A straightforward derivation of a first-quantization two-photon state vector is presented for the Hong-Ou-Mandel interferometer with a possible half-wave plate and possible linear analyzers in the ports. It is shown that one is dealing with a quantum eraser in a somewhat broader physical sense: It is not strictly the interference from version I of the experiment, the interference that has been suppressed by entanglement in version II, that is revived in version III; but it is an analogous interference. Besides, the coincidence probability for arbitrary-angle analyzers in the general case of arbitrary polarization in the lower arm of the interferometer is derived. The interference phenomenon of a complete decoupling of the partial loss of interference and the coincidence events in the ports is demonstrated. It is pointed out that the phenomenon of distant polarization (a special case of distant preparation) carries all the nonlocality between the two photons in the two ports.

The temporal behavior of the self-pumped phase conjugation in a photorefractive crystal with a variety of forms of the seed is carefully studied using a two-dimensional model which we proposed. For seeds of the small retroreflection and reflection, the model predicts that the self-pumped phase conjugator shows stable output, and the steady-state phase conjugate reflectivity versus the incident angle are in agreement with the experimental results. For the seed of the diffuse scattering, the conjugator shows either stable or unstable output, which is dependent on the incident angle. The frequency of the self-pulsation of the reflectivity increases linearly (or sublinearly) with an increase of the total light intensity. The model also predicts that there is no frequency shift between the input beam and the output phase conjugate beam for stable output. For unstable output there exists a frequency shift of ± a few Hz.

The standard single-shot estimate for the phase of a single-mode pulse of light is the argument of the complex amplitude of the field. This complex amplitude can be measured by heterodyne detection, in which the local oscillator is detuned from the system so that all quadratures are sampled equally. Because different quadratures do not commute, such a measurement introduces noise into the phase estimate, with a variance scaling as $N^{-1}$, where $N$ is the maximum photon number. This represents the shot-noise limit or standard quantum limit (SQL). Recently, one of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] proposed a way to improve upon this: a real-time feedback loop can control the local oscillator phase to be equal to the estimated system phase plus $\pi /2\mathrm{}$, so that the phase quadrature of the system is measured preferentially. The phase estimate used in the feedback loop at time $t$ is a functional of the photocurrent from time $0$ up to time $t$ in the single-shot measurement. In this paper we consider a very simple feedback scheme involving only linear electronic elements. Approaching the problem from semiclassical detection theory, we obtain analytical results for asymptotically large photon numbers. Specifically, we are able to show that the noise introduced by the measurement has a variance scaling as $N^{-3/2}$. This is much less than the SQL variance, but still much greater than the minimum intrinsic phase variance which scales as $N^{-2}$. We briefly discuss the effect of detector inefficiencies and delays in the feedback loop.

We apply two quantum-trajectory methods to a decaying system of $N$ two-level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the $\tanh$-like decay of the inversion for large $N$. This $\tanh$ behavior is also found for the jump-free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emission. However, we find that this behavior of superfluorescence is governed by the jump statistics. The jump-free evolution of the Dicke system displays other atypical behavior. We find that the energy of the system can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffusion method to the system, we find that the trajectories keep the system in a spin coherent state, which confirms the picture of superfluorescence for single trajectories as a toppling needle point. This enables us to write an approximate analytic expression for the decay of the energy for any $N$. Finally, we discuss the calculation of two-time correlation functions per trajectory and as an illustration we calculate the single-trajectory spectra. In the quantum-jump method, these single-trajectory spectra do not correspond to intuition, which we ascribe to the incompatibility of photon counting and spectral measurement.

We describe the propagation dynamics and gain line shape of pulsed, tunable, anti-Stokes Raman lasers without inversion. Analytical expressions for the gain are obtained and evaluated for inhomogeneously broadened atomic media. The inversionless gain, which requires selective pumping of one of two lower atomic states, occurs regardless of the relative populations of these states and vanishes when the atomic populations are in equilibrium.

Resonance transmission in a three-level $\Lambda$-type system of the rubidium $D1\mathrm{}$ line is controlled by adjusting the linewidth of the pumping (coupling) laser. With the change of pumping-laser linewidth from several MHz to about 100 MHz, the absorption reduction degrades from about 70% to less than 15%. The experimentally measured results are in good agreement with a simple theoretical calculation.

A comprehensive theory of sum-frequency generation (SFG) spectroscopies with infrared pump and infrared-visible probe is presented in a systematic way based on the Markovian master equation approach. A description of SFG as a five-wave mixing process is given by using a perturbation theory for both the stationary and time-resolved experiments. A criterion for the validity of the perturbation treatment is also presented in terms of the saturation parameter. Simple expressions are derived by introducing the rotating-wave approximation for a four-level model system of the adsorbed molecule. It is shown that the fourth-order induced nonlinear polarization at the SF can be expressed as a sum of three components which are induced by different field-molecule interactions. Numerical calculations for the recent experimental results of the SFG spectroscopy applied to C-H stretch modes on the hydrogen-terminated H/C(111) $(1\mathrm{}\times 1)$ surface are performed to show the applicability of our expressions as well.

Several quantum descriptions of the relative phase between an atomic dipole and a one-mode electromagnetic field are examined. Positive-operator measures for this variable are derived from dipole and field-phase formalisms. They are analyzed and compared with an operator defined by a polar decomposition. Some examples of time evolution are discussed.

I construct a quantum error correction code (QECC) in higher spin systems using the idea of multiplicative group character. Each $N$-state quantum particle is encoded as five $N$-state quantum registers. By doing so, this code can correct any quantum error arising from any one of the five quantum registers. This code generalizes the well-known five qubit perfect code in spin-1/2 systems and is shown to be optimal for higher spin systems. I also report a simple algorithm for encoding. The importance of multiplicative group character in constructing QECCs will be addressed.

We present an ab initio calculation of single ionization, harmonic generation, and double excitation of helium by short (3.8–15.2 fs) moderately strong (peak intensity $1.49\times {10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2)$ laser pulses with wavelengths between 40 and 152 nm. We find excitation to be dominated by resonances with bound and doubly excited states. The processes are nonperturbative. The finite pulse duration leads to resonance broadening and far-off-resonant transitions.

It is shown that molecules can be focused in the gradient of a moderately intense laser field under standard molecular-beam conditions. Simple relationships are given for the focal length and the minimum molecular beam size. Both can be controlled and varied over a wide range by choice of the molecular beam and field parameters. Molecular focusing is proposed as a route to nanoscale processing (deposition, etching, doping, etc.) of materials. Molecular trapping is obtained as the strong interaction limit of a general “molecular optics” scheme.

The generation of entangled states of three or more photons through the nonlinear process of spontaneous parametric down-conversion requires the use of a femtosecond pump to provide an indistinguishability of photon pairs generated from different nonlinear crystals. We demonstrate experimentally that the quantum interference between two photons generated in each of the nonlinear crystals will degrade significantly as the duration of the femtosecond pump pulse becomes shorter than the coherence time of the signal and idler photons. Spectral postselection using narrow-band filters compensates this effect at the expense of the photon flux available for detection.

A simple semiclassical formula is given for the oscillator strengths of high Rydberg states of a hydrogen atom in an electric field. The oscillator strength of a state is proportional to the square of the function representing the quantum angular distribution of outgoing waves, evaluated at the classical angle of ejection from the atom that sends the electron into a semiclassically quantized eigentrajectory. The formula gives an interpretation of the envelopes of Stark manifolds in photoabsorption spectra; it is in good agreement with quantum calculations. The formula may also be used for other integrable or near-integrable systems.

We show that internal state transitions may induce energy transfer among different directions of motion and lead efficiently to large scattering angles in atomic reflection from evanescent-wave mirrors. The proposed scattering mechanism is reminiscent of the so-called Sisyphus effect of laser cooling. Perturbative calculations are presented and discussed for the diffraction of atomic beams at grazing incidence on evanescent fields with polarization gradients and for the reflection of atoms by a rough mirror.

We consider general time-dependent quadratic Hamiltonian systems which are connected by canonical transformations and give the same classical equations of motion. In those systems, we demonstrate that canonical transformations in classical mechanics correspond to unitary transformations in quantum mechanics. The wave functions and the propagators are evaluated using the invariant operator method. However, the values of some functions of the canonical variables q and p are not equal to the values of the same functions of the other canonical variables Q and P, but the values of the functions of q and the kinetic momentum ${\mathrm{p}}_{\mathrm{k}}$ are equal to those of the other Q and ${\mathrm{P}}_{\mathrm{k}}$ in classical mechanics. We prove that these also hold in the quantum treatment. The uncertainty relations of momentum and position are evaluated for the two Hamiltonians.

In standard quantum theory, the ideas of information entropy and of pure states are closely linked. States are represented by density matrices ρ on a Hilbert space and the information entropy - tr(ρ ln ρ) is minimized on pure states (pure states are the vertices of the boundary of the convex set of states). The space of decoherence functions in the consistent histories approach to generalized quantum theory is also a convex set. However, by showing that every decoherence function can be written as a convex combination of two other decoherence functions, we demonstrate that there are no ``pure'' decoherence functions. The main content of the paper is a notion of information entropy in generalized quantum mechanics which is applicable in contexts in which there is no a priori notion of time. Information entropy is defined first on consistent sets and then we show that it decreases upon refinement of the consistent set. This information entropy suggests an intrinsic way of giving a consistent set selection criterion.

The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit [W. H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982)]. This limit, and other simplifying assumptions, have allowed the derivation of several simple results characterizing the onset of environmentally induced superselection; but these results are increasingly often regarded as a complete phenomenological characterization of decoherence in any regime. This is not necessarily the case: the examples presented in this paper counteract this impression by violating several of the simple general rules. This is relevant because decoherence is now beginning to be tested experimentally [C. Monroe et al., Science 272, 1131 (1996); M. Brune et al., Phys. Rev. Lett. 77, 4887 (1996)], and one may anticipate that, in at least some of the proposed applications (e.g., quantum computers), only the basic principle of ``monitoring by the environment'' will survive. The phenomenology of decoherence may turn out to be significantly different.

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities. Using this result—which applies to degenerate as well as nondegenerate codes—previously established necessary conditions for classical linear codes can be easily translated into necessary conditions for quantum stabilizer codes. Examples of specific consequences are as follows: for a quantum channel subject to a δ fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H(+$\sqrt{2\delta \left(1\mathrm{}-2\delta \right)}$); and, for the depolarizing channel with fidelity parameter δ, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H(δ).

The interaction between two identical atoms, separated by a distance r that is large compared to an optical wavelength, is considered using an amplitude approach in the Schrödinger picture. When atom 1 is excited by a radiation pulse whose duration is long compared to an optical period but short compared to the time it takes for light to travel between the atoms, the probability for atom 2 to be excited is found to be identically zero for times t

We analyze the evolution of a quantum Brownian particle starting from an initial state that contains correlations between this system and its environment. Using a path-integral approach, we obtain a master equation for the reduced density matrix of the system finding relatively simple expressions for its time-dependent coefficients. We examine the evolution of delocalized initial states (Schrödinger cats) investigating the effectiveness of the decoherence process. Analytic results are obtained for an Ohmic environment (Drude's model) at zero temperature.