Path integral in a magnetic field using the Trotter product formula

The derivation of the Feynman path integral based on the Trotter product formula is extended to the case where the system is in a magnetic field.Comment: To appear in the American Journal of Physics, 200

Slow relaxation, confinement, and solitons

Millisecond crystal relaxation has been used to explain anomalous decay in doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons. Our model exhibits confinement of mechanical energy released by excitation. Extending the model to long times is justified by its relation to solitons, excitations previously proposed to occur in alkali halides. Soliton damping and observation are also discussed

HINDERED DECAY : QUANTUM ZENO EFFECT THROUGH ELECTROMAGNETIC FIELD DOMINATION

The lifetime of an unstable atom can be extended by watching it closely, i.e., illuminating it with an intense electromagnetic field of appropriate frequency. This is an example of ``dominated evolution'' and is closely related to the so-called ``quantum Zeno effect.'' For a metastable atom bathed in a laser beam at the frequency of another of its transitions, we obtain an expression for the modified lifetime as a function of beam intensity. This provides an example of the quantum Zeno effect on a truly decaying system, and also should be useful for probing short distance features of atomic wave functions

Stability of quantum breathers

Using two methods we show that a quantized discrete breather in a 1-D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as the zeroth order system relative to which numerical, cutoff-insensitive diagonalization of the Hamiltonian is performed.Comment: 4 pages, 3 figure

Quantum Zeno and anti-Zeno effects by indirect measurement with finite errors

We study the quantum Zeno effect and the anti-Zeno effect in the case of `indirect' measurements, where a measuring apparatus does not act directly on an unstable system, for a realistic model with finite errors in the measurement. A general and simple formula for the decay rate of the unstable system under measurement is derived. In the case of a Lorentzian form factor, we calculate the full time evolutions of the decay rate, the response of the measuring apparatus, and the probability of errors in the measurement. It is shown that not only the response time but also the detection efficiency plays a crucial role. We present the prescription for observing the quantum Zeno and anti-Zeno effects, as well as the prescriptions for avoiding or calibrating these effects in general experiments.Comment: 4 pages, 3 figure

Quantum Zeno effect in a probed downconversion process

The distorsion of a spontaneous downconvertion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the coupling as a nontrivial phase--matching technique is pointed out.Comment: 11 pages, 4 figure

Spontaneous emission and lifetime modification caused by an intense electromagnetic field

We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi "golden rule" still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an "inverse" quantum Zeno effect and can be analyzed in terms of dressed states.Comment: 25 pages, 6 figure

Nanocrystalline lanthanide-doped Lu3Ga5O12 garnets: interesting materials for light-emitting devices

Nanocrystalline Lu3Ga5O12, with average particle sizes of 40 nm, doped with a wide variety of luminescent trivalent lanthanide ions have been prepared using a sol\u2013gel technique. The structural and morphological properties of the powders have been investigated by x-ray powder diffraction, high resolution transmission electron microscopy and Raman spectroscopy. Structural data have been refined and are presented for Pr3+, Eu3+, Gd3+, Ho3+, Er3+ and Tm3+ dopants, while room temperature excited luminescence spectra and emission decay curves of Eu3+-, Tm3+- and Ho3+-doped Lu3Ga5O12 nanocrystals have been measured and are discussed. The Eu3+ emission spectrum shows typical bands due to 5D0 \u21927FJ (J = 0, 1, 2, 3, 4) transitions and the broadening of these emission bands with the non-exponential behaviour of the decay curves indicates the presence of structural disorder around the lanthanide ions. Lanthanide-doped nanocrystalline Lu3Ga5O12 materials show better luminescence intensities compared to Y2O3, Gd3Ga5O12 and Y3Al5O12 nanocrystalline hosts. Moreover, the upconversion emission intensity in the blue-green region for the Tm3+- and Ho3+-doped samples shows a significant increase upon 647.5 nm excitation with respect to other common oxide hosts doped with the same lanthanide ions

Hindered decay: Quantum Zeno effect through electromagnetic field domination

The lifetime of an unstable atom can be extended by watching it closely, i.e., illuminating it with an intense electromagnetic field of appropriate frequency. This is an example of ''dominated evolution'' and is closely related to the so-called ''quantum Zeno effect.'' For a metastable atom bathed in a laser beam at the frequency of another of its transitions, we obtain an expression for the modified lifetime as a function of beam intensity. This provides an example of the quantum Zeno effect on a truly decaying system, and also should be useful for probing short distance features of atomic wave functions