By making use of the Green-function concept of quantization of the electromagnetic field in Kramers-Kronig consistent media, a rigorous quantum-mechanical derivation of the rate of intermolecular energy transfer in the presence of arbitrarily shaped, dispersing, and absorbing material bodies is given. Applications to bulk material, multislab planar structures, and microspheres are studied. It is shown that when the two molecules are near a planar interface, then surface-guided waves can strongly affect the energy transfer and essentially modify both the (Förster) short-range $R^{-6}$ dependence of the transfer rate and the long-range $R^{-2}$ dependence, which are typically observed in free space. In particular, enhancement (inhibition) of energy transfer can be accompanied by inhibition (enhancement) of donor decay. Results for four- and five-layered planar structures are given and compared with experimental results. Finally, the energy transfer between two molecules located at diametrically opposite positions outside a microsphere is briefly discussed.

In this paper, we present a measure to quantify the degree of entanglement for two qubits in a pure state.

The role of electronic resonances due to a laser field of appropriate frequency is investigated in laser-assisted internal conversion (IC). After the IC creates a vacancy in the electron shell, Rabi oscillations of an electron may take place in the presence of a resonant laser field. By deriving a no-go theorem, we show that a resonant process of this or, in fact, any related sort has no effect on the nuclear decay rate. This finding seems to contradict some earlier theoretical predictions in this field.

We explore an efficient method for preparing large samples of ultracold calcium atoms. An optimized conventional (Doppler-limited) magneto-optical trap collects atoms from a Zeeman cooled atomic beam using a strong dipole transition within the singlet system. This transition is not completely closed thus yielding an intense flux of atoms into the metastable triplet state ${}^3{P}_2.$ A second magneto-optical trap sharing the same magnetic-field gradient is superimposed which captures and further cools the metastables using the narrow-band infrared transition ${}^3{\overrightarrow{P_2}}^3{D}_3.$ In our present experiment we were able to prepare $3\times {10}^8$ atoms at temperatures below 20 microkelvin within 250 ms. Minor technical improvements of our setup promise to yield above ${10}^{10}$ atoms at submicrokelvin temperatures within 1 s.

We address the problem of simulating pair-interaction Hamiltonians in n-node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair interaction can be used to simulate any other by applying sequences of appropriate local control sequences. Conditions on time optimal simulation are formulated in terms of spectral majorization of matrices characterizing the coupling parameters. Efficient schemes for decoupling and time reversal can be constructed from orthogonal arrays provided that the dimensions of all nodes are equal to the same prime power. Moreover, we consider a specific system of n harmonic oscillators with bilinear interaction. In this case, decoupling can efficiently be achieved using the combinatorial concept of difference schemes. For this type of interaction we present optimal schemes for inversion.

A thermal vapor of three-level atoms irradiated by two copropagating laser beams of suitable frequencies exhibits the phenomenon of coherent population trapping, leading to an electromagnetically induced transparency (EIT). When a mirror reflects the beams back onto themselves one finds that depending on the position along the resulting standing wave the fluorescence intensity from the sample (cesium in our case) decreases (EIT) or even increases [electromagnetically induced absorption (EIA)] with a period on the centimeter scale. An intuitive picture is based on the interference of coherent dark states but the explanation of the EIA effect requires consideration of Doppler effects in the thermal vapor. This allows for a quantitative comparison between experimental and calculated results.

We investigate the spatial behavior of nonclassical light produced by type I second-harmonic generation in the traveling-wave configuration. An input-output transformation for the system of fundamental and second-harmonic field is derived in the framework of a linearization approach and used to investigate the properties of an optical system, which consists of a crystal with a quadratic nonlinearity pumped at frequency $\omega$ and enclosed in a two-lens telescopic system. If a faint input image at frequency $2\omega$ is injected into this device, for a sufficiently large interaction length, the output displays a pair of symmetric amplified versions of the input image at both fundamental and second-harmonic frequency. The analysis of the quantum fluctuations in the output images shows that under certain conditions, this optical device operates noiselessly with respect to the output at frequency $\omega ,$ whereas the output images at frequency $2\omega$ are affected by a slight degradation of the signal-to-noise ratio.

A four-level system is proposed to explore the quantum-interference effects on optical amplification. It is found that the gain of the probe including positions and values of gain peaks can be adjusted by changing the coherent field and the incoherent pumping. As an application of the results, a scheme composed of three same ${\mathrm{Er}}^{3+}$-doped ${\mathrm{ZrF}}_4-{\mathrm{BaF}}_2-{\mathrm{LaF}}_3-{\mathrm{AlF}}_3-\mathrm{NaF}$ Optical Fibers with different coherent fields and incoherent pumpings is brought forward to equalize the gain of the probe.

Collisional transitions between molecular lines give rise to relevant modifications of the spectral distribution of absorption. We discuss here the consistency of such a coupling effect with the conservation of resonance frequency for the scattered lines, a requirement that, in the frame of the usually adopted impact approximation models, should follow from the conservation of energy in the collisions. This problem, leads either to the need for a more appropriate theoretical treatment of collisional coupling or to the existence of a decoupling between well resolved lines which could heavily affect the line shape in the far wings. A check allowing discrimination between these two events could be obtained by measurement of the microwave far wing absorption of deuterated ammonia.

We present numerical simulations of two-photon ionization of ${\mathrm{He}}^{+}$ by 27th harmonic pulses of a Ti:sapphire laser. This process is chosen as a candidate for the experimental observation of a nonlinear optical effect in the soft-x-ray domain. We solve the time-dependent Schrödinger equation and evaluate the ionization probability as the number of electrons absorbed by the mask function at the outer radial boundary. Our model can address questions concerning possible saturation and quantum interference in ionization at high intensity and ultrashort pulse duration with no ambiguity. According to our results, in spite of saturation of ionization found at intensity higher than ${10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ the ionization probability by a 30 fs harmonic pulse with a peak intensity of $(2\mathrm{}–5)\times {10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ attainable with the latest progress in high-order harmonic generation, should be sufficiently high to put the second-order nonlinear optical process in the soft-x-ray region within experimental reach, along with desirable properties such as its nearly quadratic dependence on intensity and approximate linearity in pulse width. Our simulations also show that the variation of the yield with the pulse width of the 27th harmonic is no longer linear for a pulse width shorter than 5 fs, while the dependence on intensity is still quadratic. Our analysis on the ionization of ${\mathrm{He}}^{+}$ by a double pulse in such an ultrashort pulse regime shows that the yield is not simply twice as large as that by a single pulse, but exhibits an oscillation of quantum origin with the interval and the phase difference between the two pulses. A simple model of the oscillation is discussed.

We show the existence of stationary solutions of a one-dimensional Gross-Pitaevskii equation in the presence of a multiwell external potential that do not reduce to any of the eigenfunctions of the associated Schrödinger problem. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.

We propose a scheme for quantum key distribution using macroscopic nonclassical pulses of light having of the order ${10}^6$ photons per pulse. Sub-shot-noise quantum correlation between the two polarization modes in a pulse gives the necessary sensitivity to eavesdropping that ensures the security of the protocol. We consider pulses of two-mode squeezed light generated by a type-II seeded parametric amplification process. We analyze the security of the system in terms of the effect of an eavesdropper on the bit error rates for the legitimate parties in the key distribution system. We also consider the effects of imperfect detectors and lossy channels on the security of the scheme.

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which tends to the solution. We apply this time-dependent Hamiltonian approach to Grover’s problem, i.e., searching a marked item in an unstructured database. We find that by adjusting the evolution rate of the Hamiltonian so as to keep the evolution adiabatic on each infinitesimal time interval, the total running time is of order $\sqrt{N},$ where N is the number of items in the database. We thus recover the advantage of Grover’s standard algorithm as compared to a classical search, scaling as N. This is in contrast with the constant-rate adiabatic approach of Farhi et al. (e-print quant-ph/0001106), where the requirement of adiabaticity is expressed only globally, resulting in a time of order N.

The ground-state dissociation (GSD) of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ molecular ions induced by ionizing and electron-capture collisions of ${\mathrm{He}}^{+}$ projectiles with hydrogen and deuterium molecules was investigated at impact velocities of 0.25 and 0.5 a.u. Momentum distributions of slow ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ fragments were measured and compared with calculations based on GSD theory. At the higher velocity, and for both capture and ionization, these distributions are well accounted for by a model that attributes the momenta to the vibrational wave function of the parent ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ molecule. For the lower velocity, this model remains successful for capture but not for ionization. For the latter case we observe a large transverse-momentum component imparted to the vibrationally excited ${\mathrm{H}}_2^{+}$ or ${\mathrm{D}}_2^{+}$ system beyond that predicted by the model. This feature is interpreted as being caused by momentum transferred to the motion of the nuclei within the molecule’s center-of-mass frame by way of a direct interaction between the projectile and one of the molecule’s nuclei.

For an attractive trapped Bose-Einstein condensate an imaginary three-body recombination loss term and an imaginary linear source term are usually included in the Gross-Pitaevskii (GP) equation for a proper account of dynamics. Under the action of an impulsive force, generated by suddenly changing the atomic interaction or the trapping potential, the solution of this complex GP equation for attractive interaction is found to lead to a very long-term chaotic oscillation.

A model is presented to describe the recently proposed experiment [J. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett 79, 1964 (1997)] in which a mesoscopic superposition of radiation states is prepared in a high-Q cavity that is coupled to a similar resonator. The dynamical coherence loss of such a state in the absence of dissipation is reversible and can be observed in principle. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that the phenomenon can still be observed provided the ratio between the damping constant and the intercavities coupling does not exceed about a few percent. This observation is favored for superpositions of states with a large overlap.

We present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than $\mathrm{}(M+1\mathrm{})\mathrm{}(N+1\mathrm{})\mathrm{}$ laser pulses are needed to generate a pure state with a phonon number limit M and N.

Two-dimensional Schrödinger equations with rotationally symmetric potentials $\left[V_a\right(\rho )=-a^2{g}_a{\rho }^{2\left(a-1\right)}$ with $\rho =\sqrt{x^2{+y}^2}$ and $a\ne 0]$ are shown to have zero-energy states. For the zero energy eigenvalue the equations for all a are reduced to the same equation representing two-dimensional free motions in the constant potential $V_a=-g_a$ in terms of the conformal mappings of ${\zeta }_a{=z}^a$ with $z=x+iy.\mathrm{}$ Namely, the zero-energy eigenstates are described by plane waves with the fixed wave numbers $k_a=\sqrt{{2mg}_a}/ħ$ in the mapped spaces. All the zero-energy states are infinitely degenerate similar to the case of the parabolic potential barrier (PPB) shown by Shimbori and Kobayashi [J. Phys. A 33, 7637 (2000)]. Following hydrodynamical arguments, we see that such states describe stationary flows around the origin, which are represented by the complex velocity potentials $W_a=\sqrt{{2g}_a/m}{z}^a,$ and their linear combinations create almost arbitrary vortex patterns. Examples of the vortex patterns in constant potentials and PPB are presented. In the extension to three-dimensional problems with potentials being separable into $2+1$ dimensions we show that the states in three dimensions have the same structure as the two-dimensional states with the zero energy but they can generally have nonzero total energies.

We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.

We show that entanglement-assisted transformations of bipartite entangled states can be more efficient than catalysis [Jonathan and Plenio, Phys. Rev. Lett. 83, 3566 (1999)], i.e., given two incomparable bipartite states not only can the transformation be enabled by performing collective operations with an auxiliary entangled state, but the entanglement of the auxiliary state itself can be enhanced. We refer to this phenomenon as supercatalysis. We provide results on the properties of supercatalysis and its relationship with catalysis. In particular, we obtain a useful necessary and sufficient condition for catalysis, and provide several sufficient conditions for supercatalysis and study the extent to which entanglement of the auxiliary state can be enhanced via supercatalysis.