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 pulse experiments reported herein involve the preparation and quantum interference of two nuclear wave packet amplitudes in an excited electronic 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 determination of wave packet phase evolution is possible because phase locking effectively transforms the interferogram to a frame which is referenced to the optical carrier frequency, thereby eliminating the high (optical) frequency modulations. This has the effect of isolating the rovibrational molecular dynamics. The phase locking scheme is demonstrated for molecular iodine. The excited state population following the passage of both pulses is detected as the resultant two-beam dependent fluorescence emission from the B state. The observed signals have periodically recurring features that result from the vibrational dynamics of the molecule on the electronically excited potential energy surface. In addition, coherent interference effects cause the magnitUde and sign of the periodic features to be strongly modulated. The two-pulse phase-locked interferograms are interpreted herein by use of a simple analytic model, by first order perturbation theory and by quantum mechanical wave packet calculations. We find the form of the interferogram to be determined by the ground state level from which the amplitude originates, the deviation from impulsive preparation of the wave packet due to nonzero pulse duration, the frequency and anharmonicity of the target vibrational levels in the B state, and the detuning of the phase-locked frequency from resonance. The dependence of the interferogram on the phase-locked frequency and phase angle is investigated in detail.

A gas of interacting atoms confined by a three dimensional anisotropic harmonic potential is studied. It is shown that there appear "new" thermodynamic variables instead of the usual pressure and volume: the latter is replaced by (the inverse of) the cube of the geometric average of the oscillator frequencies of the trap, and the former by the harmonic pressure responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these quantities and show that the equation of state of the gas is given in terms of these variables. The equation of state of a cold gas of interacting Bose atoms in the Hartree-Fock approximation is presented. We indicate how the harmonic pressure can be measured in current experiments.

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We present theoretical aspects concerning the thermodynamics of an ideal bosonic gas trapped by a harmonic potential. Working in the Grand Canonical ensemble we are able to properly identify the extensive thermodynamic variable equivalent to the volume and the intensive thermodynamic variable equivalent to the pressure. These are called the "harmonic volume" and the "harmonic pressure" and their physical meaning is discussed. With these variables, the problem of Bose-Einstein condensation is studied in terms of the behavior of the corresponding equation of state and in terms of measurable susceptibilities such as the heat capacities, the isothermal compressibility and the coefficient of thermal expansion. From the analysis, an interesting analogy with BlackBody radiation emerges, showing that at and below the critical temperature, the non-condensate fraction of atoms behaves thermodynamically like a gas of massless particles.

We present the full thermodynamics of an interacting fluid confined by an arbitrary external potential. We show that for each confining potential, there emerge "generalized" volume and pressure variables V and P , that replace the usual volume and hydrostatic pressure of a uniform system. This scheme is validated with the derivation of the virial expansion of the grand potential. We discuss how this approach yields experimentally amenable procedures to find the equation of state of the fluid, P=P(VN,T) with N the number of atoms, as well as its heat capacity at constant generalized volume C_{V}=C_{V}(V,N,T) . With these two functions, all the thermodynamics properties of the system may be found. As specific examples we study weakly interacting Bose gases trapped by harmonic and by linear quadrupolar potentials within the Hartree-Fock approximation. We claim that this route provides an additional and useful tool to analyze both the thermodynamic variables of an ultracold trapped gas as well as its elementary excitations.