Victor Romero-Rochin

Fluorescence‐detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase‐locked pulses

We introduce a novel spectroscopic technique which utilizes a two‐pulse sequence of femtosecond duration phase‐locked optical laser pulses to resonantly excite vibronic transitions of a molecule. In contrast with other ultrafast pump–probe methods, in this experiment a definite optical phase angle between the pulses is maintained while varying the interpulse delay with interferometric precision. For the cases of in‐phase, in‐quadrature, and out‐of‐phase pulse pairs, respectively, the optical delay is controlled to positions that are integer, integer plus one quarter, and integer plus one half multiples of the wavelength of a selected Fourier component. In analogy with a double slit optical interference experiment, the two the two pulse experiments reported herein involve the preparation and quantum interference of two nuclear wave packet amplitudes state of a molecule.These experiments are designed to be sensitive to the total phase evolution of the wave packet prepared by the initial pulse. The direct de...

On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Predictions from Hartree–Fock (HF), Popov (P), Yukalov–Yukalova (YY) and t-matrix approximations regarding the thermodynamics from the normal to the Bose–Einstein condensation (BEC) phase in weakly interacting Bose gases are considered. By analysing the dependence of the chemical potential μ on the temperature T and particle density ρ, we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work, we find that the isothermal compressibility κT predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover, the isotherms μ = μ(ρ, T) typically exhibit non-single-valued behaviour in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behaviour can be avoided if a first-order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature, they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.

Stress tensor of curved interfaces

We use density functional theory to analyse the structure of the stress tensor σ for fluid interfaces of arbitrary shape, and determine the spatially non-local components of σ that correspond to a description with a semi-orthogonal set of coordinates (ˆn, t 1, t 2). We then study a local, van der Waals-type, density functional with squared-Laplacian term and arrive at closed and general expressions for the surface tension γ, the bending constants κ and κ and the spontaneous curvature c 0. These expressions have the same general form for all interfacial shapes, but their precise values are curvature-dependent. In the case of γ this dependence is that already known and measured by the Tolman length δ. We discuss and compare our results with those of others and resolve existing discrepancies.

Time development of geometric phases in the Longuet‐Higgins model

Using a time‐dependent variational method, we study the evolution of nonstationary states in Longuet‐Higgin’s model of a Jahn–Teller molecule. Conditions are found for the nuclear motion to be adiabatic. The effects of wave‐packet spreading are neglected upon specializing to the case of nearly harmonic motion. It is shown explicitly how the effective vector potential introduced by Mead and Truhlar gives rise to an electronic Berry phase. In a semiclassical approximation sufficient to produce the electronic adiabatic phase anticipated from the result for a given sequence of nuclear configurations, it is demonstrated that the effective vector potential has a negligible effect on the nuclear motion; the effective vector potential, the source of an effective field proportional to ℏ, is seen to affect the nuclear trajectory only in higher order. For the special case of periodic nuclear motion the electronic adiabatic phase is seen as a contribution to the geometric phase attending an arbitrary cyclic evolution...

Density functional theory beyond the surface tension. Interfacial width, elastic bending constants and line tension

The long wavelength behavior of the Ornstein-Zernike direct correlation function for nonuniform fluids c(r,r′) has provided important results that comprise our current understanding of fluid interfaces. As we know, the surface tension is obtained from the second moment of c(r,r′), and long-ranged correlations parallel to the surface stand among the main predictions. Also, conventional capillary wave theory leads to its notorious divergent results for the interfacial width when the surface tension cost of thermally excited fluctuations is considered. Here we discuss the consequences of the higher moments of c(r,r′) in the density functional theory of fluid interfaces. We find that in an appropriately extended capillary wave model the interfacial width is finite in the absence of external fields. We derive the expression for the elastic curvature energy and find that the bending moduli are given by the fourth moment of c(r,r′). We obtain too in the same fashion the line tension that originates when interfaces meet.

Optical impulsive excitation of molecular pseudorotation in Jahn–Teller systems

We analyze the use of vibrationally abrupt nonresonant laser pulses to prepare coherently pseudorotating states in a model Jahn–Teller molecule. Our derivation of impulsive excitation invokes the dynamical adiabatic phase for the perturbed electronic ground state. Polarization selection between two Raman active distortion coordinates allows creation of an orbit of arbitrary eccentricity. Repetition of the pulse pair at the pseudorotational frequency amplifies the nuclear motion. Timing of a resonant pulse of given polarization, or choice of polarization for a given delay, transfers the moving wave packet to either or both Jahn–Teller branches of an electronic excited state.

Analysis on the Cina–Harris proposal for the preparation and detection of chiral superposition states

We study the preparation and measurement of superpositions of molecular chiral states with sequences of phase-locked ultrashort laser pulses following the scheme proposed by Cina and Harris [J. Chem. Phys. 100, 2531 (1994)]. The model is a parity-invariant molecule with a handed electronic ground state and a harmonic electronic excited state. We analyze the problem by numerically solving the Schrodinger equation. We find that the process of preparation of the superposition of chiral states works very well, in agreement with the analytic approximate solution of Cina and Harris. The detection part, in terms of a fluorescence interferogram, however, turns out to be more delicate. That is, in order to reproduce the main features in the interferogram that reveal the superposition of the chiral states, very stringent conditions on the involved time scale must be satisfied. The most unrealistic characteristic is that very high vibrational states of the (harmonic) excited electronic states are involved. Neverthel...

Measuring the heat capacity in a Bose-Einstein condensation using global variables

Phase transitions are well understood and generally followed by the behavior of the associated thermodynamic quantities, such as in the case of the

Overdamped thermal ratchets in one and more dimensions. Kinesin transport and protein folding

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Preparation and resolution of molecular states by coherent sequences of phase-locked ultrashort laser pulses

point superfluid transition of liquid helium, which is observed in its heat capacity. In the case of a trapped Bose-Einstein condensate (BEC), the heat capacity cannot be directly measured. In this work, we present a technique able to determine the global heat capacity from the density distribution of a weakly interacting gas trapped in an inhomogeneous potential. This approach represents an alternative to models based on local density approximation. By defining a pair of global conjugate variables, we determine the total internal energy and its temperature derivative, the heat capacity. We then apply the technique to a trapped