We study the properties of a Bose-Einstein-condensate (BEC)–impurity mixture at finite temperature employing the time-dependent Hartree-Fock Bogoliubov (TDHFB) theory which is a set of coupled nonlinear equations of motion for the condensate and its normal and anomalous fluctuations on the one hand and for impurity on the other. The numerical solutions of these equations in the static quasi-one-dimensional regime show that the thermal cloud and the anomalous density are deformed as happens to the condensate and the impurity becomes less localized at nonzero temperatures. Effects of the BEC fluctuations on the self-trapping state are studied in homogeneous weakly interacting BEC-impurity at low temperature. The self-trapping threshold is also determined in such a system. The formation of solitons in the BEC-impurity mixture at finite temperature is investigated.

The linear driving for a single-mode optical field in a cavity can result from the external driving of a classical field even when the coupling between the classical field and the cavity is weak. We revisit this well-known effect with a microscopic model where a classical field is applied to a wall of the cavity to excite the atoms in the wall, and recombination of the low excitations of the wall mediates a linear driving for the single-mode field inside the cavity. With such modeling about the indirect driving through the quantum excitations of the wall, we theoretically predict several nonlinear optical effects for the strong-coupling cases, such as photon antibunching and photon squeezing. We propose a greatly simplified nonlinear quantum photonics model.

The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the relativistic Dirac equation and second-order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W\left(\theta \right)\sim 1+{cos}^2\theta$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W\left(\theta \right)\sim 1-1/3{cos}^2\theta$ while the polarizations of the emitted photons are orthogonal, where $\theta$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.

We present a simple tomographic protocol, for two-qubit systems, that relies on a single discriminatory transition and no direct spatially selective imaging. This scheme exploits excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. We demonstrate a two-qubit entangling gate with a Bell state production fidelity of 0.981(6), and apply the above protocol to perform the first quantum process tomography of a Mølmer-Sørensen entangling gate. We characterize its $\chi$-process matrix, the simplest for an entanglement gate on a separable-states basis, and observe that our dominant source of error is accurately modeled by a quantum depolarization channel.

We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete measurements can improve the tomographic efficiency significantly over minimal measurements when the states of interest have high purities. Nevertheless, the efficiency is still too limited to be satisfactory with respect to figures of merit based on monotone Riemannian metrics, such as the Bures metric and quantum Chernoff metric. In this way, we also pinpoint the limitation of nonadaptive measurements and motivate the study of more sophisticated measurement schemes. In the course of our study, we introduce the best linear unbiased estimator and show that it is equally efficient as the maximum likelihood estimator in the large sample limit. This estimator may significantly outperform the canonical linear estimator for states with high purities. It is expected to play an important role in experimental designs and adaptive quantum state tomography besides its significance to the current study.

Recent attoclock experiments using the attosecond angular streaking technique enabled the measurement of the tunneling time delay during laser-induced strong-field ionization. One of the theoretical models for the tunneling time delay is the Wigner time delay, which is the asymptotic time difference between the quasiclassical and the Wigner trajectories. The latter is derived from the derivative of the phase of the electron steady-state wave function with respect to energy. Here, we present an alternative method for the calculation of the Wigner trajectory by using the fixed-energy propagator. The developed formalism is applied to the nonrelativistic regime as well as to the relativistic regime of the tunnel-ionization process from a zero-range potential. Finally, it is shown that the Wigner time delay is measurable in the near-threshold-tunneling regime within the current state of the momentum spectroscopy via detecting the induced electron momentum shift in a mixture of two gas species.

Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite separability of continuous-variable three-mode quantum states. These conditions have the form of inequalities for higher-order moments of linear combinations of the mode operators. They enable one to distinguish between all possible kinds of tripartite separability, while the strongest violation of these inequalities is a sufficient condition for genuine tripartite entanglement. We construct Gaussian states for which the violation of our conditions grows exponentially with the order of the moments of the mode operators. By going beyond second moments, our conditions are expected to be useful as well for the detection of tripartite entanglement of non-Gaussian states. We also demonstrate that our conditions can be easily implemented experimentally.

We develop a theory for the interaction of multilevel atoms with multimode cavities yielding cavity-enhanced multiphoton resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realized when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the Fredkin gate and iswap operation; the system seems promising for scalability.

The transformation design method of momentum for matter waves in a harmonic trap is proposed. As applications, we design (1) a momentum invisibility cloak to control the distribution of a wave function in momentum space, (2) a quantum localization cloak that localizes a matter wave around zero momentum, and (3) the unusual quantum states of momentum space. Comprehension of these momentum cloaks in position space through the Fourier transformation is presented. In contrast to the construct of quantum cloaks in position space, the momentum cloaks presented here can only be reached by controlling the spring parameter of the trap and offering a potential there, without needing to control the effective mass of quantum particles themselves. The presented discussions also provide a possible inspiration to help localize and maintain a quantum state in momentum space by way of controlling the shape of a trap and a supplied potential.

Floquet states are signatured by pseudoeigenvalues which are discretely separated by the photon energy. Similarly, the laser-assisted photoemission effect (LAPE) induces electron-photon energy exchange (with momentum change), and also results in a discrete energy distribution. Both effects result from coherent interactions of electrons and photons. Here, we investigate the coherent interference between a Floquet state and the LAPE effect.

We generate spin currents in an ${}^{87}\mathrm{Rb}$ spin-2 Bose-Einstein condensate by application of a magnetic field gradient. The spin current destroys the spin polarization, leading to a sudden onset of two-body collisions. In addition, the spin coherence, as measured by the fringe contrast using Ramsey interferometry, is reduced drastically but experiences a weak revival due to in-trap oscillations. The spin current can be controlled using periodic $\pi$ pulses (bang-bang control), producing longer spin-coherence times. Our results show that spin coherence can be maintained even in the presence of spin currents, with applications to quantum sensing in noisy environments.

The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude.

We show that the propagation direction of the Dirac-cone modes of photonic-crystal slabs can be continuously controlled by the polarization of the incident wave. This property is realized by their isotropic dispersion relation and anisotropic mixture of two dipolar wave functions. To clarify these features, we formulate a Green-function method to describe the excitation process of the Dirac-cone modes and analyze the coupling strength with the incident wave by group theory. This angular dependence of the intensity distribution of the excited wave can be used for experimentally detecting the Dirac cones and distinguishing their mode symmetry.

It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of Einstein-Podolsky-Rosen (EPR)-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loophole, of course), for a given number $n$ of measurement settings. We allow for arbitrary measurement directions, and arbitrary weightings of the outcomes in the EPR-steering inequality. This is a difficult optimization problem for large $n$, so we also consider more practical ways of constructing near-optimal EPR-steering inequalities in this limit.

In this paper, we have calculated parity nonconserving electric dipole amplitudes of the hyperfine components for the transitions between the ground and first excited states of ${}^{137}{\mathrm{Ba}}^{+}$ and ${}^{87}{\mathrm{Sr}}^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin-dependent amplitudes from experimental measurements. The wave functions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.

We follow the alignment-assisted orientation technique proposed by Zhang et al. [Phys. Rev. A 83, 043410 (2011)] to experimentally demonstrate a substantial enhancement of the field-free orientation by using a combination of single- and two-color laser pulses. When a two-color orienting pulse is preceded by a single-color aligning pulse by a suitable time, the resulting orientation is thrice as large as that obtained with the two-color pulse alone. We ensure that the orientation is the result of the hyperpolarizability interaction rather than ionization depletion by keeping the ionization due to the pump pulses small and demonstrate a useful level of orientation without the complications of a partially ionized target.

We present a general theory for calculating the damping rate of elementary density-wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density-wave mode, predicted recently by Kónya et al. [Phys. Rev. A 89, 051601(R) (2014)]. The given density-wave mode constitutes the polaritonlike soft mode of the self-organization phase transition. The resonant enhancement takes place, in both the normal and the ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density-wave modes.

We analyze the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the nonlinear Schrödinger model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first-order correlation function behave with respect to the mass, the energy, and the size of the system. By relating the free-particle energy to the temperature, we are able to estimate the Berezinskii-Kosterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size independent, leading to a power-law dependence of the condensate fraction with respect to the system size.

We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory.