We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially, the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength $U$ suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of $U$, it does equilibrate or relax well into a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decohered density matrix, a second quench is considered. It turns out that the answer is affirmative or negative depending on whether the intermediate value of $U$ is zero or not.

We study the polarization-dependent second-order correlation of a pair of photons emitted in a four-level radiative cascade driven by an external field. It is found that the quantum correlations of the emitted photons, degraded by the energy splitting of the intermediate levels in the radiative cascade, can be efficiently revived by a far-detuned external field. The physics of this revival is linked to an induced Stark shift and the formation of dressed states in the system by the nonresonant external field. Furthermore, we investigated the competition between the effect of the coherent external field and incoherent dephasing of the intermediate levels. We find that the degradation of quantum correlations due to the incoherent dephasing can be contained for small dephasing with the external field. We also studied the nonlocality of the correlations by evaluating the Bell inequality in the linear polarization basis for the radiative cascade. We find that the Bell parameter decreases rapidly with increase in the intermediate-level energy splitting or incoherent dephasing rate to the extent that there is no violation. However, the presence of an external field leads to control over the degrading mechanisms and preservation of nonlocal correlation among the photons. This in turn can induce a violation of Bell’s inequality in the radiative cascade for arbitrary intermediate-level splitting and small incoherent dephasing.

Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate nonclassicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of nonclassicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.

We present a generalized variational method to analytically obtain the ground-state properties of the Jaynes-Cummings model with the ultrastrong coupling. An explicit expression for the ground-state energy, which agrees well with the numerical simulation in a wide range of the experimental parameters, is given. In particular, the introduced method can successfully solve this Jaynes-Cummings model with the positive detuning (the atomic resonant level is larger than the photon frequency), which cannot be treated in the adiabatical approximation and the generalized rotating-wave approximation. Finally, we also demonstrate analytically how to control the mean photon number by means of the current experimental parameters including the photon frequency, the coupling strength, and especially the atomic resonant level.

We have observed a linear pressure dependence of longitudinal relaxation time $T_1$ at 4.2 and 295 K in gaseous ${}^3\mathrm{He}$ cells made of either bare Pyrex glass or Cs- or Rb-coated Pyrex due to paramagnetic sites in the cell wall. The paramagnetic wall relaxation is previously thought to be independent of ${}^3\mathrm{He}$ pressure. We develop a model to interpret the observed wall relaxation by taking into account the diffusion process, and our model gives a good description of the data.

We analyze an ambiguity in previous works on entanglement of fermionic fields in noninertial frames. This ambiguity, related to the anticommutation properties of field operators, leads to nonunique results when computing entanglement measures for the same state. We show that the ambiguity disappears when we introduce detectors, which are in any case necessary as a means to probe the field entanglement.

We analyze correlated photoelectron spectra of single-photon two-electron ionization [double photoionization (DPI)] of helium to reconstruct the phase of the spectral amplitude of this process. The phase can be reconstructed reliably in a wide range of photoelectron momenta, thus allowing one to retrieve information about the wave function of the DPI process and its temporal evolution. Our simulation indicates that the proposed phase reconstruction technique can be applied in experiment to trace dynamics of the DPI process with attosecond precision.

We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$-orbital bands in both two- and three-dimensional optical lattices. Due to the quasi-one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$ orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high-dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in the phase diagram. These FFLO phases are stable with the imposition of the inhomogeneous trapping potential. Their entropies are comparable to the normal states at finite temperatures.

We investigate the single-particle time evolution and two-particle quantum correlations in a one-dimensional $N$-site lattice with a site-dependent nearest-neighbor tunneling function $t_{\alpha }(k)=t_0[k(N-k)]{}^{\alpha /2}$. Since the bandwidth and the energy-level spacings for such a lattice both depend upon $\alpha$, we show that the observable properties of a wave packet, such as its spread and the relative phases of its constituents, vary dramatically as $\alpha$ is varied from positive to negative values. We also find that the quantum correlations are exquisitely sensitive to the form of the tunneling function. Our results suggest that arrays of waveguides with position-dependent evanescent couplings will show rich dynamics with no counterpart in present-day, traditional systems.

We present a procedure for subwavelength optical microscopy. The identical atoms are distributed on a plane and shined with a standing wave. We rotate the plane to different angles and record the resonant fluorescence spectra in the far field, from which we can obtain their distance and location information. This procedure also works for atomic separation above one wavelength and therefore provides a seamless microscopy.

Recent experiments [K. R. Brown et al., Nature (London) 471, 196 (2011); M. Harlander et al., Nature (London) 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the ions. Our proposal operates beyond the usual Lamb-Dicke limits and could be applied to the scalable ion traps coupled by their vibrations.

The dynamics of entanglement between two-level atoms interacting with a common squeezed reservoir is investigated. It is shown that for spatially separated atoms there is a unique asymptotic state depending on the distance between the atoms and the atom-photons detuning. In the regime of strong correlations there is a one-parameter family of asymptotic steady states depending on the initial conditions. In contrast to the thermal reservoir, both types of asymptotic states can be entangled. We calculate the amount of entanglement in the system in terms of concurrence.

We perform close-coupling molecular and classical trajectory Monte Carlo (CTMC) calculations of charge-exchange probabilities in low-energy ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}+\mathrm{H}$ collisions. We consider head-on collisions with a zero impact parameter and study the dependence of the charge-exchange probability on the impact velocity. This probability exhibits oscillations generally understood as signatures of quantum phase effects. CTMC calculations with dimensionality reduced to one fairly reproduce the oscillations and show that these latter stem from the back and forth motion of the electron between the nuclear centers in the internuclear region. In three dimensions, the probability oscillations are generally washed out in the statistical CTMC framework because of the electron transverse degrees of freedom. However three-dimensional Bohmian trajectories ascertain the classical interpretation of the oscillations in a quantum framework.

Nonperturbative $R$-matrix and perturbative distorted-wave methods are used to calculate electron-impact ionization cross sections for ${\mathrm{C}}^{3+}$ in excited states. Convergence studies for the cross sections of the $1s^{2}5s$ excited configuration reveal that both the $R$-matrix and distorted-wave methods need fairly high ejected electron angular momenta. Reasonable agreement is found between the converged $R$-matrix and distorted-wave cross sections. Thus, the use of the computationally less demanding distorted-wave method as a tool for the $n$ scaling of excited-state ionization cross sections appears to be reasonable for atomic ions with charge $q⩾3$.

The symmetry-adapted-cluster (SAC) configuration-interaction (CI) theory was introduced to interpret the non-coplanar symmetric ($e$,$2e$) results. Dyson orbitals derived from the bench-marked SAC CI general-R method were utilized for computing the electron momentum distributions. The corresponding excitation energies and spectroscopic factors can be used to reproduce the ionization spectra. The implementation was demonstrated by examples of ${\mathrm{N}}_2$ and ${\mathrm{H}}_2$O. The electron momentum distributions calculated using SAC CI method were compared with recent experimental results, as well as the Hartree-Fock and density-functional-theory calculations. The SAC CI method gave the best performance on the description of the experimental momentum distributions. It was found that the electron momentum distributions of Dyson orbitals related to the satellite lines can be notably different from those of their parent orbitals due to the electron correlation in the initial target states. Present work demonstrated that the SAC CI theory is a very useful and accurate tool for interpreting high-resolution electron momentum spectroscopy results.

We theoretically investigate the high-temperature thermodynamics of a strongly interacting trapped Fermi gas near either $s$-wave or $p$-wave Feshbach resonances, using a second-order quantum virial expansion. The second virial coefficient is calculated based on the energy spectrum of two interacting fermions in a harmonic trap. We consider both isotropic and anisotropic harmonic potentials. For the two-fermion interaction, either $s$-wave or $p$-wave, we use a pseudopotential parametrized by a scattering length and an effective range. This turns out to be the simplest way of encoding the energy dependence of the low-energy scattering amplitude or phase shift. This treatment of the pseudopotential can be easily generalized to higher partial-wave interactions. We discuss how the second virial coefficient and thermodynamics are affected by the existence of these finite-range interaction effects. The virial expansion result for a strongly interacting $s$-wave Fermi gas has already been proved very useful. In the case of $p$-wave interactions, our results for the high-temperature equation of state are applicable to future high-precision thermodynamic measurements for a spin-polarized Fermi gas near a $p$-wave Feshbach resonance.

The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different ab initio methods: Hamiltonian lattice formalism using iterated eigenvector methods, Euclidean lattice formalism with auxiliary-field projection Monte Carlo methods, and continuum diffusion Monte Carlo methods with fixed and released nodes. We have calculated the ground-state energy of the unpolarized four-particle system in a periodic cube as a dimensionless fraction of the ground-state energy for the noninteracting system. We obtain values of $0.211(2)$ and $0.210(2)$ using two different Hamiltonian lattice representations, $0.206(9)$ using Euclidean lattice formalism, and an upper bound of $0.212(2)$ from fixed-node diffusion Monte Carlo methods. Released-node calculations starting from the fixed-node result yield a decrease of less than $0.002$ over a propagation of $0.4E_F^{-1}$ in Euclidean time, where $E_F$ is the Fermi energy. We find good agreement among all three ab initio methods.

A light impurity in a Fermi sea undergoes a transition from a polaron to a molecule for increasing interaction. We develop a method to compute the spectral functions of the polaron and molecule in a unified framework based on the functional renormalization group with full self-energy feedback. We discuss the energy spectra and decay widths of the attractive and repulsive polaron branches as well as the molecular bound state, and confirm the scaling of the excited-state decay rate near the transition. The quasiparticle weight of the polaron shifts from the attractive to the repulsive branch across the transition, while the molecular bound state has a very small residue characteristic for a composite particle. We propose an experimental procedure to measure the repulsive branch in a ${}^6\mathrm{Li}$ Fermi gas using rf spectroscopy and calculate the corresponding spectra.

We have theoretically studied the pulsed regime of electromagnetically induced transparency. In particular, simulations of propagation of Gaussian and $0\pi$ copropagating laser pulses in a medium consisting of three-level $\Lambda$ atoms have been performed. It has been found that even at the two-photon resonance, the length of propagation for the $0\pi$ pulses is much smaller than the one for the Gaussian probe pulses. Using the dark and bright basis, we explain this behavior. Some possible applications are discussed.