Quantum Gas Experiments:Exploring Many-Body States: Volume 3 (Cold Atoms)
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Quantum phenomena of many-particle systems are fascinating in their complexity and are consequently not fully understood and largely untapped in terms of practical applications. Ultracold gases provide a unique platform to build up model systems of quantum many-body physics with highly controlled microscopic constituents. In this way, many-body quantum phenomena can be investigated with an unprecedented level of precision, and control and models that cannot be solved with present day computers may be studied using ultracold gases as a quantum simulator.
This book addresses the need for a comprehensive description of the most important advanced experimental methods and techniques that have been developed along with the theoretical framework in a clear and applicable format. The focus is on methods that are especially crucial in probing and understanding the many-body nature of the quantum phenomena in ultracold gases and most topics are covered both from a theoretical and experimental viewpoint, with interrelated chapters written by experts from both sides of research.
Graduate students and post-doctoral researches working on ultracold gases will benefit from this book, as well as researchers from other fields who wish to gain an overview of the recent fascinating developments in this very dynamically evolving field. Sufficient level of both detailed high level research and a pedagogical approach is maintained throughout the book so as to be of value to those entering the field as well as advanced researchers. Furthermore, both experimentalists and theorists will benefit from the book; close collaboration between the two are continuously driving the field to a very high level and will be strengthened to continue the important progress yet to be made in the field.
where ferromagnetism can emerge.88,89 By explicitly populating higher bands, orbital degrees of freedom can be investigated.90,91 So far, metastable p- and d-wave superﬂuid phases have been realized in bosonic systems.92 In the long term, the interplay of spin and orbit may be studied with fermionic atoms in higher bands of optical lattices. References 1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose–Einstein condensation in a dilute atomic
blue detunings, however, the eﬀect of higher energy transitions like nS1/2 → (n + 1)P1/2 and nS1/2 → (n + 1)P3/2 or multi-photon transitions needs to be incorporated in the calculation of the eﬀective dipole moment. In general, the dipole potential comprises two components. The ﬁrst part, also referred to as the scalar part of the polarizability, represents a spin (mF ) independent potential with the same spatial dependence as the light ﬁeld intensity I(x). This potential is spatially modulated
the expected amplitude for the correlation signal can be easily computed. As shown in Section 8.1.3, the normalized correlation signal actually reduces for increasing atom number N as 1/N for constant density. However, in a trapped ensemble, the density is aﬀected by the trapping potential and atom–atom interactions, the quantum statistics of the particles, and the temperature. From expression (8.16), we can see that the normalized correlation signal increases with the on-site density, for
Nature 434, 481–484 (2005). 6. E. Altman, E. Demler, and M. D. Lukin, Probing many-body states of ultracold atoms via noise correlations, Phys. Rev. A 70(1), 013603 (2004). Doi: 10.1103/PhysRevA.70.013603. 7. J. Grondalski, P. M. Alsing, and I. H. Deutsch, Spatial correlation diagnostics for atoms in optical lattices, Opt. Exp. 5, 249–261 (1999). 8. A. Kolovsky, Interference of cold atoms released from an optical lattice, Europhys. Lett. 68, 330–336 (2004). 9. R. Bach and K. Rz¸az˙ ewski,
= 0 and N = −∂Ω/∂µ, respectively. Note that the solution once again corresponds to minimizing the grand potential Ω: the gap equation gives the condition for a stationary point, so in principle one must also calculate ∂ 2 Ω/∂∆2 to assess whether or not it is a minimum. In practice, one can often guess this from the number of stationary points when Ω is bounded from below, e.g., if there are only two stationary points, one at ∆ = 0 and one at ∆0 , then ∆0 corresponds to the global minimum. The