Robust unravelings for resonance fluorescence

Monitoring the fluorescent radiation of an atom unravels the master equation evolution by collapsing the atomic state into a pure state which evolves stochastically. A robust unraveling is one that gives pure states that, on average, are relatively unaffected by the master equation evolution (which applies once the monitoring ceases). The ensemble of pure states arising from the maximally robust unraveling has been suggested to be the most natural way of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf 250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly driven atom requires an adaptive interferometric measurement proposed by Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant ensemble consists of just two pure states which, in the high driving limit, are close to the eigenstates of the driving Hamiltonian $\Omega\sigma_{x}/2$. This ensemble is the closest thing to a classical limit for a strongly driven atom. We also find that it is possible to reasonably approximate this ensemble using just homodyne detection, an example of a continuous Markovian unraveling. This has implications for other systems, for which it may be necessary in practice to consider only continuous Markovian unravelings.Comment: 12 pages including 5 .eps figures, plus one .jpg figur

The Bogoliubov Theory of a BEC in Particle Representation

In the number-conserving Bogoliubov theory of BEC the Bogoliubov transformation between quasiparticles and particles is nonlinear. We invert this nonlinear transformation and give general expression for eigenstates of the Bogoliubov Hamiltonian in particle representation. The particle representation unveils structure of a condensate multiparticle wavefunction. We give several examples to illustrate the general formalism.Comment: 10 pages, 9 figures, version accepted for publication in Phys. Rev.

Survival-Time Distribution for Inelastic Collapse

In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power-law in time, and that the exponent governing this decay is non-universal. An approximate calculation of the collapse-time exponent confirms this behaviour and shows how inelastic collapse can be viewed as a generalised persistence phenomenon.Comment: 4 pages, RevTe

Adiabatic Output Coupling of a Bose Gas at Finite Temperatures

We develop a general theory of adiabatic output coupling from trapped atomic Bose-Einstein Condensates at finite temperatures. For weak coupling, the output rate from the condensate, and the excited levels in the trap, settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state where the population in the trap is not appreciably depleted. We show how the composition of the output beam, containing condensate and thermal component, may be controlled by changing the frequency of the output coupler. This composition determines the first and second order coherence of the output beam. We discuss the changes in the composition of the bose gas left in the trap and show how nonresonant output coupling can stimulate either the evaporation of thermal excitations in the trap or the growth of non-thermal excitations, when pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from the previous submission have been fixe

Foundations of Dissipative Particle Dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the rules governing our new form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular all the underlying conservation laws carry over from the microscopic to the mesoscopic descriptions. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure which may be applied iteratively and thus represents a form of renormalisation-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.Comment: 18 pages, 7 figure

Input-output theory for fermions in an atom cavity

We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an "atom cavity". In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multi-mode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity

Implications of Space-Time foam for Entanglement Correlations of Neutral Kaons

The role of $CPT$ invariance and consequences for bipartite entanglement of neutral (K) mesons are discussed. A relaxation of $CPT$ leads to a modification of the entanglement which is known as the $\omega$ effect. The relaxation of assumptions required to prove the $CPT$ theorem are examined within the context of models of space-time foam. It is shown that the evasion of the EPR type entanglement implied by $CPT$ (which is connected with spin statistics) is rather elusive. Relaxation of locality (through non-commutative geometry) or the introduction of decoherence by themselves do not lead to a destruction of the entanglement. So far we find only one model which is based on non-critical strings and D-particle capture and recoil that leads to a stochastic contribution to the space-time metric and consequent change in the neutral meson bipartite entanglement. The lack of an omega effect is demonstrated for a class of models based on thermal like baths which are generally considered as generic models of decoherence

Quantum superchemistry: Role of trapping profile and quantum statistics

The process of Raman photoassociation of a trapped atomic condensate to form condensed molecules has been labeled superchemistry because it can occur at 0 K and experiences coherent bosonic stimulation. We show here that the differences from ordinary chemical processes go even deeper, with the conversion rates depending on the quantum state of the reactants, as expressed by the Wigner function. We consider different initial quantum states of the trapped atomic condensate and different forms of the confining potentials, demonstrating the importance of the quantum statistics and the extra degrees of freedom which massive particles and trapping potentials make available over the analogous optical process of second-harmonic generation. We show that both mean-field analyses and quantum calculations using an inappropriate initial condition can make inaccurate predictions for a given system. This is possible whether using a spatially dependent analysis or a zero-dimensional approach as commonly used in quantum optics

Bose-Einstein condensates in atomic gases: simple theoretical results

These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic interaction potential - finite temperature Hartree-Fock approximation - Gross-Pitaevskii equation for the condensate wavefunction - what we learn from a linearization of the Gross-Pitaevskii equation - Bogoliubov approach and thermodynamical stability - phase coherence properties of Bose-Einstein condensates - symmetry breaking description of condensatesComment: 146 pages, 17 figures, Lecture Notes of Les Houches Summer School 199