Measurement-device-independent quantum key distribution (MDI-QKD) with weak coherent sources has been widely and meticulously analyzed. However, the analysis for MDI-QKD with spontaneous-parametric-down-conversion sources (SPDCS) is incomplete. In this paper, we propose two passive decoy protocols suitable for parameter estimation in MDI-QKD using SPDCS. By accounting for practical parameters of SPDCS with thermal distribution, we present an investigation on the performances of MDI-QKD under the active three-intensity decoy protocol, the passive two-intensity decoy protocol, and the modified passive three-intensity protocol, respectively. Phase randomization, inherently a prerequisite for decoy protocol, is taken into consideration for evaluating the overall quantum bit gain and quantum bit error rate. The numerical simulations show that the MDI-QKD using SPDCS with practical decoy protocols can be demonstrated to be comparable to the asymptotical case and has apparent superiority both in transmission distance and key generation rate compared to the one using weak coherent sources. Our results also indicate that the modified passive three-intensity decoy protocol can perform better than the active three-intensity decoy protocol in MDI-QKD using practical SPDCS.

The Bethe logarithm is calculated for the hydrogen molecular ion H${{}_2}^{+}$ in the states of the rotational quantum number $L=0$ and the vibrational quantum number $v=0–1$ by using the Drake-Goldman method. The precision that is achieved for these two states is a few parts in ${10}^9$, which demonstrates the feasibility of the Drake-Goldman method for simple molecular systems. Comparison with the best published results is made.

We explore the possibility to create hybrid quantum systems that combine ultracold atoms with graphene membranes. We investigate a setup in which a cold atom cloud is placed close to a free-standing sheet of graphene at distances of a few hundred nanometers. The atoms then couple strongly to the graphene membrane via Casimir-Polder forces. Temporal changes in the atomic state of the atomic cloud changes the Casimir-Polder interaction, thereby leading to the creation of a back-action force in the graphene sheet. This setup provides a controllable way to engineer ripples in a graphene sheet with cold atoms.

We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a non-self-consistent $T$-matrix approximation by comparing analytical results to numerical data obtained from a fully self-consistent $T$-matrix approach. The latter takes into account an infinite number of bosons excited from the condensate.

We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body $T$-matrix approximation. We assess these approximations with respect to the transition temperature $T_{\mathrm{c}}$, the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long-standing problem in cold atom physics, our results would be useful for this important challenge.

Scattering theory traditionally deals with the asymptotic behavior of a system far removed from the actual scattering event. Here we present an experimental study of the one-dimensional scattering of a noninteracting condensate of ${}^{87}\mathrm{Rb}$ atoms from a potential barrier in the nonasymptotic regime for which the collision dynamics are still ongoing. We show that, for near-transparent barriers, there are two distinct transient scattering effects that arise and dramatically change the momentum distribution during the collision: a deceleration of wave-packet components in midcollision and an interference between incident and transmitted portions of the wave packet. Both effects lead to the re-distribution of momenta giving rise to a rich interference pattern that can be used to reconstruct the single-particle phase profile.

We theoretically investigate the critical behavior of a second-sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature $T_c$, the frequency or the sound velocity of the second-sound mode crucially depends on the critical exponent $\beta$ of the superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like ${(1-T/T_c)}^{\beta -1/2}$ when $\beta <1/2$. In a highly elongated trap, the speed of the second sound reduces by a factor of $1/\sqrt{2\beta +1}$ from that in a homogeneous three-dimensional superfluid. Our prediction could readily be tested by measurements of second-sound wave propagation in a setup, such as that exploited by Sidorenkov et al. [Nature (London) 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.

A soleakon—a recently proposed entity in nonlinear wave dynamics [O. Peleg et al., Phys. Rev. A 80, 041801(R) (2009)]—is a nonlinear localized wave that induces a leaky waveguide and populates its mode self-consistently and robustly. Soleakons quasitrap themselves for large propagation distances, during which they slowly emit radiation that eventually results in their abrupt disintegration. We propose bright soleakons that are solely supported by self-defocusing nonlinearity. We demonstrate numerically scalar bell (fundamental) and dipole soleakons, as well as multimode vector soleakons. We find that the threshold power for disintegration of dipole soleakons is much larger than the threshold disintegration power of bell soleakons. In the bell-dipole vector soleakon case, the two modes can disintegrate collectively when their joint power reaches a threshold value that is between the threshold power for the scalar fundamental and dipole soleakons.

We investigate dispersive optical nonlinearities that arise from a Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the nonlinear response to a weak optical probe in the presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be evaluated in a steady-state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple “universal scaling” formula to determine the dispersive optical nonlinearity of the medium. We also develop a technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that only involve two-body correlations, which can be solved numerically. All average populations and coherences are then obtained straightforwardly.

We investigate optical bistability in a multilayer one-dimensional photonic crystal where the central layer is doped with $\Lambda$-type three-level atoms. We take into account the influence of spontaneously generated coherence when the lower atomic levels are sufficiently close to each other, in which case Kerr-type nonlinear response of the atoms is enhanced. We calculate the propagation of a probe beam in the defect mode window using the numerical nonlinear transfer matrix method. We find that Rabi frequency of a control field acting on the defect layer and the detuning of the probe field from the atomic resonance can be used to control the size and contrast of the hysteresis loop and the threshold of the optical bistability. In particular we find that at the optimal spontaneously generated coherence, a three orders of magnitude lower threshold can be achieved relative to the case without the coherence.

We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.

The tunneling time through an arbitrary bounded one-dimensional barrier is investigated using the dwell-time operator. We relate the tunneling time to the conditioned average of the dwell-time operator because of the natural postselection in the case of successful tunneling. We discuss an indirect measurement by timing the particle and show that we are able to reconstruct the conditioned average value of the dwell-time operator by applying the contextual values formalism for generalized measurements based on the physics of Larmor precession. The experimentally measurable tunneling time in the weak interaction limit is given by the weak value of the dwell-time operator plus a measurement-context-dependent disturbance term. We show how the expectation value and higher moments of the dwell-time operator can be extracted from measurement data of the particle's spin.

We extend the notion of compressed quantum simulation to the $XY$ model. We derive a quantum circuit processing $\log \left(n\right)$ qubits which simulates the one-dimensional $XY$ model describing $n$ qubits. In particular, we demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which witnesses a quantum phase transition, can be observed. Furthermore, we analyze several dynamical processes, like quantum quenching and finite time evolution, and derive the corresponding compressed quantum circuit.

Recent experimental work on superconducting transmon qubits in three-dimensional (3D) cavities shows that their coherence times are increased by an order of magnitude compared to their two-dimensional cavity counterparts. However, to take advantage of these coherence times while scaling up the number of qubits it is advantageous to address individual qubits which are all coupled to the same 3D cavity fields. The challenge in controlling this system comes from spectral crowding, where the leakage transition of qubits is close to computational transitions in other qubits. Here, it is shown that fast pulses are possible which address single qubits using two-quadrature control of the pulse envelope, while the derivative removal by adiabatic gate method of Motzoi et al. [Phys. Rev. Lett. 103, 110501 (2009)] alone only gives marginal improvements over the conventional Gaussian pulse shape. On the other hand, a first-order result using the Magnus expansion gives a fast analytical pulse shape which gives a high-fidelity gate for a specific gate time, up to a phase factor on the second qubit. Further numerical analysis corroborates these results and yields to even faster gates, showing that leakage-state anharmonicity does not provide a fundamental quantum speed limit.

We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bob's auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bob's measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.

In this paper, we present the details of the ab initio high-precision configuration interaction and many-body perturbation theory calculations that were used by Berengut et al. [Phys. Rev. Lett. 111, 010801 (2013)] to place limits on the dependence of the fine-structure constant, $\alpha$, on the gravitational field of the white-dwarf star G191-B2B. These calculations were combined with laboratory wavelengths and spectra from the Hubble Space Telescope Imaging Spectrograph to obtain the result $\Delta \alpha /\alpha =(4.2\pm 1.6)\times {10}^{-5}$ and $(-6.1\pm 5.8)\times {10}^{-5}$ using Fe v and Ni v transitions, respectively. The uncertainty in these results are dominated by the uncertainty in the laboratory wavelengths. In this work we also present ab initio calculations of the isotopic shifts of the Fe v transitions. We show that improved laboratory spectra will enable determination of the relative isotope abundances in Fe v to an accuracy of $\sim$20%. Therefore this work provides a strong motivation for new laboratory measurements.

In this study, accurate static dipole polarizability and hyperpolarizability are calculated for Al${}^{+}$ ground state $3s^2{}^1{S}_0$ and excited state $3s3p{}^3{P}_J$ with $J=0,1,2$. The finite-field computations use energies obtained with the relativistic configuration interaction approach and the relativistic coupled-cluster approach. Excellent agreement with previously recommended values is found for the dipole polarizability of Al${}^{+}$ ground state $3s^2$ ${}^1{S}_0$ and excited state $3s3p{}^3{P}_0$ as well as the hyperpolarizability of the ground state $3s^2$ ${}^1{S}_0$. The recommended values of the dipole polarizability of the Al${}^{+}3s3p{}^3{P}_1$ and ${}^3{P}_2$ and the hyperpolarizability of Al${}^{+}3s3p{}^3{P}_0$, ${}^3{P}_1$, and ${}^3{P}_2$ are also given. The impacts of the relativity and spin-orbit coupling are elucidated by analyzing the angular momentum dependence of the dipole polarizability and the hyperpolarizability, and comparing the fully and scalar relativistic calculated data. It is shown that the impact of the relativity and spin-orbit coupling are small for the dipole polarizability but become significant for the hyperpolarizability. Finally, the blackbody radiation shifts contributed by the dipole polarizability and hyperpolarizability, respectively, are evaluated for transitions of Al${}^{+}3s^2$ ${}^1{S}_0$ to $3s3p{}^3{P}_J$ with $J=0,1,2$.

Constructing approximations for the exchange-correlation (xc) potential in density functional theory instead of the energy appears attractive because it may provide for a way of easily incorporating desirable features such as a particle number discontinuity into xc functionals. However, xc potentials that are constructed directly are problematic: An xc potential that is not a priori derived as a functional derivative of some xc energy functional is most likely not a functional derivative of any density functional at all. This severely limits the usefulness of directly constructed xc potentials, e.g., for calculating electronic excitations. For the explicit example of the Becke-Johnson (BJ) potential we discuss defining corresponding energy expressions by density path integrals. We show that taking the functional derivative of these energies does not lead back to potentials that are close to the BJ one, and the new potentials do not share the attractive features of the original BJ expression. With further examples we demonstrate that this is a general finding and not specific to the BJ potential form.

A Sturmian theory of three-body recombination is presented which provides a unified treatment of bound states, quasibound states, and continuum states. The Sturmian representation provides a numerical quadrature of the two-body continuum which may be used to generate a complete set of states within any desired three-body recombination pathway. Consequently, the dynamical calculation may be conveniently formulated using the simplest energy transfer mechanism, even for reactive systems which allow substantial rearrangement. The Sturmian theory generalizes the quantum kinetic theory of Snider and Lowry [J. Chem. Phys. 61, 2330 (1974)] to include metastable states which are formed as independent species. Steady-state rate constants are expressed in terms of a pathway-independent part plus a nonequilibrium correction which depends on tunneling lifetimes and pressure. Numerical results are presented for H${}_2$ recombination due to collisions with H and He using quantum-mechanical coupled states and infinite-order sudden approximations. These results may be used to remove some of the uncertainties that have limited astrophysical simulations of primordial star formation.

We have developed an approach based on first principles to study the process of radiative electron attachment (REA) to linear molecules of astrophysical interest in collisions between the molecules and electrons at energies below 1 eV. The approach is based on accurate ab initio calculations of electronic bound and continuum states of the negative ion. The electronic continuum states are obtained with the complex-Kohn variational method. The benchmark calculation for the REA to the simplest negative ion CN${}^{-}$, which was recently observed in the interstellar medium, has produced a relatively low rate coefficient $\alpha \left(T\right)=7.3\times {10}^{-16}$ cm${}^3/$s at $T=30$ K. Moreover, our results are shown to agree well with microscopic reversibility applied on a recent photodetachment experiment on CN${}^{-}$. Finally, the study confirms a previous assessment that the CN${}^{-}$ ion is unlikely be formed by REA in the interstellar medium.