By Y. Castin (auth.), R. Kaiser, C. Westbrook, F. David (eds.)
Progress in atomic physics has been so energetic in the past decade that one is difficult pressed to keep on with the entire new advancements. within the early Nineteen Nineties the 1st atom interferometers opened a brand new box during which now we have been in a position to use the wave nature of atoms to probe primary 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 examine curiosity in learning the wave nature of topic, specially in a website during which "macro scopic" quantum results (vortices, motivated scattering of atomic beams) are seen. whilst there was a lot development in our realizing of the habit of waves (notably electromagnetic) in complicated media, either periodic and disordered. An visible subject of hypothesis and possibly of destiny examine is whether or not any new perception or functions will improve 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 additionally to workout effective keep watch over over the quantum states of a small variety of atoms. This has complicated to the learn of quantum entanglement and its relation to the speculation of size and the idea of data. The Nineties have additionally obvious an explosion of curiosity in an exhilarating capability program of this high quality keep watch over: quantum computation and quantum cryptography.
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Extra info for Coherent atomic matter waves: 27 July–27 August 1999
At time t = 0+ there is no trapping potential anymore so that the total energy of the gas reduces to Etot (0+ ) = Ekin + Eint . 50) In the limit t → +∞ the gas expands, the density and therefore the interaction energy drop, and all the energy Etot (0+ ) is converted into kinetic energy, which is measured. In Figure 4 we show the results of JILA for Etot (0+ ) for temperatures around Tc0  together with the ideal Bose gas prediction. The main feature of the ideal Bose gas prediction is a change in the slope of the energy as function of temperature when T crosses Tc .
23) It is shifted by the mean ﬁeld eﬀect with respect to the ideal Bose gas. 5ρ1/3 N 1/6 . 5 × 10 , an eﬀect for the moment smaller than the experimental accuracy. The fact that δTc is negative for eﬀective repulsive interactions (a > 0) is intuitive: for ﬁxed values of N and T the interacting gas has a lower density at the center of the trap than the ideal Bose gas, so that one needs to further cool the gas to get Bose–Einstein condensation. • A calculation of δTc beyond mean ﬁeld The purest situation to study the eﬀect of the interactions on the critical temperature Tc is the case of atoms trapped in a ﬂat bottom potential; in Y.
The semiclassical calculation that we have just presented was initially put forward in . We do not discuss in details the validity of this semi∆E classical approximation. Intuitively a necessary condition is kB T where ∆E is the maximal level spacing of the single particle Hamiltonian among the states thermally populated. Some situations, where the trapping potential is not just a single well, may actually require more care. The case of Bose–Einstein condensation in a periodic potential is an interesting example that we leave as an exercise to the reader.