We generally derive complex geometric phases in non-Hermitian quantum mechanics. The formalism of complex geometric phases for non-Hermitian quantum systems is general and can be applied in the cases of cyclic and noncyclic states in non-Hermitian quantum mechanics. As an example, we show the interpretation of complex geometric phases by a generalized density matrix defined on a two-level non-Hermitian quantum system and the two-level Bethe-Lamb model. Also, in the Hermitian case, our theoretical framework of a complex geometric phase reduces to the counterpart of the Pancharatnam phase.

We investigate the problem of closing the detection loophole in multipartite Bell tests, and show that the required detection efficiencies can be significantly lowered compared to the bipartite case. In particular, we present Bell tests based on $n$-qubit Greenberger-Horne-Zeilinger states, which can tolerate efficiencies as low as $38\%$ for a reasonable number of parties and measurements. Even in the presence of a significant amount of noise, efficiencies below $50\%$ can be tolerated, which is encouraging given recent experimental progress. Finally, we give strong evidence that, for a sufficiently large number of parties and measurements, arbitrarily small efficiencies can be tolerated, even in the presence of an arbitrary large amount of noise.

Studies in string theory and quantum gravity lead to the generalized uncertainty principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and, thus, the equivalence principle is violated. Analyzing the kinetic energy of a composite body, we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets and, thus, GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets.

We consider realistic, multiparameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli “depolarization” channel via the Pauli twirl approximation, and obtain the logical error rate as a function of the qubit $T_{1,2}$ and state preparation, gate, and readout errors. A numerical Monte Carlo simulation is performed to obtain the logical error rates, and a leading-order analytic formula is derived to estimate their behavior below threshold. Our results suggest that scalable fault-tolerant quantum computation should be possible with existing superconducting devices.

Practical schemes for measurement-device-independent quantum key distribution using phase and path or time encoding are presented. In addition to immunity to existing loopholes in detection systems, our setup employs simple encoding and decoding modules without relying on polarization maintenance or optical switches. Moreover, by employing a modified sifting technique to handle the dead-time limitations in single-photon detectors, our scheme can be run with only two single-photon detectors. With a phase-post-selection technique, a decoy-state variant of our scheme is also proposed, whose key generation rate scales linearly with the channel transmittance.

We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a “double-kick” scheme) or a longer pulse sequence (a “chiral-pulse-train” scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization-sensitive resonance-enhanced multiphoton ionization, we show that both methods produce significant rotational directionality. We demonstrate that increasing the number of excitation pulses supplements the ability to control the sense of molecular rotation with quantum-state selectivity, i.e., predominant excitation of a single rotational state. We also demonstrate the ability of both techniques to generate counterrotation of molecular nuclear-spin isomers (here, ortho- and para-nitrogen) and molecular isotopologs (here, ${}^{14}$N${}_2$ and ${}^{15}$N${}_2$).

We provide a detailed theoretical analysis of molecular rotational excitation by a chiral pulse train, a sequence of linearly polarized pulses with the polarization direction rotating from pulse to pulse by a controllable angle. Molecular rotation with a preferential rotational sense (clockwise or counterclockwise) can be excited by this scheme. We show that the directionality of the rotation is caused by quantum interference of different excitation pathways. The chiral pulse train is capable of selective excitation of molecular isotopologs and nuclear spin isomers in a mixture. We demonstrate this using ${}^{14}$N${}_2$ and ${}^{15}$N${}_2$ as examples for isotopologs and para- and ortho-nitrogen as examples for nuclear-spin isomers.

By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane-wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.

In recent years there has been enormous progress in matter wave interferometry. The Colella-Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer are the prototypes of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question as to what extent the gravitational redshift and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the nonvanishing, nonrelativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.

We describe methods for the fast production of highly coherent-spin-squeezed many-body states in bosonic Josephson junctions. We start from the known mapping of the two-site Bose-Hubbard (BH) Hamiltonian to that of a single effective particle evolving according to a Schrödinger-like equation in Fock space. Since, for repulsive interactions, the effective potential in Fock space is nearly parabolic, we extend recently derived protocols for shortcuts to adiabatic evolution in harmonic potentials to the many-body BH Hamiltonian. A comparison with current experiments shows that our methods allow for an important reduction in the preparation times of highly squeezed spin states.

We show a method to accelerate quantum adiabatic transport of identical spinless particles interacting with each other by developing the preceding fast-forward scaling theory formed for one-particle systems [Masuda and Nakamura, Proc. R. Soc. A 466, 1135 (2010)]. We derive a driving potential which accelerates adiabatic dynamics of quantum systems composed of identical particles in order to obtain the final adiabatic states in any desired short time. We also exhibit an ideal rapid manipulation of dilute Bose gas in the ground state without energy excitation by using the fast-forward scaling theory.

We consider an ensemble of three-level particles in Lambda configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first- and a second-order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas-Reiche-Kuhn sum rule, the system still shows a superradiant phase transition.

We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of “macroscopic” qubits. We propose an optical scheme, which is a relatively simple, albeit nonideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization-neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam-splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam-splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is nonexistent (a necessary condition for preserving superpositions).

We apply a large-deviation method to study the diffusive trajectories of the quadratures of light emitted from open quantum systems. We formulate the study of quadrature trajectories in terms of characteristic operators and show that, in the long-time limit, the statistics of such trajectories obey a large-deviation principle. We take our motivation from homodyne detection schemes which allow the statistics of light quadratures to be measured. We illustrate our approach with four examples of increasing complexity: a driven two-level system, a “blinking” three-level system, a pair of weakly coupled two-level driven systems, and the micromaser. We discuss how quadrature operators can serve as alternative order parameters for the classification of dynamical phases, which is particularly useful in cases where the statistics of quantum jumps cannot distinguish such phases. The formalism we introduce also allows us to analyze the properties of the light emitted in quantum-jump trajectories which deviate far from the typical dynamics.

We describe a method to measure the spectral radiance of a source in an absolute way without the need of a reference. Here we give the necessary detail to allow for the device to be reproduced from standard fiber-optic components. The device is suited for fiber-optic applications at telecom wavelengths and calibration of power meters and spectrometers at light levels from 1 nW to 1 $\mu$W.

We study the minimal input sets which can determine completely the universal and the phase-covariant quantum cloning machines. We find that the universal quantum cloning machine, which can copy an arbitrary input qubit to two identical copies, however, can be determined completely by only four input states located at the four vertices of a tetrahedron in a Bloch sphere. The phase-covariant quantum cloning machine, which can create two copies from an arbitrary qubit located on the equator of the Bloch sphere, can be determined by three qubits located symmetrically on the equator of the Bloch sphere with equal relative phase. These results sharpen further the well-known results that Bennett-Brassard 1984 protocol (BB84) states and six states used in quantum cryptography can determine completely the phase-covariant and universal quantum cloning machines. This can simplify the testing procedure of whether the quantum clone machines are successful or not; namely, we only need to check that the minimal input sets can be cloned optimally, which can ensure that the quantum clone machines can work well for all input states.

Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel [Phys. Rev. Lett. 107, 170502 (2011)]. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally, we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.

We consider procedures to realize an approximate universal-not gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the universality of operation. We show that one-qubit operations have a sharp trade-off relation between average fidelity and fidelity deviation, and two-qubit operations show a looser trade-off relation. The genuine universality holds for operations of more than two qubits, and those of even more qubits are beneficial to compensating imperfection of control. In addition, we take into account operational noises which contaminate quantum operation in realistic circumstances. We show that the operation recovers from the contamination by a feedback procedure of differential evolution. Our feedback scheme is also applicable to finding an optimal and universal not operation.

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the generalized Woods-Saxon potential. It is exactly shown that the generalized Woods-Saxon potential and the well-known Rosen-Morse potential are the same empirical potential-energy function for diatomic molecules. Based on the measure of inner-shell radii of two atoms, we propose a modified Rosen-Morse potential-energy model. Evaluation of the average deviations from the experimental data is carried out on six molecules. The modified Rosen-Morse potential is found to be more accurate than the Morse and Rosen-Morse potentials in fitting experimental data for the six molecules examined.

High-energy electron-impact ($e$,2$e$) measurements under large momentum-transfer kinematics for molecular nitrogen are reported over an extended binding-energy range. These measurements are supplemented with symmetry-adapted cluster configuration-interaction calculations to provide insight into the behavior of ionization mechanisms above the double-ionization threshold. Here, it was found that ionization-excitation processes make a significant partial contribution to the ionization phenomena for binding energies above the lowest double-ionization potential.