We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze the situation in which the cyclotron (${\omega }_c$) and the crystal rotation (${\omega }_r$) frequencies do not fulfill the condition ${\omega }_c=2{\omega }_r$. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme.

We investigate how the distinguishability of a “noise” particle degrades interference of the “signal” particle. The signal, represented by an equatorial state of a photonic qubit, is mixed with noise, represented by another photonic qubit, via linear coupling on a beam splitter. We report on the degradation of the signal photon interference depending on the degree of indistinguishability between the signal and noise photons. When the photons are completely distinguishable in principle but technically indistinguishable, the visibility drops to the value $1/\sqrt{2}$. As the photons become more indistinguishable, the maximal visibility increases and reaches the unit value for completely indistinguishable photons. We have examined this effect experimentally using a setup with a fiber-optics two-photon Mach-Zehnder interferometer.

We address continuous-variable quantum key distribution (QKD) in non-Markovian lossy channels and show how the non-Markovian features may be exploited to enhance security and/or to detect the presence and the position of an eavesdropper along the transmission line. In particular, we suggest a coherent-state QKD protocol which is secure against Gaussian individual attacks based on optimal $1\to 2$ asymmetric cloning machines for arbitrarily low values of the overall transmission line. The scheme relies on specific non-Markovian properties, and cannot be implemented in ordinary Markovian channels characterized by uniform losses. Our results give a clear indication of the potential impact of non-Markovian effects in QKD.

Recent interest in Sommerfeld-Brillouin optical precursors has brought attention to the possibility of optical precursor observation in bulk matter. We investigate the possible formation of optical precursors in an organic dye solution with a sharp absorption band and anomalous dispersion at a wavelength of approximately 800 nm. We explore this regime experimentally with sub-10-fs pulses with a central wavelength of approximately 800 nm from a Ti : sapphire oscillator. The pulses are passed through a thin layer of the dye solution and characterized by interferometric autocorrelation. The obtained autocorrelation traces are compared with simulations, and we observe important dispersion effects on the shape of the propagated pulses, including precursorlike behavior in their time evolution.

We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementation with current technology.

We present angle-resolved correlation measurements between photons after propagation through a three-dimensional disordered medium. The multiple-scattering process induces photon correlations that are directly measured for light sources with different photon statistics. We find that multiple-scattered photons between different angular directions with angles much larger than the average speckle width are strongly correlated. The time dependence of the angular photon correlation function is investigated, and the coherence time of the light source is determined. Our results are found to be in excellent agreement with the continuous mode quantum theory of multiple scattering of light. The presented experimental technique is essential in order to study quantum phenomena in multiple-scattering random media, such as quantum interference and quantum entanglement of photons.

By solving the three-dimensional, time-dependent Schrödinger equation, we have demonstrated that the ultrafast charge-transfer process in ion-atom collisions can be mapped out with attosecond extreme uv (xuv) pulses. During the dynamic-charge transfer from the target atom to the projectile ion, the electron coherently populates the two sites of both nuclei, which can be viewed as a “short-lived” molecular state. A probing attosecond xuv pulse can instantly unleash the delocalized electron from such a “transient molecule,” so that the resulting photoelectron may exhibit a “double-slit” interference. On the contrary, either reduced or no photoelectron interference will occur if the attosecond xuv pulse strikes well before or after the collision. Therefore, by monitoring the photoelectron interference visibility, one can precisely time the ultrafast charge-transfer process in atomic collisions with time-delayed attosecond xuv pulses.

The effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob, by using a bounded quantum memory and an unbounded classical memory, estimates a message that was encoded in qubits by Alice in one of the bases $X$ or $Z$. Our theorem gave a nontrivial effect of the memory boundedness. In addition, a generalization of the uncertainty principle in the presence of quantum memory has been obtained.

We study discrete-time quantum walks on the line and on general undirected graphs with two interacting or noninteracting particles. We introduce two simple interaction schemes and show that they both lead to a diverse range of probability distributions that depend on the correlations and relative phases between the initial coin states of the two particles. We investigate the characteristics of these quantum walks and the time evolution of the entanglement between the two particles from both separable and entangled initial states. We also test the capability of two-particle discrete-time quantum walks to distinguish nonisomorphic graphs. For strongly regular graphs, we show that noninteracting discrete-time quantum walks can distinguish some but not all nonisomorphic graphs with the same family parameters. By incorporating an interaction between the two particles, all nonisomorphic strongly regular graphs tested are successfully distinguished.

The Hong-Ou-Mandel interference dip is caused by an entangled state, a delocalized biphoton state. We propose a method of detecting this entanglement by utilizing inverse Hong-Ou-Mandel interference, while taking into account vacuum and multiphoton contaminations, phase noise, and other imperfections. The method uses just linear optics and photodetectors, and for single-mode photodetectors we find a lower bound on the amount of entanglement.

We have considered a mechanism for inducing a time-reversal violating electric dipole moment (EDM) in atoms through the interaction of a nuclear EDM $d_N$ with the hyperfine interaction, the “magnetic moment effect”. We have derived the operator for this interaction and presented analytical formulas for the matrix elements between atomic states. Induced EDMs in the diamagnetic atoms ${}^{129}\mathrm{Xe}$, ${}^{171}\mathrm{Yb}$, ${}^{199}\mathrm{Hg}$, ${}^{211}\mathrm{Rn}$, and ${}^{225}\mathrm{Ra}$ have been calculated numerically. From the experimental limits on the atomic EDMs of ${}^{129}\mathrm{Xe}$ and ${}^{199}\mathrm{Hg}$ we have placed the following constraints on the nuclear EDMs, $|d_N({}^{129}\mathrm{Xe})|<1.1\times {10}^{-21}\left|e\right|\mathrm{cm}$ and $|d_N({}^{199}\mathrm{Hg})|<2.8\times {10}^{-24}\left|e\right|\mathrm{cm}$.

We study the gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices, taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap solitons and nonlinear Bloch waves exists for the whole span of the interaction strength. The linear stability analysis indicates that the gap solitons are stable when their energies are near the bottom of the linear Bloch band gap. By increasing the interaction strength, the stable gap solitons can become unstable. It is argued that the stable gap solitons can easily be formed in a weakly interacting system with energies near the bottom of the lower-level linear Bloch band gaps.

We have investigated the doubly excited ${}^{1,3}{P}^e$ resonance states of helium and the hydrogen negative ion interacting with Coulomb and screened Coulomb potentials using exponential correlated wave functions. In the pure Coulomb case, calculations have been carried out by using the complex-coordinate rotation and the stabilization method. The ${}^1{P}^e$ resonance states of He below the $N=$ 3, 4, and 5 thresholds of He${}^{+}$, and the ${}^3{P}^e$ resonance states of He below the $N=$ 3 thresholds of He${}^{+}$, are reported. The $5p^2$ ${}^3{P}^e$ state, which has attracted recent interest, is also reported and discussed. In the screened Coulomb case, we have used the stabilization method to obtain two different series (3pnp and 3dnd) of resonance states below the $N=$ 3 He${}^{+}$ threshold as a function of the screening parameters. Resonance widths for the 3dnd series show some interesting behaviors. The resonance parameters (position and width) for helium and the hydrogen negation ion as functions of the screening parameters are reported.

Nonsequential two-photon double ionization of a two-electron system (He and He-like ions) in a circularly polarized intense laser field is developed in a relativistic field theoretic way. Antisymmetry is maintained in the correlated wave functions of He in the initial state after modification to include Dirac spinor, and in the Volkov wave functions of the two electrons in the final free state. The present theory endeavors to provide an estimate of the helicity-dependent angular asymmetry in spin-current generation in nonsequential two-photon double ionization. Angular dependence of circular dichroism obtained in this paper, in coplanar and orthogonal geometries, is compared with the only existing nonrelativistic result obtained using lowest-order perturbation theory. Present result for dichroism underestimates the nonrelativistic result. Entanglement in the spins of the ejected electrons is concluded.

An on-demand single-photon source is a fundamental building block in quantum science and technology. We experimentally demonstrate the proof of concept for a scheme to generate on-demand single photons via actively multiplexing several heralded photons probabilistically produced from pulsed spontaneous parametric down-conversions (SPDCs). By utilizing a four-photon-pair source, an active feed-forward technique, and an ultrafast single-photon router, we show a fourfold enhancement of the output photon rate. Simultaneously, we maintain the quality of the output single-photon states, confirmed by correlation measurements. We also experimentally verify, via Hong-Ou-Mandel interference, that the router does not affect the indistinguishability of the single photons. Furthermore, we give numerical simulations, which indicate that photons based on multiplexing of four SPDC sources can outperform the heralding based on highly advanced photon-number-resolving detectors. Our results show a route for on-demand single-photon generation and the practical realization of scalable linear optical quantum-information processing.

We present an experimental demonstration of dual-channel memory in a single tripod atomic system. The total readout signal exhibits either constructive or destructive interference when the dual-channel spin-wave excitations (SWEs) are retrieved by two reading beams with a controllable relative phase. When the two reading beams have opposite phases, the SWEs will remain in the medium, which can be retrieved later with two in-phase reading beams. Such a phase-sensitive storage and retrieval scheme can be used to measure and control the relative phase between the two SWEs in the memory medium, which may find applications in quantum-information processing.

A different point of view on the phenomenon of self-pulsations is presented, which shows that they are a balanced state formed by two counteracting processes: beating of modes and bistable switching. A structure based on two coupled nonlinear microcavities provides a generic example of a system with enhanced ability to support this phenomenon. The specific design of such a structure in the form of multilayered media is proposed, and the coupled-mode theory is applied to describe its dynamical properties. It is emphasized that the frequency of self-pulsations is related to the frequency splitting between resonant modes and can be adjusted over a broad range.

The problem of deriving macroscopic properties from the Hamiltonian of the hydrogen atom is resumed by extending previous results in the literature, which predicted elliptic orbits, into the region of hyperbolic orbits. As a main tool, coherent states of the harmonic oscillator are used which are continued to imaginary frequencies. The Kustaanheimo-Stiefel (KS) map is applied to transform the original configuration space into the product space of four harmonic oscillators with a constraint. The relation derived between real time and oscillator (pseudo) time includes quantum corrections. In the limit $\hslash \to 0$, the time-dependent mean values of position and velocity describe the classical motion on a hyperbola and a circular hodograph, respectively. Moreover, the connection between pseudotime and real time comes out in analogy to Kepler’s equation for elliptic orbits. The mean-square-root deviations of position and velocity components behave similarly in time to the corresponding ones of a spreading Gaussian wave packet in free space. To check the approximate treatment of the constraint, its contribution to the mean energy is determined with the result that it is negligible except for energy values close to the parabolic orbit with eccentricity equal to 1. It is inevitable to introduce a suitable scalar product in ${\mathbb{R}}^4$ which makes both the transformed Hamiltonian and the velocity operators Hermitian. An elementary necessary criterion is given for the energy interval where the constraint can be approximated by averaging.