Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field [Atala et al., Nat. Phys. 10, 588 (2014)], we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the nonequilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We present a striking “slowing down” effect in the collective mode dynamics near the phase transition. This manifestation of a slowing down phenomenon near a quantum phase transition can be visualized unusually directly: The collective mode dynamics can be followed experimentally in real time and real space by imaging the atomic cloud.

We explain the probe field transmission spectrum under the influence of a strong pump field in a hybrid optomechanical system, composed of an optical cavity, a mechanical resonator, and a two-level atom. We show fast (superluminal) and slow (subluminal) light effects of the transmitted probe field in the hybrid system for suitable parametric regimes. For the experimental accessible domain, we find that the fast light effect obtained for the single optomechanical coupling can further be enhanced with the additional atom-field coupling in the hybrid system. Furthermore, we report the existence of a tunable switch from fast to slow light by adjusting the atomic detuning with the anti-Stokes and Stokes sidebands, respectively, as ${\mathrm{\Delta }}_a=+{\omega }_m$ and $-{\omega }_m$. The reported characteristics are realizable in state-of-the-art laboratory experiments.

The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in the optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation on the phase sensitivity. This kind of active SU(1,1) interferometer can also be realized in other systems, such as circuit quantum electrodynamics in microwave systems, which provides a different method for basic measurement using the hybrid interferometers.

We discuss the deterministic Gaussian entangling procedure between continuous variables of two directly noninteracting oscillators. The oscillators can only couple to the same mediating oscillator, which is initially at arbitrary noisy state and can be lost after the procedure. Unitary idealization of the procedure can generate large entanglement for any initial thermal noise of the mediator, thanks to the quantum version of the geometric phase. The generation of entanglement may considerably change when the procedure contains a weak dissipation. A robustness of this entangling procedure for weak dissipation is therefore a basic test of feasibility, especially in the limit of noisy mediator. We theoretically confirm the basic robustness of entanglement generation. Moreover, we suggest a nontrivial numerical optimization of the entangling procedure to approach an absolute robustness. For the weak dissipation, the optimization allows complete avoiding of the impact of the mediator noise. The suggested entangling procedure is therefore verified to be sufficiently robust for further development of quantum transducers.

We propose a dark-state cooling method of trapped ion systems in the Lamb-Dicke limit. By microwave dressing the ion, we can obtain two electromagnetically induced transparency structures. The heating effects caused by the carrier and the blue sideband transition vanish due to electromagnetically induced transparency effects and the final mean phonon numbers can be much lower than the recoil limit. Our scheme is robust to fluctuations of microwave power and laser intensities, which provides a broad cooling bandwidth to cool motional modes of a linear ion chain. Moreover, it is more suitable to cool four-level ions on a large-scale ion chip.

We study propagation of $\gamma$ radiation from a Mössbauer radioactive source through a vibrating recoilless resonant absorber and find the optimal conditions to produce a periodic train of $\gamma$-ray pulses with maximum peak intensity, several times higher than the intensity from the source, and minimum duration, much shorter than the lifetime of the emitting nuclear state of the source. The shape, duration, and repetition rate of the pulses are tunable in a wide range. We propose modifications of the recently reported experiment [F. Vagizov et al., Nature (London) 508, 80 (2014)] to produce pulses with higher peak intensity and shorter duration using absorbers enriched by the resonant nuclei and discuss possible applications of the generated pulses for the time-domain Mössbauer spectroscopy.

We investigate theoretically the quantum Rabi model in the large-detuning regime. When the frequency of the cavity field is near one-third of the atomic transition frequency, we show that there exists a resonant three-photon coupling via intermediate states connected by counter-rotating processes. We derive an effective Hamiltonian of the three-photon coupling, which determines the magnitude of the energy splitting and the position of the resonance analytically. In addition, we present a scheme of three-photon generation based on adiabatic passage across the resonance.

We investigate the weak measurement experiment demonstrated by Ritchie et al. [N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991)] from the viewpoint of the statistical hypothesis testing for the weak-value amplification proposed by Susa and Tanaka [Y. Susa and S. Tanaka, Phys. Rev. A 92, 012112 (2015)]. We conclude that the weak-value amplification is a better method to determine whether the crystal used in the experiment is birefringent than the measurement without postselection, when the angles of two polarizers are almost orthogonal. This result gives a physical description and intuition of the hypothesis testing and supports the experimental usefulness of the weak-value amplification.

We have measured the $3s_{1/2}\text{−}3p_{3/2}$ transition in sodiumlike ${\mathrm{Eu}}^{52+}$ situated at 41.232 Å with an uncertainty of 73 ppm. Our measurement extends previous high-precision measurements into the $56<Z<78$ range of atomic numbers. We also present measurements of $3s_{1/2}\text{−}3p_{3/2}$ and $3p_{1/2}\text{−}3d_{3/2}$ transitions in the neighboring magnesiumlike, aluminumlike, and siliconlike europium ions.

A fully quantum procedure, based on the numerical solution of the time-dependent Schrödinger equation (TDSE) with two spatial dimensions for every electron, is developed to study the attosecond double-ionization (DI) dynamics from aligned ${\mathrm{H}}_2$ molecules in strong laser fields. Our simulations are able to reproduce the orientation dependence of DI, as observed for ${\mathrm{N}}_2$ in experiments [D. Zeidler et al., Phys. Rev. Lett. 95, 203003 (2005)]. Our TDSE analyses reveal the important roles of the lateral motion of the electron and two-center interference in the orientation-dependent DI. Our results give suggestions on the ultrafast probing of the dynamics of DI from aligned molecules.

We present calculations of the Zeeman effect of narrow photoassociation lines of ${}^{40}\mathrm{Ca}$ near the ${}^{3}P_1+{}^{1}S_0$ asymptote. Using a coupled-channel model we find a nonlinear Zeeman effect that even at low fields of a few mT amounts to several kHz. With this model we analyze previous measurements and give corrected long-range dispersion coefficients of the ${}^3\mathrm{\Pi }_u$ and ${}^3\mathrm{\Sigma }_u^{+}$ states.

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of $2\pi$. In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of $m/2h$, where $m$ is the mass of the atoms and $h$ is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

We observe experimentally the spectral signature of the collision between a soliton and the dispersive wave initially emitted from the soliton itself. This collision, interpreted in terms of an optical event horizon, is controlled by the use of an axially varying fiber which allows us to shape both the soliton and dispersive wave trajectories so that they both collide at a precise location within the fiber. The interaction of the dispersive wave with the soliton generates a reflected wave with a conversion efficiency which can be controlled by the input pump power. These experimental results are confirmed by numerical solution of the generalized nonlinear Schrödinger equation and by the analytical calculation of the conversion efficiency.

The photon blockade based on weak nonlinearities is called the unconventional photon blockade. The study of the unconventional photon blockade in recent decades has mainly focused on the ${\chi }^{\left(3\right)}$ Kerr nonlinearity. In this paper, we study the photon blockade in two weakly coupled nonlinear cavities via ${\chi }^{\left(2\right)}$ nonlinearity, where ${\chi }^{\left(2\right)}$ mediates the conversion of a single photon in the cavity with high frequency into two photons with low frequency in another cavity. When the two cavity modes are driven simultaneously, our calculations show that the strong photon antibunching can be obtained in the cavity. The optimal condition for strong antibunching is found by analytic calculations and numerical simulations, and discussions of the optimal condition are presented. The differences between the present scheme and that with ${\chi }^{\left(3\right)}$ nonlinearity are discussed. This scheme is not sensitive to the change of decay rates, which makes the experimental realization easy.

We show that confluent Darboux-Crum transformations with emergent Jordan states are an effective tool for the design of optical systems governed by the Helmholtz equation under the paraxial approximation. The construction of generic, asymptotically real and periodic, $PT$-symmetric systems with local complex periodicity defects is discussed in detail. We show how the decay rate of the defect is related with the energy of the bound state trapped by the defect. In particular, the bound states in the continuum are confined by the periodicity defects with power law decay. We show that these defects possess complete invisibility; the wave functions of the system coincide asymptotically with the wave functions of the undistorted setting. The general results are illustrated with explicit examples of reflectionless models and systems with one spectral gap. We show that the spectral properties of the studied models are reflected by Lax-Novikov-type integrals of motion and associated supersymmetric structures of bosonized and exotic nature.

We investigate the spatiotemporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe and control fields, weaker probe pulses may propagate through the medium with low absorption and pulse shape distortion. In contrast, we find that increasing the probe pulse intensity leads to a splitting of the initially Gaussian pulse into a sequence of subpulses in the time domain. The number of subpulses arising throughout the propagation can be controlled via a suitable choice of the probe and control field parameters. Employing a simple theoretical model for the nonlinear pulse propagation, we conclude that the splitting occurs due to an interplay of Kerr nonlinearity and group-velocity dispersion.

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Postselection is the process of discarding outcomes from statistical trials that are not the event one desires. Postselection can be useful in many applications where the cost of getting the wrong event is implicitly high. However, unless this cost is specified exactly, one might conclude that discarding all data is optimal. Here we analyze the optimal decision rules and quantum measurements in a decision theoretic setting where a prespecified cost is assigned to discarding data. Our scheme interpolates between unambiguous state discrimination (when the cost of postselection is zero) and a minimum error measurement (when the cost of postselection is maximal). We also relate our formulation to previous approaches which focus on minimizing the probability of indecision.