Download Ultracold Atoms in Optical Lattices: Simulating quantum by Maciej Lewenstein PDF
By Maciej Lewenstein
Quantum desktops, although now not but in the marketplace, will revolutionize the way forward for info processing. Quantum pcs for unique reasons like quantum simulators are already close by. The physics of ultracold atoms, ions and molecules supply unheard of chances of regulate of quantum many physique structures and novel chances of purposes to quantum details processing and quantum metrology. fairly attention-grabbing is the opportunity of utilizing ultracold atoms in lattices to simulate condensed topic or maybe excessive power physics.
This ebook offers an entire and complete evaluate of ultracold lattice gases as quantum simulators. It opens up an interdisciplinary box regarding atomic, molecular and optical physics, quantum optics, quantum details, condensed subject and excessive power physics. The ebook contains a few introductory chapters on simple recommendations and strategies, after which makes a speciality of the physics of spinor, dipolar, disordered, and annoyed lattice gases. It studies intimately the physics of man-made lattice gauge fields with ultracold gases. The final a part of the booklet covers simulators of quantum desktops. After a quick path in quantum info concept, the implementations of quantum computation with ultracold gases are mentioned, in addition to our present realizing of condensed topic from a quantum details point of view.
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Extra resources for Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems
Example text
Operators are placed in time-descending order from the left to the right. This correlation is easily expressed in terms of the Green function for ˆ t)θ(0, ˆ 0)] as: the phase iGθˆ(x, t) = T [θ(x, ˆ 0) = ρ exp (iG (x, t)) exp (iG (0, 0)) . 39): Gθ (k, ω) = (ω 2 g/ . 42) The inverse Fourier transform in ω can easily be calculated using Cauchy’s residuum method; the remaining integrations over k for finite systems are conveniently replaced by the summation over k = 2πn/L, where L is the size of the system and n is an integer, with the standard substitution dk/2π = k 1/L.
Dh/dl = (d/2 + 1)h − 4ht + . . , du/dl = u − t2 − 16tu − 72u2 + . . 17) where l = ln b for b 1, and = 4 − d. Here we have done some of the work already: we used perturbation theory in u in order to treat the coupling between the high momentum modes that were integrated out and the low momentum ones. The Gaussian part of the theory was treated exactly. As can readily be seen, apart from the Gaussian fixed point there is another one for h = 0, u = /72 + O( 2 ), t = O( 2 ). This is the celebrated Wilson–Fisher fixed point, which gives yt = 2 − (24/27) + O( 2 ) and ν = 1/2 + /12 + O( 2 ).
14) √ ˜ Jd. In where the dimensionless parameters are t = −μ/Jd, u = g/2(Jd)2 , and h = −h/ this case, however, it is much more convenient to work in the momentum space, as pointed out in the seminal works of Wilson (Wilson, 1970a,b,c, 1975, Cardy, 1996). )/2 . 15) The theory makes sense only if one introduces an ultraviolet (high-energy, high-momentum) cut-off, Λ = 1/a. The renormalization transformation consists of introducing a new cut-off Λ = Λ/b < Λ, with b > 1, integrating out the contributions from large momenta Λ ≤ |k| ≤ Λ, and then rescaling Λ back to the original value.