We examine a parametric cycle in the $N$-body Lieb-Liniger model that starts from the free system and goes through Tonks-Girardeau and super-Tonks-Girardeau regimes and comes back to the free system. We show the existence of exotic quantum holonomy, whose detailed workings are analyzed with the specific sample of two- and three-body systems. The classification of eigenstates based on clustering structure naturally emerges from the analysis.

We examine the notion of nonclassicality in terms of quasiprobability distributions. In particular, we not only ask if a specific quasiprobability can be interpreted as a classical probability density, but we also require that characteristic features of classical electrodynamics are resembled. We show that the only quasiprobabilities that correctly describe the superposition principle of classical electromagnetic fields are the $s$-parametrized quasiprobabilities. Furthermore, the Glauber-Sudarshan $P$ function is the only quantum-mechanical quasiprobability that is transformed at a classical attenuator in the same way as a classical probability distribution. This result strengthens the definition of nonclassicality in terms of the $P$ function, in contrast to possible definitions in terms of other quasiprobabilities.

We derive sampling functions for estimation of quantum-state fidelity with Schrödinger-cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity with squeezed Fock states that can approximate the catlike states and can be generated from Gaussian squeezed states by conditional photon subtraction. The fidelities can be determined by averaging the sampling functions over quadrature statistics measured by homodyne detection. The sampling functions are designed such that they can compensate for losses and inefficient homodyning provided that the overall efficiency exceeds a certain threshold. The fidelity with an odd coherent state and the fidelity with a squeezed odd Fock state provide convenient witnesses of negativity of the Wigner function of the measured state. The negativity of the Wigner function at the origin of phase space is certified if any of these fidelities exceeds $0.5$. Finally, we discuss the possibility of reducing the statistical uncertainty of the fidelity estimates by a suitable choice of the dependence of the number of quadrature samples on the relative phase shift between the local oscillator and the signal beam.

In a recent, modified double-pinhole diffraction experiment the existence of an interference pattern was established indirectly along with a near-perfect imaging of the double pinhole. Our theoretical analysis shows that the experiment constitutes a preparation of a quantum state that is, to a good approximation, a joint eigenstate of commuting functions of position and momentum. Gaining information about the momentum distribution by means of the particular experimental setup is thus possible with negligible impact on the position distribution. Furthermore, we construct explicitly a class of states simultaneously localized on periodic sets in position and momentum space, which are therefore eigenstates of the observables being measured jointly (to a good approximation) in multislit interferometry. Finally, we show that with an appropriate change of settings the experiment demonstrates the mutual disturbance of position and momentum measurements.

The structural physical approximation (SPA) to a positive map is considered to be one of the most important methods to detect entanglement in the real physical world. We first show that an arbitrary entanglement witness (EW) $W$ can be constructed from a separable density matrix $\sigma$ in the form of $W=\sigma -c_{\sigma }I$, where $c_{\sigma }$ is a non-negative number and $I$ is the identity matrix. Following the general form of EWs from separable states, we show a sufficient condition and a sufficient and necessary condition in low dimensions of that SPAs to positive maps do not define entanglement-breaking channels. We show that either the SPA of an EW or the SPA of the partial transposition of the EW in low dimensions is an entanglement-breaking channel. We give sufficient conditions of violating the SPA conjecture [Phys. Rev. A 78, 062105 (2008)]. Our results indicate that the SPA conjecture is independent of whether or not positive maps are optimal.

For the transmon, its dephasing has experimentally been suppressed to an extent that dephasing time is mainly limited by the relaxation process [Schreier et al., Phys. Rev. B 77, 180502(R) (2008)]. In the Hilbert space of two transmons, there exists a two-dimensional subspace immune to the collective relaxation. In this paper, by encoding a logical qubit in this subspace, we demonstrate how to realize universal quantum computation in the decoherence-free subspace. In our scheme, the transmons are coupled through a one-dimensional superconducting transmission-line resonator. With the help of some classical driving fields, two noncommutable single-logical-qubit rotation operators and a controlled-phase gate between two logical qubits are obtained. We always work in the detuning regime, which largely decreases relaxation induced by the Purcell effect.

We propose an entanglement sharing protocol based on separable states. Initially, two parties, Alice and Bob, share a two-mode separable Gaussian state. Alice then splits her mode into two separable modes and distributes them between two players. Bob is separable from the players but he can create entanglement with either of the players if the other player moves to his location and collaborates with him. Any two parties are separable and the creation of entanglement is thus mediated by transmission of a mode which is separable from individual modes on Alice's side and Bob's side. For the state shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to Gaussian measurements and the state thus carries a nontrivial signature of bound entanglement. The present protocol also demonstrates switching between different separability classes of tripartite systems by coherent operations on its bipartite parts and complements studies on protocols utilizing mixed partially entangled multipartite states.

Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.

We have performed a measurement of the spectral shape from the two-photon decay of the $1s2s{}^1{S}_0$ state in He-like uranium. The two-photon emission followed the ionization of initially Li-like uranium ions in collisions with a N${}_2$ gas-jet target. The measured shape of the two-photon energy distribution shows good agreement with results of the relativistic calculations that take into account the electron-electron interaction rigorously up to the first order in quantum electrodynamic perturbation expansion. From the full width at half maximum of the measured two-photon energy distribution, we confirm the theoretically predicted modification of the shape due to the relativistic effects.

We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high-order harmonic generation spectra of a one-dimensional model of atomic beryllium interacting with a strong laser pulse, the TD-RASSCF method is reasonably accurate while largely reducing the computational complexity. The TD-RASSCF method has the potential to treat large atoms and molecules beyond the capability of the MCTDHF method.

Carbon $1s$ photoelectron asymmetry parameters $\beta$ for the chlorinated and the methyl carbon atom of CH${}_3$CH${}_2$Cl, CH${}_3$CHCl${}_2$, and CH${}_3$CCl${}_3$ have been measured using synchrotron radiation in the 340–600 eV energy range. We provide experimental evidence that the intramolecular scattering strongly affects $\beta$ values, even far from the ionization threshold. The results are in agreement with B-spline density functional theory calculations, making it possible to single out the behavior of the various continuum partial waves. We conclude that the intramolecular scattering makes electron angular distributions sensitive to the chemical environment, even in isolated gas phase molecules.

We investigate the collective modes in the spin-orbit-coupled Fermi gas with repulsive $s$-wave interaction. The interplay between spin-orbit coupling and atom-atom interactions plays the crucial role in the collective behaviors of Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit-coupled Fermi gas has strongly correlated spin and density excitations. Within the scheme of random-phase approximation, we classify collective modes based on the symmetry group and determine their properties via the poles of corresponding correlation functions. Besides, the particle-hole continuum is obtained, where the imaginary part of these correlation functions becomes nonvanishing. We also propose an experimental protocol for detecting these collective modes and discuss corresponding experimental signatures in the ultracold Fermi gases experiment.

We study formation of solitons induced by counterflows of immiscible superfluids. Our setting is based on a quasi-one-dimensional binary Bose-Einstein condensate, composed of two immiscible components with large and small numbers of atoms in them. Assuming that the “small” component moves with constant velocity, either by itself, or being dragged by a moving trap, and intrudes into the “large” counterpart, the following results are obtained. Depending on the velocity, and on whether the small component moves in the absence or in the presence of the trap, two-component dark-bright solitons, scalar dark solitons, or multiple dark solitons may emerge, the last outcome taking place due to breakdown of the superfluidity. We present two sets of analytical results to describe this phenomenology. In an intermediate velocity regime, where dark-bright solitons form, a reduction of the two-component Gross-Pitaevskii system to an integrable Mel'nikov system is developed, demonstrating that solitary waves of the former are very accurately described by analytically available solitons of the latter. In the high-velocity regime, where the breakdown of the superfluidity induces the formation of dark solitons and multisoliton trains, an effective single-component description, in which a strongly localized wave packet of the “small” component acts as an effective potential for the “large” one, allows us to estimate the critical velocity beyond which the coherent structures emerge in good agreement with the numerical results.

We consider a binary Bose-Einstein condensate with linear and nonlinear interactions between its components, which emulate the spinor system with spin-orbit (SO) and Rabi couplings. For a relatively dense condensate, one-dimensional coupled equations with the nonpolynomial nonlinearity of both repulsive and attractive signs are derived from the three-dimensional Gross-Pitaevskii equations. Profiles of modes confined in an external potential under the action of the self-repulsion, and self-trapped solitons in the case of the self-attraction, are found in a numerical form and by means of analytical approximations. In the former case, the interplay of the SO and Rabi couplings with the repulsive nonlinearity strongly distorts shapes of the trapped modes, adding conspicuous sidelobes to them. In the case of the attractive nonlinearity, the most essential result is reduction of the collapse threshold under the action of the SO and Rabi couplings.

We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature $T_c$. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below $T_c$ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.

Warm-atomic-vapor cells may be employed as quantum-memory components in an experimentally convenient implementation of the Duan-Lukin-Cirac-Zoller protocol. Previous studies have shown the performance of these cells is limited by the combination of collisional fluorescence during the writing process and four-wave mixing during the reading process and have proposed to overcome this by a combination of optimized detuning and prepumping with circularly polarized write and read beams. Here we show that the Raman matrix elements involving the excited $P$ ($F^{\prime }=I-\frac{1}{2}$ and $F^{\prime }=I+\frac{1}{2}$) levels of all alkali atoms are always equal in magnitude and opposite in sign when the write and the anti-Stokes (Stokes) photons have the opposite helicity, and the Raman transitions via the two levels interfere destructively. The existence of an optimal detuning is demonstrated for a given dark-count rate of the single-photon detector. The predicted behavior is observed experimentally in a warm Rb cell with buffer gas.

The response of spinor Bose-Einstein condensates to dynamical modulation of magnetic fields is discussed with linear response theory. As an experimentally measurable quantity, the energy absorption rate (EAR) is considered, and the response function is found to access quadratic spin correlations which come from the perturbation of the quadratic Zeeman term. By applying our formalism to spin-1 condensates, we demonstrate that the EAR spectrum as a function of the modulation frequency is able to characterize the different magnetically ordered phases.

In $\mathcal{PT}$-symmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under $\mathcal{PT}$, where $\mathcal{P}$ denotes parity and $\mathcal{T}$ denotes time reversal. Here we study the role of boundary conditions in $\mathcal{PT}$-symmetric quantum mechanics by constructing a simple model that is the $\mathcal{PT}$-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect $\mathcal{PT}$ symmetry rather than Hermiticity. We find that for a broad class of $\mathcal{PT}$-symmetric boundary conditions the model respects the condition of unbroken $\mathcal{PT}$ symmetry, namely, that the Hamiltonian and the symmetry operator $\mathcal{PT}$ have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the $\mathcal{PT}$-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of $\mathcal{PT}$-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for $\mathcal{PT}$-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the $\mathcal{PT}$-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.

We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against collective attacks. The protocol, which represents a QKD analog of pulse position modulation, is compatible with standard fiber telecommunications channels and wavelength division multiplexers. We describe several physical implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at $>4$ bits per character of distilled key across over 200 km of fiber.