We investigate the time evolution of a Gaussian wave packet (GWP) in a tight-binding chain with a uniform nearest-neighbor hopping integral. Analytical investigations and numerical simulations show that fractional revivals of the quantum state occur in this system, i.e., at appropriate times, a GWP can evolve into many copies of the initial state at different positions. The application of this quantum phenomenon to quantum information transfer in solid-state systems is discussed.

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a $N$-fold reduction in computational complexity, where $N$ is the number of voters.

We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We obtain a necessary and sufficient condition to distill a secret key using this type of schemes for Pauli qubit channels and generalized Pauli channels in higher dimension. Our results can be applied to standard protocols such as Bennett-Brassard 1984 or six-state, giving a critical error rate of 20% and 27.6%, respectively. We explore several possibilities to enlarge these bounds, without any improvement. These results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.

We study the time-resolved photoassociation of ultracold sodium in an optical dipole trap. The photoassociation laser excites pairs of atoms to molecular states of large total angular momentum at high intensities (above $20\mathrm{kW}∕{\mathrm{cm}}^2$). Such transitions are generally suppressed at ultracold temperatures by the centrifugal barriers for high partial waves. Time-resolved ionization measurements reveal that the atoms are accelerated by the dipole potential of the photoassociation beam. We change the collision energy by varying the potential depth, and observe a strong variation of the photoassociation rate. These results demonstrate the important role of light forces in cw photoassociation at high intensities.

The effects of a static, homogeneous, and strong electric field on the radiative and steric properties of the LiCs molecule in its ${}^1\Sigma ^{+}$ electronic ground state are investigated. Combining discretization and basis-set methods, the rovibrational Schrödinger equation is solved and dipole transition rates are calculated. Spontaneous emission decay rates and radiative lifetimes of rovibrationally excited states have been studied extensively and particularly in the presence of the external homogeneous electric field. The intriguing possibility to control the alignment and orientation by applying a sufficiently strong field while switching between different configurations via absorption and emission processes is demonstrated.

Energy band structure and stability of Bose-Einstein condensate with both two- and three-body interactions in one-dimensional periodic optical lattices are discussed. It is demonstrated that the lowest energy band can show a loop structure at the boundary of the first Brillouin zone only when the number of atoms is larger than a critical value. When the loop structure is excited, an analytical expression of the loop width is obtained. The energetical and dynamical stabilities of the system are determined by considering the behavior of the Gross-Pitaevskii energy functional when the condensate wave function diverge away from a stationary state upon small perturbation, and its dependence on the number of atoms, the magnitude of the periodic potential, especially, the strength of the three-body force are studied. In addition, a criteria of the stability for excitations with long wavelengths is given by applying the hydrodynamic approach. The influence of the three-body interaction on the band properties and the stabilities are discussed in detail. It is shown that the critical density for developing the loop structure, the loop width, and the instability criteria are modified dramatically by the three-body interaction.

Polarization rotation of weak probe light induced by circularly polarized strong coupling light in a $\Lambda$ configuration is studied. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to remove complications from Zeeman distribution, Doppler broadening, and collisional decoherence. By using a very low probe intensity and short illumination period we work in a strictly linear regime. The probe and the coupling fields are optically phase locked to eliminate phase fluctuation and consequent atomic decoherence. Using this idealized situation we clarify the roles of optically induced Faraday rotation, circular dichroism, and electromagnetically induced transparency (EIT) in determining the final state of the probe light. In particular, we identify an experimental situation where the roles of atomic coherence and EIT are important.

Light propagation in an atomic medium whose coupled energy levels form a $◇$-configuration exhibits a critical dependence on the input conditions. Depending on the relative phase of the input light fields, the response of the medium can be dramatically modified and switch from opaque to semitransparent. These different types of behavior are caused by the formation of coherences due to interference in the atomic excitations. Alkaline-earth-metal atoms with zero nuclear spin are ideal candidates for observing these phenomena which could offer new perspectives in control techniques in quantum electronics.

We study the interference structure of the second-order intensity correlation function for polarization-entangled two-photon light obtained from type-II collinear frequency-degenerate spontaneous parametric down conversion. The structure is visualized due to the spreading of the two-photon amplitude in an optical fiber with group-velocity dispersion. A birefringent material inserted at the output of the nonlinear crystal leads to a more complicated interference structure of the correlation function.

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterize noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of $c=0.5\pm 0.2$ using the error correction protocol, and $c=0.3\pm 0.2$ using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.

We investigate quantum entanglement between two (spin-$1∕2$) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single-particle density matrix as the pure-state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.

The $3p$ photoelectron spectra of oriented and aligned free Fe atoms are presented. The atomic polarization was achieved by optical pumping. For this purpose single-mode ultraviolet continuous wave laser radiation was produced by second harmonic generation in an external ring resonator. The ground state Fe $3d^{6}4s^2$ ${}^{5}D_4$ was oriented by circularly polarized laser radiation and aligned by linearly polarized laser radiation. Switching from right handed to left handed circularly polarized laser radiation or by changing the polarization angle of the linearly polarized laser radiation by 90° allowed for the measurement of the orientation or the alignment dichroism in the Fe $3p$ photoelectron spectra excited by linearly polarized synchrotron radiation. The spectra are compared to the predictions of the single configuration $LS$-coupling model and the results of single and multiconfiguration calculations. Strong configuration interactions in the final core-hole states manifest themselves in marked deviations from the characteristic patterns. The comparison of the spectra of the free Fe atoms with spectra of thin magnetized Fe films reveals similarities but also marked differences between the dichroism curves of free and bound Fe atoms. The common atomic origin of the dichroism of free and bound Fe atoms is discussed; changes in the intra-atomic electron interactions as well as changes in valence electronic configuration when going from free to bound Fe atoms are addressed.

We analyze the alignment of molecules generated by a pair of crossed ultrashort pump pulses of different polarizations by a technique based on the induced time-dependent gratings. Parallel polarizations yield an intensity grating, while perpendicular polarizations induce a polarization grating. We show that both configurations can be interpreted at moderate intensity as an alignment induced by a single polarized pump pulse. The advantage of the perpendicular polarizations is to give a signal of alignment that is free from the plasma contribution. Experiments on femtosecond transient gratings with aligned molecules were performed in ${\mathrm{CO}}_2$ at room temperature in a static cell and at $30\mathrm{K}$ in a molecular expansion jet.

We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length $a_F$. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As $1∕a_F$ is increased from a negative value to the Feshbach resonance $(1∕a_F=0)$, the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance $(1∕a_F>0)$, pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when $1∕a_F$ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of ${}^6\mathrm{Li}\text{−}{}^{23}\mathrm{Na}$ and ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ atoms.

A relativistic quantum-mechanical description of guided waves is given, based on which we present an alternative way to describe and interpret the propagation of electromagnetic wave packets through an undersized waveguide. In particular, we show that the superluminal phenomenon of evanescent modes is actually a known conclusion in quantum field theory, and it preserves a quantum-mechanical causality.

Continuously mode-locked lasers combine a broad bandwidth with a fine comb structure that enables high resolution spectroscopy. Independent control of the pulse duration, center of gravity of the spectrum, the mode position, and spacing are essential for spectral applications and metrology. Exact analytical expressions are derived for the first, second, and third order dispersion in a cavity with a pair of intracavity prisms. The influence of cavity controls such as tilt and translation of the end mirror on the frequency comb parameters are analyzed and calculated.

We present two linear optical schemes using nonideal photodetectors to demonstrate the inseparability of $W$-type $N$-partite entangled states containing only a single photon. First, we show that the pairwise entanglement of arbitrary two modes chosen from $N$ optical modes can be detected using the method proposed by Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting a full inseparability among $N$ parties. In particular, this scheme is found to succeed for any nonzero quantum efficiency of photodetectors. Second, we consider a quantum teleportation network using linear optics without auxiliary modes. The conditional teleportation can be optimized by a suitable choice of the transmittance of the beam splitter in the Bell measurement. Specifically, we identify the conditions under which maximum fidelity larger than the classical bound 2/3 is achieved only in cooperation with other parties. We also investigate the case of on-off photodetectors that cannot discriminate between the number of detected photons.

A quantum string seal encodes the value of a (bit) string as a quantum state in such a way that everyone can extract a non-negligible amount of available information on the string by a suitable measurement. Moreover, such measurement must disturb the quantum state and is likely to be detected by an authorized verifier. In this way, the intactness of the encoded quantum state plays the role of a wax seal in the digital world. Here we analyze the security of quantum string seal by studying the information disturbance trade-off of a measurement. This information disturbance trade-off analysis extends the earlier results of Bechamann-Pasquinucci, D’Ariano, and Macchiavello [Int. J. Quant. Inform. 3, 435 (2005)] and Chau [Phys. Lett. A 354, 31 (2006)] by concluding that all quantum string seals are insecure. Specifically, we find a way to obtain nontrivial available information on the string that escapes the verifier’s detection with at least 50% chance.

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state $\mid \psi ⟩$ of the quantum system. Such expectation values can be measured by repeatedly preparing $\mid \psi ⟩$ and coupling the system to an apparatus. For this method, the precision of the measured value scales as $\frac{1}{\sqrt{N}}$ for $N$ repetitions of the experiment. For the problem of estimating the parameter $\varphi$ in an evolution $e^{-i\varphi H}$, it is possible to achieve precision $\frac{1}{N}$ [the quantum metrology limit; see Giovannetti et al., Phys. Rev. Lett. 96, 010401 (2006)] provided that sufficient information about $H$ and its spectrum is available. We consider the more general problem of estimating expectations of operators $A$ with minimal prior knowledge of $A$. We give explicit algorithms that approach precision $\frac{1}{N}$ given a bound on the eigenvalues of $A$ or on their tail distribution. These algorithms are particularly useful for simulating quantum systems on quantum computers because they enable efficient measurement of observables and correlation functions. Our algorithms are based on a method for efficiently measuring the complex overlap of $\mid \psi ⟩$ and $U\mid \psi ⟩$, where $U$ is an implementable unitary operator. We explicitly consider the issue of confidence levels in measuring observables and overlaps and show that, as expected, confidence levels can be improved exponentially with linear overhead. We further show that the algorithms given here can typically be parallelized with minimal increase in resource usage.