It is shown that a simplified version of the error correction code recently suggested by Shor [Phys. Rev. A 52, R2493 (1995)] exhibits manifestation of the quantum Zeno effect. Thus, under certain conditions, protection of an unknown quantum state is achieved. Error prevention procedures based on four-particle and two-particle encoding are proposed and it is argued that they have feasible practical implementations.

A variational calculation is presented of energy levels for the nonrelativistic Hamiltonian of the metastable antiprotonic helium atom ${\overline{p}}^{3, 4}{\mathrm{He}}^{+}$. This calculation is based on a molecular expansion of the wave function. We estimate the precision of the results to be about ${10}^{-7\mathrm{}}$ a.u.

We discuss the dynamic properties of a trapped Bose-condensed gas under variations of the confining field and find analytical scaling solutions for the evolving coherent state (condensate). We further discuss the characteristic features and the depletion of this coherent state.

Superconductivity, superfluidity, Bose-Einstein condensation, and laser amplification are all examples of a general mechanism involving the stimulated transfer of bosons into a specific quantum state. When the occupation number of the state is large, this mechanism may generate a macroscopic coherence for the state amplitude. In this paper, we demonstrate that the stimulated transfer of bosonic atoms into a given state of an optical or a magnetic trap can give rise to a coherent atomic source in analogy with the photon laser and we present a general model for such a device.

We study harmonic generation by a single atom exposed to two short perpendicularly polarized laser pulses. The two perpendicular electric fields oscillate at two different frequencies ${\omega }_1$ and ${\omega }_2$. Hence, the resultant field has a polarization which depends on time. Since harmonics are emitted when the resultant oscillating field is linearly polarized, it is expected that a short pulse of harmonics may be emitted if the external field is linearly polarized during a short period of time. We show that, indeed, the atom may emit an ultrashort pulse of a given harmonic. This result has been obtained by time-frequency analyzing the acceleration of the induced dipole moment with a filter whose frequency bandwidth is smaller than twice the frequency of the external field. Our calculation of the dipole acceleration is based on the numerical solution of the time-dependent Schrödinger equation. We then address the question of how far it is possible to reduce the duration of the emitted pulse of one given harmonic by adjusting both ${\omega }_1$ and ${\omega }_2$ and keeping the amplitude of this pulse significant. In order to answer to this question, we used the quantum version of the two-step model [M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)].

A strong-field theory is extended to the description of energetic photoelectron spectra. Experimental spectra are accurately described for both linear and circular polarizations, subject only to a single adjustment of reported peak laser intensities. Examined are single and (sequential) double ionization of helium, to energies of about 1 keV. An approximation of the spectrum as a Maxwellian distribution yields a temperature dependent on the spectrometer viewing angle. Final-state Coulomb effects in circular polarization are examined.

We propose a mechanism of generating very high harmonics at moderate laser intensities by transmission of electrons in a thin crystal. Results of nonperturbative Floquet-Bloch calculations show the possibility of controlling the height and range of high-harmonic spectra through the mechanism of interband resonances at suitable energies of the incident electrons and/or intensity of the laser field.

Velocity-selective adiabatic population transfer by time-delayed laser pulses is considered. In this process only a narrow part of an atomic momentum distribution follows the "dark" state adiabatically. The remaining atoms are excited and partially pumped into the dark state. We show that this effect can be used for cooling atoms below the photon recoil energy using pulsed laser radiation.

We report on the realization of a whispering-gallery-mode laser based on neodymium-doped silica microspheres. Absorbed pump powers at threshold are as low as 200 nW. The linear variation of the threshold with the loss factor of the cavity mode has also been observed. We discuss the potential of this system as a permanent microlaser operating with a few active ions at liquid-helium temperature.

It is shown that a recently reported realization of trapping in a two-level system with frequency-modulated fields in quantum optics is intimately related to an earlier demonstration of dynamic localization of charges moving in a crystal under the action of a time-periodic electric field. Size effects on the phenomenon are explored.

Using coherent nonlinear optical spectroscopy below the band edge of a GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{1-0.3}$As multiple quantum well, photon-number squeezed light generated by a quantum-well laser is used to resolve the exciton resonances and the Urbach tail with detection sensitivity below the semiclassical shot-noise limit. The effect of polarization-dependent noise in the nonclassical probe field is also investigated.

We present experimental evidence of spontaneous buildup of coherent exciton polariton population in a microcavity, i.e., an exciton polariton laser. The laser phase transition was confirmed by the increased differential quantum efficiency and decreased linewidth of the lasing polariton mode due to onset of final-state stimulations and the decreased differential quantum efficiency of a nonlasing polariton due to onset of gain clamping at threshold. The exciton polariton laser is distinctly different from an optical laser because of its density-dependent scattering mechanism. The rate equations, taking into account phonon-assisted polariton emission and the polariton-reservoir exciton scattering rate, explain the measurement results well.

We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order ${\mathit{K}}^3$ using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor’s algorithm) could be achieved with about 72${\mathit{K}}^3$ elementary quantum gates; implementation using a linear ion trap would require about 396${\mathit{K}}^3$ laser pulses. A proof-of-principle demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states. © 1996 The American Physical Society.

We numerically simulate the quantum measurement process by modeling the measuring apparatus as a one-dimensional Dirac comb that interacts with an incoming object particle. The global effect of the apparatus can be well schematized in terms of the total transmission probability and the decoherence parameter, which quantitatively characterizes the loss of quantum-mechanical coherence and the wave-function collapse by measurement. These two quantities alone enable one to judge whether the apparatus works well or not as a detection system. We derive simple theoretical formulas that are in excellent agreement with the numerical results, and can be very useful in order to make a ‘‘design theory’’ of a measuring system (detector). We also discuss some important characteristics of the wave-function collapse. © 1996 The American Physical Society.

We derive a set of exact solutions of the Dirac equation for a single electron moving in a multimode quantized radiation field. All the modes in this field are propagating in the same direction. Our method entails the application of the Lie-algebra procedure. We discuss the physical meaning and possible applications of these solutions. © 1996 The American Physical Society.

A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n=1-2${\mathit{H}}_2$(2t/n) where ${\mathit{H}}_2$(p) is the binary entropy function -p${\log }_2$p-(1-p)${\log }_2$(1-p). Upper bounds on this asymptotic rate are given. © 1996 The American Physical Society.

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. © 1996 The American Physical Society.

The discrete-time jump model for intrinsic decoherence in quantum mechanics proposed recently by Milburn is here generalized to explicitly time-dependent Hamiltonians. In this model, a time-dependent entropy is obtained and thus it admits of an interpretation that this is a model for an open system. Unlike in the Milburn model, we introduce a minimum uncertainty phase change dictated by the minimum ‘‘time-energy uncertainty product’’ to define the shortest time scale in the system. Implications of this model to quantum nanometric devices such as quantum dots or resonant tunneling devices are indicated. © 1996 The American Physical Society.

A calculation of the Aharonov-Bohm wave function is presented. The result is an asymptotic series of confluent hypergeometric functions which is finite at the forward direction. © 1996 The American Physical Society.

The phase loss of a wave reflected by a smooth potential generally varies continuously from π in the long-wave limit to π/2 in the limit of short waves. Incorporating the corresponding nonintegral multiples of π/2 as nonintegral Maslov indices in the formulation of the WKB approximation leads to a substantial improvement of accuracy when the conditions for applicability of the WKB method are violated only near the classical turning points. We demonstrate the efficacy of using nonintegral Maslov indices for a Woods-Saxon potential and a repulsive 1/${\mathit{x}}^2$ potential. The nonintegral Maslov index for a given 1/${\mathit{x}}^2$ potential yields far more accurate wave functions than the conventional Langer modification of the potential in conjunction with phase loss π/2. The energy spectrum of the radial harmonic oscillator (including the centrifugal potential), which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification when the nonintegral Maslov index is used. We suggest a method for approximately calculating the nonintegral Maslov index near the long-wave limit from the decaying WKB wave function in the classically forbidden region. © 1996 The American Physical Society.