Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

Chapter 7Quantum simulations of evaporativelycooled Bose-Einstein condensates7.1 Introduction7.1.1 Important issuesWe now undertake to study the quantum dynamics governed by the atom-optics Hamiltonian(Eq. (2.1)) without recourse to the two-mode approximation. Our tools are thequantum optics phase-space techniques introduced in Ch. 6. In the quantum soliton calculations,the initial state is taken to be the coherent output of a laser; in other words acoherent state. However, the precise state of a Bose condensate in an atom trap is currentlyunknown, as it forms by a dynamical evaporative cooling process, in which particleinteractions play a vital role. Also the condensate may never reach equilibrium duringits lifetime. Thus to determine the properties of the condensate state, one must study itsformation via the cooling process.The Bose-Einstein condensate that has been produced with trapped atomic samplesof neutral atoms[3, 16, 35] is often described as the atomic equivalent to laser light.Condensates are certainly matter waves characterised by what is called the off-diagonallong-range order parameter. Precise measurements of the momentum spread in recentexperiments[165] have shown that the long-range order extends over the entire length of thecondensate. Other interference and diffraction experiments[2, 4, 74] have also confirmedthe existence of this long-range coherence. But this does not mean that the condensateexists in a coherent state, for which it would have to possess coherence of all orders at all140