In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD protocol with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD protocol against general attacks.

The measurement of the absolute frequencies of the $2S\to 3S$ of atomic lithium is reported. To reduce systematic effects, we employed a frequency-comb-stabilized excitation laser, a weakly collimated atomic beam, and the cascading $2P\to 2S$ 670 nm fluorescence as the signal. The transition frequencies, including two isotopes (${}^{6,7}\mathrm{Li}$), were measured to an accuracy of $<330\text{kHz}$. In comparison with the previous GSI Group experiment, the frequency of the $2S_{1/2}\to 3S_{1/2}$ transition of ${}^7\mathrm{Li}$ is 815 618 181.45(9) MHz, which is improved by a factor of 2. The resultant hyperfine constants of the 3$S$ state and the deduced difference of the nuclear charge radii $\delta \langle r_c^2\rangle$ from the isotope shift are in good agreement with previous results. Since a more straightforward methodology is adopted, our measurement is less model dependent and serves as an independent investigation of the reported transitions.

Due to its flexibility and possible systematic improvement, the Fock-space (FS) multireference coupled-cluster (MRCC) method remains a very important tool for the computation of energy differences of spectroscopic interest. In the present work, the FS MRCC method for the electron detachment process has been applied to determine the magnetic hyperfine constant $A_J$ and nuclear quadrupole moments $Q$ (related to electric hyperfine constant $B_J$) for the lowest multiplets of ${}^{33}$S${}^{-}$, ${}^{35}$Cl, and ${}^{37}$Cl with Dirac-Fock orbitals. In addition, we also report ${}^2$$P_{3/2}$([Ne]$3s^{2}3p^5$) $\to$ ${}^2$$P_{1/2}$([Ne]$3s^{2}3p^5$) magnetic dipole transition matrix element and electron affinity of ${}^{35}\mathrm{Cl}$ (i.e., ionization energy of Cl${}^{-}$). Calculated properties are in very good agreement with the available new standard or reference values.

Pump-probe photoelectron velocity-map imaging, using 27-eV high-harmonic excitation and 786-nm ionization, is used to resolve overlapping autoionizing resonances in atomic krypton, obtaining two-photon photoelectron angular distributions (PADs) for singly and doubly excited states. Two features in the photoelectron spectrum are assigned to singly excited 4$s^1$4$p^6$$n{p}^1$ ($n$ $=$ 7,8) configurations and four features provide information about double excitation configurations. The anisotropy parameters for the singly excited 7$p$ configuration are measured to be β${}_2$ $=$ 1.61 ± 0.06 and β${}_4$ $=$ 1.54 ± 0.16 while the 8$p$ configuration gives β${}_2$ $=$ 1.23 ± 0.19 and β${}_4$ $=$ 0.60 ± 0.15. These anisotropies most likely represent the sum of overlapping PADs from states of singlet and triplet spin multiplicities. Of the four bands corresponding to ionization of doubly excited states, two are assigned to 4$s^2$4$p^4$5$s^1$6$p^1$ configurations that are probed to different $J$-split ion states. The two remaining doubly excited states are attributed to a previously observed, but unassigned, resonance in the vacuum-ultraviolet photoabsorption spectrum. The PADs from each of the double excitation states are also influenced by overlap from neighboring states that are not completely spectrally resolved. The anisotropies of the observed double excitation states are reported, anticipating future theoretical and experimental work to separate the overlapping PADs into the state resolved PADs. The results can be used to test theories of excited state ionization.

We show a method to accelerate quantum adiabatic dynamics of wave functions under electromagnetic field (EMF) by developing the preceding theory [Masuda and Nakamura, Proc. R. Soc. London Ser. A 466, 1135 (2010)]. Treating the orbital dynamics of a charged particle in EMF, we derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states in any desired short time. The scheme is consolidated by describing a way to overcome possible singularities in both the additional phase and driving potential due to nodes proper to wave functions under EMF. As explicit examples, we exhibit the fast forward of adiabatic squeezing and transport of excited Landau states with nonzero angular momentum, obtaining the result consistent with the transitionless quantum driving applied to the orbital dynamics in EMF.

We present a lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For $N=3$ unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our $0.3\%$ uncertainty; as additional benchmarks we reproduce precision calculations of $N=3,...,6$ unitary fermions in a harmonic trap to within our $\sim 1\%$ uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as ${64}^3\times 72$. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of $N$ considered.

We investigate the effects of thermal and quantum fluctuations on the phase diagram of a spin-1 ${}^{\text{87}}\text{Rb}$ Bose-Einstein condensate (BEC) under the quadratic Zeeman effect. Due to the large ratio of spin-independent to spin-dependent interactions of ${}^{\text{87}}\text{Rb}$ atoms, the effect of noncondensed atoms on the condensate is much more significant than that in scalar BECs. We find that the condensate and spontaneous magnetization emerge at different temperatures when the ground state is in the broken-axisymmetry phase. In this phase, a magnetized condensate induces spin coherence of noncondensed atoms in different magnetic sublevels, resulting in temperature-dependent magnetization of the noncondensate. We also examine the effect of quantum fluctuations on the order parameter at absolute zero and find that the ground-state phase diagram is significantly altered by quantum depletion.

The stability of nonstationary states of homogeneous spin-1 Bose-Einstein condensates is studied by performing Bogoliubov analysis in a frame of reference where the state is stationary. In particular, the effect of an external magnetic field is examined. It is found that a nonzero magnetic field introduces instability in a ${}^{23}$Na condensate. The wavelengths of this instability can be controlled by tuning the strength of the magnetic field. In a ${}^{87}$Rb condensate this instability is present already at zero magnetic field. Furthermore, an analytical bound for the size of a stable condensate is found, and a condition for the validity of the single-mode approximation is presented. Realization of the system in a toroidal trap is discussed, and the full time development is simulated.

We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined $T$-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature $T_{\mathrm{c}}$, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures $T^{*}$ and $T^{**}$ at which the pseudogap structures in these quantities completely disappear. Determining $T^{*}$ and $T^{**}$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.

We present a method for rapid modeling of new Bragg ultracold atom-interferometer (AI) designs useful for assessing the performance of such interferometers. The method simulates the overall effect on the condensate wave function in a given AI design using two separate elements. These are (1) modeling the effect of a Bragg pulse on the wave function and (2) approximating the evolution of the wave function during the intervals between the pulses. The actual sequence of these pulses and intervals is then followed to determine the approximate final wave function from which the interference pattern can be calculated. The exact evolution between pulses is assumed to be governed by the Gross-Pitaevskii (GP) equation whose solution is approximated using a Lagrangian variational method to facilitate rapid estimation of performance. The method presented here is an extension of an earlier one that was used to analyze the results of an experiment [J. E. Simsarian et al., Phys. Rev. Lett. 85, 2040 (2000)], where the phase of a Bose-Einstein condensate was measured using a Mach-Zehnder-type Bragg AI. We have developed both 1D and 3D versions of this method and we have determined their validity by comparing their predicted interference patterns with those obtained by numerical integration of the 1D GP equation and with the results of the above experiment. We find excellent agreement between the 1D interference patterns predicted by this method and those found by the GP equation. We show that we can reproduce all of the results of that experiment without recourse to an ad hoc velocity-kick correction needed by the earlier method, including some experimental results that the earlier model did not predict. We also found that this method provides estimates of 1D interference patterns at least four orders-of-magnitude faster than direct numerical solution of the 1D GP equation.

We investigate dynamics of a laser-driven and dissipative system consisting of two nitrogen-vacancy (N-$V$) centers embedded in two spatially separated single-mode nanocavities in a planar photonic crystal (PC). Spontaneous emission from the excited states of the N-$V$ centers can be effectively suppressed by virtue of the Raman transition in the dispersive regime. The system displays a series of damped oscillations under various experimental situations, where we solve the time-dependent Schrödinger equation analytically for arbitrary values of the hopping and PC–N-$V$ coupling strengths. In particular, our results indicate that some special values should be taken for the hopping strength if we hope to have high-fidelity quantum state transfer between the two distant N-$V$ centers. We have also analyzed the relevant entanglement dynamics in the presence of decoherence. The experimental feasibility and challenge are justified using currently available technology.

We describe theoretically an atomic diffraction grating that combines an electromagnetically induced grating with a coherence grating in a double-$\Lambda$ atomic system. With the atom in a condition of maximal coherence between its lower levels, the combined gratings simultaneously diffract both the incident probe beam as well as the signal beam generated through four-wave mixing. A special feature of the atomic grating is that it will diffract any beam resonantly tuned to any excited state of the atom accessible by a dipole transition from its ground state.

Highly sensitive Faraday rotation spectroscopy is used to measure the fluctuating magnetization noise of noninteracting rubidium atoms under resonant and nonresonant optical probing conditions. The spin-noise frequency spectra, in conjunction with the probe light detuning with respect to the $D_2$ transition, reveal clear signatures of coherent coupling of the participating electronic levels. The results are explained by extended Bloch equations, including homogeneous and inhomogeneous broadening mechanisms. Our measurements further indicate that spin noise originating from excited states is governed at high intensities by collective effects.

We analyze Hardy's paradox from the point of view of scattering theory. This approach has been useful for the understanding of interaction-free measurement, which is a similar setup. We calculate the forward-scattered waves generated by the beam splitters, which are replaceable in the gedanken experiment. These two-mode waves appear to have an entanglementlike structure.

Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.

Rodriguez and Salam [Phys. Rev. A 82, 062522 (2010)] find disagreement between their results for the temperature dependence of the Casimir-Polder potential and those of earlier publications. It is argued that the latter are correct.

The prospects of sympathetic cooling of polar molecules with magnetically cotrapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH(${}^2\Sigma$) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum-defect theory, opens up the possibility of sympathetic cooling of polar ${}^2\Sigma$ molecules with alkali-metal atoms in a magnetic trap and with alkaline-earth-metal atoms in an optical dipole trap.

We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.

The nonclassical properties of the noisy three-qubit Greenberger-Horne-Zeilinger (GHZ) states, ${\rho }_v=v|\text{GHZ}\rangle \langle \text{GHZ}|+(1-v)\mathbb{1}/8$ parameterized by the visibility $0\le v\le 1$ are investigated. Based on the violation of the $2\times 2\times 2$-setting Mermin inequality, ${\rho }_v$ is nonclassical for the parameter range $1/2<v\le 1$. It has been posed whether additional settings would allow to lower the threshold visibility. Here we report on Bell inequalities giving a threshold value smaller than $v=1/2$. This rules out the possibility of a local hidden variable model in the limit of $v=1/2$. In particular, the lowest threshold visibility we found is $v=0.496057$, attainable with $5\times 5\times 5$ settings, whereas the most economical one in number of settings corresponds to $3\times 3\times 4$ settings. The method which enabled us to obtain these results, and in particular the about 10 000 tight Bell inequalities giving $v<1/2$, are also discussed in detail.