We investigate the single-mode operation of a quantum optical nonlinear $\pi$ phase-shift gate implemented by a single two-level atom in one-dimensional free space. Since the single-mode property of the input photons at the atom is not preserved in the interaction at the atom, we analyze the efficiency of single-mode operation that can still be achieved. We show how the input pulse shape can be optimized to obtain high efficiencies for the nonlinear single-mode operation. With this analysis, we obtain an optimal single-mode transmittance per photon of 78% for the successful nonlinear $\pi$ phase-shift operation.

An experimental scheme for producing a four-photon entangled $W$ state directly from the parametric down-conversion of a two-crystal geometry is proposed. In our scheme, only linear optical elements and photon detectors are required. Sophisticated and fragile interferometric setups are unnecessary.

We propose a scheme for the quantum teleportation of an atomic state based on the detection of cavity decay. The internal state of an atom trapped in a cavity can be disembodiedly transferred to another atom trapped in a distant cavity by measuring interference of polarized photons through single-photon detectors. In comparison with the original proposal by Bose, Knight, Plenio, and Vedral [Phys. Rev. Lett. 83, 5158 (1999)], our protocol of teleportation has a high fidelity of almost unity, and inherent robustness, such as the insensitivity of fidelity to randomness in the atom’s position, and to detection inefficiency. All these favorable features make the scheme feasible with the current experimental technology.

We study reliable quantum-information processing (QIP) under two different types of environment. The first type is Markovian exponential decay, and the appropriate elementary strategy of protection of qubit is to apply fast gates. The second one is strongly non-Markovian and occurs solely during operations on the qubit. The best strategy is then to work with slow gates. If the two types are both present, one has to optimize the speed of gate. We show that such a trade-off is present for a single-qubit operation in a semiconductor quantum dot implementation of QIP, where recombination of exciton (qubit) is Markovian, while phonon dressing gives rise to the non-Markovian contribution.

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.

We model ideal arrival-time measurements for free quantum particles and for particles subject to an external interaction by means of a narrow and weak absorbing potential. This approach is related to the operational approach of measuring the first photon emitted from a two-level atom illuminated by a laser. By operator normalizing the resulting time-of-arrival distribution, a distribution is obtained which for freely moving particles not only recovers the axiomatically derived distribution of Kijowski for states with purely positive momenta but is also applicable to general momentum components. For particles interacting with a square barrier the mean arrival time and corresponding “tunneling time” obtained at the transmission side of the barrier become independent of the barrier width (Hartman effect) for arbitrarily wide barriers, i.e., without the transition to the ultraopaque, classical-like regime dominated by wave packet components above the barrier.

The hyperspherical adiabatic method is used to derive stability criteria for Bose-Einstein condensates in deformed external fields. An analytical approximation is obtained. For constant volume the highest stability is found for spherical traps. Analytical approximations to the stability criterion with and without zero point motion are derived. Extreme geometries of the field effectively confine the system to dimensions lower than three. As a function of deformation we compute the dimension to vary continuously between one and three. We derive a dimension-dependent effective radial Hamiltonian and investigate one choice of an effective interaction in the deformed case.

Photon-photon scattering in vacuum due to the interaction with virtual electron-positron pairs is a consequence of quantum electrodynamics. A way for detecting this phenomenon has been devised based on interacting modes generated in microwave wave guides or cavities [G. Brodin, M. Marklund, and L. Stenflo, Phys. Rev. Lett. 87, 171801 (2001)]. Here we materialize these ideas, suggest a concrete cavity geometry, make quantitative estimates and propose experimental details. It is found that detection of photon-photon scattering can be within the reach of present day technology.

A pulse-shaping algorithm for a matter wave with the purpose of controlling a binary reaction has been designed. The scheme is illustrated for an Eley-Rideal reaction where an impinging matter-wave atom recombines with an adsorbed atom on a metal surface. The wave function of the impinging atom is shaped such that the desorbing molecule leaves the surface in a specific vibrational state.

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. In this paper we examine master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel.

The saddle-point analysis of the transition amplitude shows that the quantum interference effect does not occur in the direct process of photodetachment by a circularly polarized laser field. This fact is interpreted in terms of classical electron trajectories. Comparison between the length and velocity gauges is performed by simulating spectra of photoelectrons produced in a focus of a laser pulse. A substantial discrepancy is found in the kinetic energy distribution of photoelectrons. At low energies, only the predictions in the length gauge are consistent with the Wigner threshold law.

Analytical expressions for the resonances of the long-range potential (LRP), $V\left(r\right)=a∕r-b∕r^2$, as a function of the Hamiltonian parameters were derived by Doolen a long time ago [Int. J. Quant. Chem. 14, 523 (1979)]. Here we show that converged numerical results are obtained by applying the shifted complex scaling and the smooth-exterior scaling (SES) methods rather than the usual complex coordinate method (i.e., complex scaling). The narrow and broad shape-type resonances are shown to be localized inside or over the potential barrier and not inside the potential well. Therefore, the resonances for Doolen LRP’s are not associated with the tunneling through the potential barrier as one might expect. The fact that the SES provides a universal reflection-free absorbing potential is, in particular, important in view of future applications. In particular, it is most convenient to calculate the molecular autoionizing resonances by adding one-electron complex absorbing potentials into the codes of the available quantum molecular electronic packages.

The hyperspherical adiabatic expansion method is used to describe correlations in a symmetric boson system rigorously confined to two spatial dimensions. The hyperangular eigenvalue equation turns out to be almost independent of the hyperradius, whereas the solutions are strongly varying with the strength of the attractive two-body potentials. Instability is encountered in hyperangular, hyperradial, and mean-field equations for almost identical strengths inversely proportional to the particle number. The derived conditions for stability are similar to mean-field conditions and closely related to the possible occurrence of the Thomas and Efimov effects. Renormalization in mean-field calculations for two spatial dimensions is probably not needed.

We propose a robust scheme to generate multi-photon Fock states in an atom-maser-cavity system using adiabatic passage techniques and topological properties of the dressed eigenenergy surfaces. The mechanism is an exchange of photons from the maser field into the initially empty cavity by bichromatic adiabatic passage. The number of exchanged photons depends on the design of the adiabatic dynamics through and around the conical intersections of dressed eigenenergy surfaces.

We suggest using an evanescent wave around a thin fiber to trap atoms. We show that the gradient force of a red-detuned evanescent-wave field in the fundamental mode of a silica fiber can balance the centrifugal force when the fiber diameter is about two times smaller than the wavelength of the light and the component of the angular momentum of the atoms along the fiber axis is in an appropriate range. As an example, the system should be realizable for cesium atoms at a temperature of less than $0.29\mathrm{mK}$ using a silica fiber with a radius of $0.2\mu \mathrm{m}$ and a $1.3\text{−}\mu \mathrm{m}$-wavelength light with a power of about $27\mathrm{mW}$.

The effect of the intersubsystem coupling on the off-diagonal geometric phase in a composite system is investigated. We analyze the case where the system undergoes an adiabatic evolution. Two coupled qubits driven by time-dependent external magnetic fields are presented as an example; the off-diagonal geometric phase as well as the adiabatic condition are examined and discussed.

We present a two-way protocol for the quantum key distribution with practical faint laser pulses. It is secure when the faint laser pulses contain no more than two photons. The key distribution task is completed in two transmissions. Bob first sends the laser pulses to Alice, and Alice encodes the key message through certain unitary operations and returns the laser pulses to Bob. Security is achieved by placing eavesdropping check procedures in both transmissions. This protocol is secure and is close to practical conditions. In addition, it does not require the exchange of measuring basis information between Alice and Bob, hence saving a lot of storage space.

The Abelès matrix formalism is combined with the plane-wave expansion method to calculate the radiation emitted by an oscillating dipole embedded within a periodic multilayer planar structure. This approach is implemented to account for the soft-x-ray Kossel structures recently observed with W/C multilayers [P. Jonnard et al., Phys. Rev. A 68, 032505 (2003)].

We study the motion of a pointlike impurity in a Bose-Einstein condensate at $T=0$. By solving the Gross-Pitaevskii (GP) equation in a perturbative manner we calculate the induced mass of the impurity and the drag force on the impurity in three-, two-, and one-dimensional (1D) cases. The relationship between the induced mass and the normal mass of fluid is found, and coincides with the result of the Bogoliubov theory. The drag force appears for the supersonic motion of the impurity. In 1D the drag force is investigated also on the basis of the exact Lieb-Liniger theory, using the dynamic form factor, which has been evaluated by the Haldane method of the calculation of correlation functions. In this theory the force appears for an arbitrarily small velocity of the impurity. The possibility of measuring the form factor in existing experiments is noted.

We have investigated two-photon nonlinearity in general cavity QED systems, which cover both weak- and strong-coupling regimes and include the radiative loss from an atom. One- and two-photon propagators are obtained in analytical forms. By surveying both coupling regimes, we have revealed the conditions on a photonic pulse for yielding large nonlinear effects, depending on the cavity $Q$ value. We also discuss the effects of radiative loss on nonlinearity.