber-cavity fields excited by weak classical light pulses, and the parameters of the $D_2$ line of atomic cesium are used. We examine two different switching schemes. The first scheme is based on the effect of the presence of a photon in the gate mode on the EIT of the probe mode. The second scheme is based on the use of EIT to store a photon of the gate mode in the population of an appropriate atomic level, which leads to the reduction of the transmission of the field in the probe mode. We investigate the dependencies of the switching contrast on various parameters, such as the cavity length, the mirror reflectivity, and the detunings and powers of the cavity driving field pulses. For a nanofiber cavity with fiber radius of 250 nm, cavity length of 20 mm, and cavity finesse of 313 and a cesium atom at a distance of 200 nm from the fiber surface, we numerically obtain a switching contrast on the order of about 67% for the first scheme and of about 95% for the second scheme. These switching operations require small mean numbers of photons in the nanofiber cavity gate and probe modes.

It has been found that Markovian quantum dissipative processes, described by the Lindblad equation, may have attractive steady-state manifolds, in which dissipation and decoherence can play a positive role to quantum information processing. In this article, we show that such attractive steady-state manifolds with the same positive features as in Markovian dissipative processes can exist in the non-Markovian dissipative processes. Our finding indicates that the dissipation-assisted schemes implemented in the Markovian systems can be directly generalized to the non-Markovian systems.