A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov–de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kinklike profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to the soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with the soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The “inertial” and “gravitational” masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent of the observed behavior of a solitonlike texture in related experiments in cold fermion gases [T. Yefsah et al., Nature (London) 499, 426 (2013)]. Furthermore, we calculate the full nonlinear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong nonlinearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the nonlinear soliton spectrum in superfluids.

Motivated by recent experiments, we investigate the dynamics of a line of spin-down spins embedded in the ferromagnetic spin-up ground state of a two-dimensional XXZ model close to the Ising limit. In a situation where the couplings in the $x$ and $y$ directions are different, the quench dynamics of this system is governed by the interplay of one-dimensional excitations (kinks and holes) moving along the line and single-spin excitations evaporating into the two-dimensional background. A semiclassical approximation can be used to calculate the dynamics of this complex quantum system. Recently, it became possible to perform projective quantum measurements on such spin systems, allowing us to determine, e.g., the $z$ component of each individual spin. We predict the statistical properties of such measurements which contain much more information than correlation functions.

We theoretically study the laser cooling of optomechanical cavities when the mechanical resonance frequency and damping depend on time. In the regime of weak optomechanical coupling we extend the theory of laser cooling using an adiabatic approximation. We discuss the modifications of the cooling dynamics and compare it with numerical simulations in a wide range of modulation frequencies.

We propose a concept of fractional quantum resonances based on an idea of driving a quantum system by an external field in the form of a repetitive pulse sequence. We show that, in addition to intuitively expected resonance at repetition rate ${\omega }_{\text{Rep}}$ equal to the internal quantum frequency $\omega$, the system exhibits less intuitive fractional quantum resonances at ${\omega }_{\text{Rep}}=\omega /n$, with $n$ being an integer. It is a nonintuitive phenomenon since the external repetition rate has no quantum character, yet the atom responds to it, if the rate is equal to $1/n$ of its eigenfrequency. This result is in good agreement with recent magnetometer experiments. It is also found that other resonances are possible at pulse-repetition-rate frequencies equal to $1/n$ of combination frequencies involving the internal system frequencies and Rabi frequencies. We show that quantum-interference-related phenomena of gain without population inversion and absorption with inversion are observed at these unique resonances. Fractional quantum resonances provide a spectroscopy tool, allowing us to measure optical frequency on one transition through detection of resonances on another transition. We believe that our results will have implications in other quantum-related processes, such as laser-assisted resonant enhancement of chemical reactions and biological processes.

We propose a scheme to realize storage and retrieval of two-component optical soliton in a coherent atomic system. The system under consideration is a cold, lifetime-broadened four-level atomic gas with a tripod configuration working at the condition of double electromagnetically induced transparency. We show that due to the existence of two dark states, the optical absorption of the probe pulse can be largely reduced. In addition, the two orthogonal polarization components of the probe pulse with a form of vector optical soliton cannot only be slowed down substantially but also be stored and retrieved robustly by switching a control laser field off and on. We also show that it is possible to achieve a memory of $N$-component optical soliton by using the $N$ dark states in a $\left(N+1\right)$-pod system $\left(N>2\right)$. The results reported here may have promise in applications for light information processing in a weak nonlinear regime.

In this paper we report on a numerical study of plasmonic nanoparticle chains with long-range dipole-dipole interaction. We have shown that introduction of positional disorder gives a peak in the density of resonant states at the frequency of individual nanoparticle resonance. This peak is referred to as Dyson singularity in one-dimensional disordered structures and, according to our calculations, governs the spectral properties of local density of states. This provides disorder-induced Purcell enhancement that can find applications in random lasers and for surface-enhanced Raman-scattering spectroscopy. We stress that this effect relates not only to plasmonic nanoparticles but also to an arbitrary chain of nanoparticles or atoms with resonant polarizabilities.

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective $\mathcal{PT}-\text{symmetric}$ dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the $\mathcal{PT}-\text{symmetry}$ breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

We show that any jointly measurable pair of quantum observables can be obtained in a sequential measurement scheme, even if the second observable will be decided after the first measurement. This means that it is possible to perform a measurement of any quantum observable in a way that does not disturb the subsequent measurements more than is dictated by joint measurability. Only measurements with a specific structure have this universality feature. As a supplementing result, we provide a characterization of all possible joint measurements obtained from a sequential measurement lacking universality.

We undertook a mutually complementary analytic and computational study of the full-fledged spherical (three-dimensional) quantum rotor subject to combined orienting and aligning interactions, corresponding to a linear polar and polarizable molecule interacting with an electric field. The orienting and aligning interactions are characterized, respectively, by dimensionless parameters $\eta$ and $\zeta$. By making use of supersymmetric quantum mechanics, we found two sets of conditions (cases A and B) under which the problem of a spherical quantum pendulum becomes analytically solvable. These conditions coincide with the loci $\zeta =\frac{{\eta }^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $\eta$ and $\zeta$ parameters. In case A, the topological index $k=\mp m+1$ with $m$ the angular momentum projection quantum number, whereas, in case B, $k=1$, independent of $m$. These findings have repercussions for rotational spectra and dynamics of molecules subject to combined permanent and induced dipole interactions.

We consider the gravitational correction to (electronic) vacuum polarization in the presence of a gravitational background field. The Dirac propagators for the virtual fermions are modified to include the leading gravitational correction (potential term) which corresponds to a coordinate-dependent fermion mass. The mass term is assumed to be uniform over a length scale commensurate with the virtual electron-positron pair. The on-mass shell renormalization condition ensures that the gravitational correction vanishes on the mass shell of the photon, i.e., the speed of light is unaffected by the quantum field theoretical loop correction, in full agreement with the equivalence principle. Nontrivial corrections are obtained for off-shell, virtual photons. We compare our findings to other works on generalized Lorentz transformations and combined quantum-electrodynamic gravitational corrections to the speed of light which have recently appeared in the literature.

The time-dependent multiconfiguration self-consistent-field method based on the occupation-restricted multiple-active-space model is proposed (TD-ORMAS) for multielectron dynamics in intense laser fields. Extending the previously proposed time-dependent complete-active-space self-consistent-field method [TD-CASSCF; Phys. Rev. A 88, 023402 (2013)], which divides the occupied orbitals into core and active orbitals, the TD-ORMAS method further subdivides the active orbitals into an arbitrary number of subgroups and poses the occupation restriction by giving the minimum and maximum number of electrons distributed in each subgroup. This enables highly flexible construction of the configuration-interaction (CI) space, allowing a large-active-space simulation of dynamics, e.g., the core excitation or ionization. The equations of motion for both CI coefficients and spatial orbitals are derived based on the time-dependent variational principle, and an efficient algorithm is proposed to solve for the orbital time derivatives. In-depth descriptions of the computational implementation are given in a readily programmable manner. The numerical application to the one-dimensional lithium hydride cluster models demonstrates that the high flexibility of the TD-ORMAS framework allows for the cost-effective simulations of multielectron dynamics by exploiting systematic series of approximations to the TD-CASSCF method.

We calculate the renormalized Fermi surface and the quasiparticle properties in the Fermi liquid phase of three-dimensional dipolar fermions to second order in the dipole-dipole interaction. Using parameters relevant to an ultracold gas of erbium atoms, we find that the second-order corrections typically renormalize the Hartree-Fock results by less than 1%. On the other hand, if we use the second-order correction to the compressibility to estimate the regime of stability of the system, the point of instability is already reached for a significantly smaller interaction strength than in the Hartree-Fock approximation.

We consider a Bose-Einstein-condensed cloud of atoms which rotate in a toroidal or annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.

Two-photon correlation and photon transport in periodic and disordered passive parity-time-symmetric lattices are studied. A transition on two-photon quantum correlation is observed with the increase of the loss coefficient $\gamma$ in such non-Hermitian lattices, and the introduction of lattice disorder prompts the occurrence of the transition. The unique loss-enhanced transmission and the associated critical point of loss coefficient ${\gamma }_T$ of the parity-time-symmetric lattice are also modified significantly by introducing lattice disorder. Our results show that the critical point ${\gamma }_T$ is brought forward and the loss-enhanced transmission effect is enhanced in the non-Hermitian lattices with off-diagonal lattice disorders, while the critical point ${\gamma }_T$ is delayed and the loss-enhanced transmission effect is suppressed by introducing diagonal disorder into the non-Hermitian lattices.

In recent experiments with ultracold gases a Raman coupling scheme is used to produce both spin-orbit (SO) and Zeeman-type couplings [Y.-J. Lin et al., Nature (London) 471, 83 (2011)]. Their competition drives a phase transition to a magnetized state with broken $Z_2$ symmetry. Using a hydrodynamic approach we study a confined binary condensate subject to both SO and Zeeman-type couplings. We find that in the limit of small healing length and in the phase with unbroken symmetry, the boundary magnetization profile has an analytical solution in the form of a sine-Gordon soliton. The soliton is bound to the edge of the system by the nontrivial boundary condition resulting from the combined effect of the SO coupling and the drop in the particle density. The same boundary condition is important in the magnetized phase as well, where we characterize numerically the boundary spin structure. We further discuss how the nontrivial magnetization structure affects the density profile near the boundary, yet another prediction that can be tested in current experiments of spin-orbit-coupled condensates.

We demonstrate accurate phase measurement from experimental low photon level interferograms using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods, such as balanced homodyning or phase shifting, that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase-shifting method show that when the same photon resources are used, the optimization method provides phase recoveries with tighter error bars. In particular, rms phase error performance of the optimization method for low photon number data (10 photons per pixel) shows a $>5\times$ noise gain over the phase-shifting method. In our experiments where a laser light source is used for illumination, the results imply phase measurement with an accuracy better than the conventional single-pixel-based shot-noise limit that assumes independent phases at individual pixels. The constrained optimization approach presented here is independent of the nature of the light source and may further enhance the accuracy of phase detection when a nonclassical-light source is used.

A characterization of noncontextual models which fall within the ambit of Fine's theorem is provided. In particular, the equivalence between the existence of three notions is made explicit: a joint probability distribution over the outcomes of all the measurements considered, a measurement-noncontextual and outcome-deterministic (or KS-noncontextual, where KS stands for Kochen-Specker) model for these measurements, and a measurement-noncontextual and factorizable model for them. A KS inequality, therefore, is implied by each of these three notions. Following this characterization of noncontextual models that fall within the ambit of Fine's theorem, nonfactorizable noncontextual models which lie outside the domain of Fine's theorem are considered. While outcome determinism for projective (sharp) measurements in quantum theory can be shown to follow from the assumption of preparation noncontextuality, such a justification is not available for nonprojective (unsharp) measurements which ought to admit outcome-indeterministic response functions. The Liang-Spekkens-Wiseman (LSW) inequality is cited as an example of a noncontextuality inequality that should hold in any noncontextual model of quantum theory without assuming factorizability. Three other noncontextuality inequalities, which turn out to be equivalent to the LSW inequality under relabelings of measurement outcomes, are derived for Specker's scenario. The polytope of correlations admissible in this scenario, given the no-disturbance condition, is characterized.

We propose a quantum model consisting of two remote qubits interacting with two correlated colored noises and establish an exact stochastic Schrödinger equation for this open quantum system. It is shown that the quantum dynamics of the qubit system is profoundly modulated by the mutual correlation between baths and the bath memory capability through dissipation and fluctuation. We report a physical effect on generating inner correlation and entanglement of two distant qubits arising from the strong bath-bath correlation.

We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary “adiabatic circuits,” analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that while these adiabatic algorithms fail to exhibit certain aspects of the inherent fault tolerance of traditional quantum adiabatic algorithms, they may have certain other experimental advantages acting as quantum gates.