We report loading of $1.5\times {10}^9$ metastable triplet helium atoms in a large magneto-optical trap, using far-red-detuned laser beams. We fully characterized this trap by measuring trap losses and absorption of a probe beam. From the highly nonexponential trap decay we derive Penning ionization loss rate coefficients for two detunings: $5.3\left(9\right)\mathrm{}\times {10}^{-9}{\mathrm{cm}}^3/\mathrm{s}$ at $-35\mathrm{MHz}$ and $3.7\left(6\right)\mathrm{}\times {10}^{-9}{\mathrm{cm}}^3/\mathrm{s}$ at $-44\mathrm{MHz}.$ Also, we find that the loss rate is maximum at $-5\mathrm{MHz}$ detuning, where the rate is $1.3\left(3\right)\mathrm{}\times {10}^{-8}{\mathrm{cm}}^3/\mathrm{s},$ much larger than recent theoretical and experimental values. In the absence of light the $S-S$ ionization rate constant is measured to be $1.3\left(2\right)\mathrm{}\times {10}^{-10}{\mathrm{cm}}^3/\mathrm{s}.$

In recent experiments on Na Bose-Einstein condensates [S. Inouye et al., Nature 392, 151 (1998); J. Stenger et al., Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of atom pairs that belong to the condensate many-body wave function. A mechanism is offered here to account for the observed losses. It is based on the deactivation of the resonant molecular state by interaction with a third condensate atom, with a deactivation rate coefficient of magnitude $\sim {10}^{-10}\hspace{0.5em}{\mathrm{cm}}^3/\mathrm{s}.$

We suggest measuring the one-particle density matrix of a trapped ultracold atomic cloud by the scattering of fast atoms in a pure momentum state off the cloud. The lowest-order probability for the process, resulting in a pair of outcoming fast atoms for each incoming one, as well as of its time-reversed counterpart, turns out to be given by the Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross section of these processes. Several most interesting cases of scattering — from a single condensate containing a vortex and from a split condensate characterized by some phase difference — are discussed.

Using the process of spontaneous parametric down-conversion in a two-crystal geometry, we have generated a source of polarization-entangled photon pairs that is more than ten times brighter, per unit of pump power, than previous sources, with another factor of 30 to 75 expected to be readily achievable. We have measured a high level of entanglement between photons emitted over a relatively large collection angle, and over a 10-nm bandwidth. As a demonstration of the source capabilities, we obtained a 242-σ violation of Bell’s inequalities in less than three minutes, and observed near-perfect photon correlations when the collection efficiency was reduced. In addition, both the degree of entanglement and the state purity should be readily tunable.

High-order harmonic generation by metallic carbon nanotubes exposed to an intense ultrashort pulse has been theoretically investigated in the semiclassical approximation. The mechanism of nonlinearity provided by the motion of conduction electrons below the band of optical resonances has been considered. It has been shown that the high density of states of conduction electrons in metallic carbon nanotubes and the specific dispersion law inherent in hexagonal crystalline structure as well as the transverse quantization of the electron momentum result in a uniquely high efficiency of the current conversion to high-order harmonics.

Recent experimental results on edge-filtered (also referred to as low- and high-pass filters) subpicosecond optical solitons have raised a number of theoretical questions concerning the origin of the reduced photon- number fluctuations. One of the main experimental results was that for long fibers, on the order of 100 soliton periods, the measured photon-number squeezing increased with propagation distance in contrast with theoretical calculations for picosecond solitons at that time. Here I present theoretical results on photon statistics of edge-filtered subpicosecond optical solitons. The numerical simulations include coupling to phonons via a Raman interaction, in addition to the electronic Kerr nonlinearity, and are in good agreement with the experimental data over the range of propagation distances investigated so far. The theoretical results clearly show that the phenomena observed are not related to long fiber propagation but to the Raman self-frequency shift and should be more clearly observable using cooled fiber.

The supersymmetric WKB (SWKB) approximation is known to give exact results for translationally shape-invariant potentials. To examine how this approximation fares for potentials which are not shape invariant, we investigate two such potentials: the double oscillator well and the finite square well. In the case of the double oscillator, where the energy levels are nearly degenerate, no analytic expression for the superpotential is possible and the SWKB approximation is far worse than the WKB approximation. But for the finite square well, where the energy spectrum is nondegenerate and an analytic expression for the superpotential is possible, the SWKB approximation is much better than the WKB approximation for almost all states. Thus the discreteness of the energy spectrum and the existence of an analytic expression for the superpotential are preconditions for applicability of the SWKB approximation.

Two types of destructive interference among quantum phases are discussed that play an essential role in canceling out the unquantized states and thereby leaving only the correct projection of true eigenstates behind. Without these mechanisms, the Fourier spectra of the autocorrelation function, from which the energy spectra can be deduced numerically, can suffer from spurious features. We show two such examples: One is a spurious spectrum that appears in the negative energy domain of the Fourier frequencies for a positive potential. The other is a family of harmonic and subharmonic frequencies that are born from the “quantizing orbits,” which are responsible for forming eigenstates like the periodic orbits or those satisfying the Einstein-Brillouin-Keller condition. The mechanisms for the spurious spectra to appear are analyzed, emphasizing their relationship to the quality of semiclassical wave functions.

The adiabatic approximation usually applies to a collection of lighter particles (the “fast” system) and heavier particles (the “slow” system), where the geometric phase naturally appears. With the help of the recently introduced gauge potential in the context of adiabatic Berry phase for open paths, we establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change (of the “slow” system) to the time integral of the quantum correlation function between the projection operator and force operator acting on the “fast” system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalized susceptibility. The relation between the open-path geometric phase, diagonal elements of the quantum metric tensor, and the force-force correlation function are provided and the classical limit of the fluctuation-correlation theorem is discussed.

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean-average fidelity. We do this for up to three copies of the unknown state in a way that leads to the generalization to any number of copies, which we then present and prove.

State-dependent cloning machines that have so far been considered either deterministically copy a set of states approximately or probablistically copy them exactly. In considering the case of two equiprobable pure states, we derive the maximum global fidelity of N approximate clones given M initial exact copies, where $N>M$. We also consider strategies that interpolate between approximate and exact cloning. A tight inequality is obtained that expresses a trade-off between the global fidelity and success probability. This inequality is found to tend, in the limit $N\overrightarrow{}\infty$, to a known inequality that expresses the trade-off between error and inconclusive result probabilities for state-discrimination measurements. Quantum-computational networks are also constructed for the kinds of cloning machine we describe. For this purpose, we introduce two gates: the distinguishability transfer and state separation gates. Their key properties are described and we show how they may be decomposed into basic operations.

Single ions in a linear string have been addressed with a tightly focused laser beam and an acousto-optic deflector. The excitation into a long-lived metastable level is detected with a quantum jump technique. Single-quantum bit operations for quantum information processing with trapped ions are shown to be feasible.

A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and sequences are “refueled” from a shared provably secret key transferred through the quantum channel. Two identification protocols are devised. The first protocol can be applied when legitimate users have an unjammable public channel at their disposal. The deception probability is derived for the case of a noisy quantum channel. The second protocol employs unconditionally secure authentication of information sent over the public channel, and thus can be applied even in the case when an adversary is allowed to modify public communications. An experimental realization of a quantum identification system is described.

This paper proposes a quantum communication scheme for sending a definite binary sequence while confirming the security of the transmission. The scheme is very suitable for sending a ciphertext in a secret-key cryptosystem so that we can detect any eavesdropper who attempts to decipher the key. Thus we can continue to use a secret key unless we detect eavesdropping and the security of a key that is used repeatedly can be enhanced to the level of one-time-pad cryptography. In our scheme, a pair of entangled photon twins is employed as a bit carrier which is encoded in a two-term superposition of four Bell states. Different bases are employed for encoding the binary sequence of a ciphertext and a random test bit. The photon twins are measured with a Bell state analyzer and any bit can be decoded from the resultant Bell state when the receiver is later notified of the coding basis through a classical channel. By opening the positions and the values of test bits, ciphertext can be read and eavesdropping is simultaneously detected.

We put forward a method for optimized distillation of partly entangled pairs of quantum bits into a smaller number of more entangled pairs by recurrent local unitary operations and projections. Optimized distillation is achieved by minimization of a cost function with up to 30 real parameters, which is chosen to be sensitive to the fidelity and the projection probability at each step. We show that in many cases this approach can significantly improve the distillation efficiency in comparison to the present methods.

The notion of distillable entanglement is one of the fundamental concepts of quantum information theory. Unfortunately, there is an apparent mismatch between the intuitive and rigorous definitions of distillable entanglement. To be precise, the existing rigorous definitions impose the constraint that the distillation protocol produce an output of constant dimension. It is therefore conceivable that this unnecessary constraint might have led to underestimation of the true distillable entanglement. We give a definition of distillable entanglement which removes this constraint, but could conceivably overestimate the true value. Since the definitions turn out to be equivalent, neither underestimation nor overestimation is possible, and both definitions are arguably correct.

The best bound known on 2-locally distillable entanglement is that of Vedral and Plenio, involving a certain measure of entanglement based on relative entropy. It turns out that a related argument can be used to give an even stronger bound; we give this bound, and examine some of its properties. In particular, and in contrast to the earlier bounds, the new bound is not additive in general. We give an example of a state for which the bound fails to be additive, as well as a number of states for which the bound is additive.

The effect of off-diagonal interactions between quantum bits is studied in a simple quantum computer algorithm designed to calculate the sum of two n-bit numbers. Scaling laws are derived numerically for the dependence of the error on the number n of bits, the strength of the interaction, and the calculation time. The case of diagonal interactions, previously studied in the context of the quantum Fourier transform algorithm, is also considered. No substantial differences are found between the off-diagonal and diagonal forms of the interaction: in both cases, the errors accumulate almost coherently, despite the fact that the system’s free evolution is constantly being interrupted by the logical gates, which scramble the coefficients of the wave function. Some comments on the possibility of using “field-insensitive” atomic states in ion-chain quantum computers are also given.

We investigate the purification of entangled states by local actions using a variant of entanglement swapping. We show that there exists a measure of entanglement which is conserved in this type of purification procedure.

Using time-resolved UV laser-induced fluorescence from a laser-produced plasma, natural radiative lifetimes have been measured for 21 levels of Ge I belonging to the odd-parity $4p4d,4p5d,$ and $4p6s$ configurations. Stimulated Brillouin scattering in water has allowed us to compress Nd:YAG laser pulses pumping a dye laser (where YAG denotes yttrium aluminum garnet), thus yielding 1-ns tunable laser pulses to enable accurate measurements of short lifetimes. Branching ratios of Ge I have been measured by inductively coupled plasma emission spectrometry, the intensity calibration being performed by means of Ar lines emitted by a hollow-cathode lamp. The experimental lifetimes and branching ratios have been combined in order to provide a set of accurate transition probabilities for the $4p-5s$ and $4p-4d$ transitions. A relativistic Hartree-Fock calculation, taking configuration-interaction and polarization effects into account, has been combined with a least-squares optimization procedure of the Slater and spin-orbit integrals in order to test the ability of this approach to correctly predict radiative properties of the group-IV elements. Good agreement between experimental and theoretical transition probability values has been achieved for most of the transitions considered.