The vibrational state of a polyatomic molecule excited with a transform limited light pulse is determined analytically. We analyze how the properties of the vibrational state depend on the duration of the exciting pulse and the possible geometrical configurations of the nuclear potential surfaces. It is pointed out that a finite exciting pulse results in an entangled vibrational state. The magnitude of the entanglement is described by the von Neumann entropy associated with the vibrational modes. It is shown that in the case of a very short excitation, the change of the geometrical configuration of the vibrionic potential surface may also lead to entanglement. © 1996 The American Physical Society.

We discuss a simple implementation of a quantum nondemolition measurement of the vibronic state of a trapped ion. This scheme allows the production of Fock states associated to the center-of-mass motion and the determination of the population distribution of the trap levels, and is based on the vibronic level dependence of the frequency of Rabi oscillations between two internal states of the ion, induced by a resonant carrier field. The same scheme can be used to produce a Schrödinger-cat-like state after a single interaction between the trapped ion and the carrier pulse, followed by the detection of the ionic internal state. © 1996 The American Physical Society.

A (2+1) resonance-enhanced multiphoton-ionization photoelectron spectroscopy study of the sulfur atom was performed in the one-photon energy region between 260 and 240 nm. Some 20 previously unobserved even-parity Rydberg states of the sulfur atom are reported, which were accessed by two-photon transitions from the ${}_{}{}^3{}_{}{}^{}$P ground state of the atom, prepared by in situ photodissociation of ${\mathrm{H}}_2$S. The ${(}^4$${\mathit{S}}^{\mathit{o}}$)np${\mathrm{}}^3$P series could be followed up to n=25. This series is perturbed around n=7 by an interloping Rydberg state converging to the first excited ionic limit ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$. A two-channel quantum defect theory analysis was performed in order to estimate the composition of the wave functions of the perturbed series members, which is compared with the ionic state branching ratios obtained from photoelectron spectra. This analysis, moreover, enabled the determination of the ionization energy of the lowest ionic state ${}_{}{}^4{}_{}{}^{}$${\mathit{S}}^{\mathit{o}}$ with an improved accuracy as compared to the previously reported value. © 1996 The American Physical Society.

Laser cooling of trapped multilevel ions is studied numerically. The ions are assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke regime). A master equation for the center-of-mass motion is used to numerically evaluate cooling rates and final temperatures for arbitrary light field configurations. The results show both well-known cooling mechanisms (Doppler cooling, sideband cooling) and effects introduced by the presence of multiple atomic levels. Quantitative results are given for a trapped ${\mathrm{Ba}}^{+}$ ion. The numerical procedure can easily be adapted for all ions used in today’s trapping experiments. © 1996 The American Physical Society.

We show that a series of quantum computations involving an isolated N-quantum-bit ion register can be used to make an approximate quantum nondemolition measurement of the number state distribution of a collective vibrational mode. A unitary transformation is applied to the Fourier transformed state of the ion register to copy the vibrational statistics to the electronic mode, and the number state distribution is then measured in the electronic number state basis using the quantum jumps technique. © 1996 The American Physical Society.

We show that efficient transfer of molecules or atoms from one bound state to another is possible via the continuum in some cases, using two overlapping laser pulses. The structure of the continuum determines the pulse delay, laser frequencies, and laser intensities that should be used. We present simple formulas that relate the optimum values of pulse intensities, pulse separation, and detuning; these estimates can be used as a guide. More detailed calculations give quantitative results for two specific potentials. © 1996 The American Physical Society.

Iterative techniques for the interaction of weak and very strong fields with multilevel systems are developed. They are based on the expansion of the density matrix in powers and inverse powers of the respective dipole field strengths, as appropriate. The specific cases of three incident weak fields, and of three incident very strong fields having equal dipole field strengths are discussed in detail and applied to the 3s-3p transitions in sodium. Comparison with numerical results indicates the regions of validity of these analytical results. © 1996 The American Physical Society.

We examine the role of the dipole moment induced by an intense nonresonant infrared laser field on exchange reactions of the type A+BC→AB+C. This is compared to previous work which included the effect of the permanent dipole moment and its variation along the reaction coordinate. The formalism for laser-molecule interaction is developed for the cases where the reciprocal laser frequency is comparable to or much shorter than the time required for the system to cross the transition state. It is predicted that the induced dipole moment will both lower the electronic barrier to reaction and also create bound states along the reaction path. Results of classical trajectory calculations are presented for the collinear H+${\mathrm{H}}_2$→${\mathrm{H}}_2$+H reaction, using ab initio dipole moment and polarizability surfaces. It is found that the collisional energy threshold for reaction is lowered significantly, and that the effects of the induced dipole moment dominate over those of the permanent dipole moment. A time-dependent analysis of the reaction shows that the fluctuating barrier can occasionally be very low when the transition state is approached, allowing trajectories to be reactive with very low collision energies. © 1996 The American Physical Society.

The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time of flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time of flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times of flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them. © 1996 The American Physical Society.

We report a systematic investigation of the angular energy distribution and temporal evolution of pulses emitted from low-Z neonlike J=0–1 lasers by comparing prepulse-induced lasing in different materials (S, Cl, Ca, Ti, Ni, Cu, and Zn) and at different driving energies in the main pulse and the prepulse. It is found that with a main pulse energy of 350±35 J and a prepulse energy of 50±5 J, the laser peaks about 4 mrad off axis with a divergence of 4.5–7.5 mrad for the low-Z materials S, Cl, Ca, Ti, and Ni. Under the same conditions for Cu, Zn, and Ge the laser peaks about 6–7 mrad off axis with a divergence of 5–8.2 mrad. The lasing pulse durations range from 146 to 349 ps for Z=30–16 and peak at 237–413 ps before the peak of the L-band emission or the J=2–1 lasing line. The beam deflection and divergence, as well as the pulse duration are quite insensitive to the energies of the main pulse and the prepulse. However, a lower driving main pulse energy brings lasing close to the peak of the L-band emission. © 1996 The American Physical Society.

A theory of multimode oscillation in an optical unidirectional ring resonator with photorefractive gain was given in the weak-field limit, in which the mode coupling is considered carefully. The characteristics of single-mode oscillation in steady state were analyzed in detail, especially when the externally applied dc electric field is not zero. By numerical simulation, we investigated a three-mode oscillation and observed instability phenomena which are similar to the periodic oscillation of several transverse family modes observed in experiment. © 1996 The American Physical Society.

The theory of the laser amplifier is developed for conditions in which the strength of the input signal is increased from small values, where the amplification is linear, to larger values, where the amplification becomes nonlinear. The below-threshold laser amplifier oscillates at a single frequency equal to that of the input signal, and its properties are found by solution of the nonlinear equation of motion for the single excitation amplitude. For the above-threshold laser amplifier, the effects of the nonlinear behavior are to shift the laser frequency from its free-running value and to transfer intensity from the laser line to the signal frequency and to a range of satellite lines, whose frequency detunings are integer multiples of the signal detuning. The intensities of the various emission lines of the laser are calculated by power-series expansions of the field amplitudes up to terms of fourth order in the input signal strength. The onset of injection locking is determined by the conditions for which the intensity at the shifted free-running laser frequency falls to zero. The injection-locked state is characterized by a single excitation frequency equal to that of the input signal, and its properties are found by solution of the same nonlinear equation of motion as for the below-threshold amplifier. The ranges of input signal strength and detuning are determined for which the injection-locked state is stable. The energy conservation properties of the laser amplifier are considered for each of its operating states. © 1996 The American Physical Society.

The lifetime of an excited atom near an absorbing dielectric surface is calculated from an exact solution of a microscopic Hamiltonian model, which includes the effects of dispersion, local-field correction, and near-field Coulomb interaction. Results for the total decay rate are shown to be in excellent agreement with those based on classical electromagnetic theory and to yield the well-known result for the rate of nonradiative energy transfer in the limit of very small distance from the surface. © 1996 The American Physical Society.

We analyze nonlinear transverse mode coupling in a Kerr medium placed in an optical cavity and its influence on bistability and different kinds of quantum noise reduction. Even for an input beam that is perfectly matched to a cavity mode, the nonlinear coupling produces an excess noise in the fluctuations of the output beam. Intensity squeezing seems to be particularly robust with respect to mode coupling, while quadrature squeezing is more sensitive. However, it is possible to find a mode whose quadrature squeezing is not affected by the coupling. © 1996 The American Physical Society.

We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state, and can be equivalently defined by some eigenvalue equations. The system prepared initially in the reference state will evolve into the coherent state during the first instants of the interaction process. Some properties of the coherent states are discussed. In particular, the resolution of the identity is derived and the related analytic representation in the complex plane is developed. It is shown that this analytic representation coincides with a double representation based on the Glauber coherent states of the pump mode and on the SU(1,1) Perelomov coherent states of the signal-idler system. Entanglement between the field modes and photon statistics of the coherent states are studied. Connections between the coherent states and the long-time evolution induced by the trilinear Hamiltonian are considered. © 1996 The American Physical Society.

We have developed a general technique for obtaining analytical expressions for coherent transient signals arising from atoms interacting with two or more laser pulses having Gaussian spatial profiles. After deriving the Maxwell-Bloch equations for short laser pulses incident on an ensemble of three-level atoms, we specialize to photon echo spectroscopy. As an example, the stimulated photon echo signal is calculated as a function of the time delay between pulses. Our exact results are compared with both the lowest-order perturbative limit and a calculation in which transit time is treated phenomenologically. We conclude by commenting on the extension of our technique to atoms undergoing velocity-changing collisions. © 1996 The American Physical Society.

The Monte Carlo wave-function method has recently proved to be an efficient tool in the analysis of linear dissipative quantum systems, i.e., systems with linear equations of motion for their density matrix. We generalize this method to systems with nonlinear master equations of a parametrized Lindblad form, which includes master equations obtained by Hartree-Fock approximations. Convergence properties of the algorithm are discussed in detail. The method is illustrated by a numerical analysis of the bosonic enhancement of laser cooling of trapped particles. © 1996 The American Physical Society.

The reconstruction of the density operator from the tomographic data (rotated quadrature components) via the normally ordered moments of the density operator is investigated. It is shown how arbitrary normally ordered moments of arbitrary order n can be obtained from the quadrature components for n+1 discrete angles that can be chosen arbitrarily. An integration over the angles of the rotated quadrature components multiplied by discrete phase factors is not necessary and uses more than the minimally necessary information about the rotated quadrature components. © 1996 The American Physical Society.

By contour integration we show that the phase operator ${\mathit{e}\mathit{⁁}}^{\mathrm{-}\mathit{i}\mathrm{\phi }}$ (one of the pair of Susskind-Glogower operators) also possesses eigenkets |γ${\mathrm{〉}}_{\mathrm{*}}$, which are the dual vector of ${\mathit{e}\mathit{⁁}}^{\mathit{i}\mathrm{\phi }}$’s eigenkets. The properties of |γ${\mathrm{〉}}_{\mathrm{*}}$ are studied and we see that |γ${\mathrm{〉}}_{\mathrm{*}}$ and ${\mathit{e}\mathit{⁁}}^{\mathit{i}\mathrm{\phi }}$’s eigenkets can also make up a phase-state representation. © 1996 The American Physical Society.

We study the temporal behavior of generic transient signals originating from multilevel quantum systems. Such signals typically arise in the physics of wave packets in atoms, molecules, cavity QED, and ion traps and consist of a sum of a large number of harmonics whose frequencies depend nonlinearly on the sequential number of the harmonic. In particular, we focus on the semiclassical limit. Here, quantum beats between individual terms in the underlying sum lead to characteristic features of the signal in different time regimes, such as collapse, fractional revivals, and full revivals. We present a universal recipe for describing analytically all of the details of these features. Our approach is based on a specific representation of the sum of harmonics, which is most convenient in each of these time regions of interest. This brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains their fine structures observed in recent experiments. © 1996 The American Physical Society.