By Y. Castin (auth.), R. Kaiser, C. Westbrook, F. David (eds.)
Progress in atomic physics has been so full of life prior to now decade that one is tough pressed to persist with the entire new advancements. within the early Nineteen Nineties the 1st atom interferometers opened a brand new box within which we've got been capable of use the wave nature of atoms to probe basic quantum me chanics questions in addition to to make precision measurements. Coming speedy at the heels of this improvement used to be the demonstration of Bose Einstein condensation in dilute atomic vapors which intensified learn curiosity in learning the wave nature of subject, specifically in a website within which "macro scopic" quantum results (vortices, influenced scattering of atomic beams) are obvious. while there was a lot development in our figuring out of the habit of waves (notably electromagnetic) in advanced media, either periodic and disordered. An visible subject of hypothesis and doubtless of destiny examine is whether or not any new perception or functions will increase if one examines the habit of de Broglie waves in analogous events. eventually, our skill to govern atoms has allowed us not just to create macroscopically occupied quantum states but in addition to workout high-quality regulate over the quantum states of a small variety of atoms. This has complex to the research of quantum entanglement and its relation to the speculation of dimension and the speculation of data. The Nineties have additionally noticeable an explosion of curiosity in a thrilling capability software of this positive keep watch over: quantum computation and quantum cryptography.
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Extra info for Coherent atomic matter waves: 27 July–27 August 1999
45) We are now interested in the spatial density of the non-condensed particles in the semiclassical limit. 29). The condition for Bose–Einstein condensation is z → eβUmin where Umin = minr U (r ) is the minimal value of the trapping potential, achieved in the point rmin . 612... 48) Again Einstein’s formula is recovered with ρ being the maximal density of the non-condensed cloud, that is the non-condensed density at the center of the trap. The semiclassical calculation that we have just presented was initially put forward in .
2 Energy of the gas as a function of temperature and the number of particles In the experiments one produces ﬁrst a Bose condensed gas at thermal equilibrium. Then one switches oﬀ suddenly the trapping potential. The cloud then expands ballistically, and after a time long enough that the expansion velocity has reached a steady state value one measures the kinetic energy of the expanding cloud. Y. Castin: Bose–Einstein Condensates in Atomic Gases 19 Suppose that the trap is switched oﬀ at t = 0.
3) involves a commutator to which ξ(t) does not contribute. In general the precise value of ξ(t) is considered as a matter of convenience, as it can be absorbed in a redeﬁnition of the global phase of φ. The knowledge of the value of ξ(t) can become important when one is interested in the evolution of the relative phase of two Bose–Einstein condensates. The value of ξ(t) has been derived in  assuming a well deﬁned number of particles in the condensate. If the condensate is assumed to be in a Glauber coherent state that is a quasi-classical state of the atomic ﬁeld with a well deﬁned relative phase (see Sect.
Coherent atomic matter waves: 27 July–27 August 1999 by Y. Castin (auth.), R. Kaiser, C. Westbrook, F. David (eds.)