By Maciej Lewenstein
Quantum pcs, notwithstanding no longer but in the marketplace, will revolutionize the way forward for details processing. Quantum pcs for exact reasons like quantum simulators are already nearby. The physics of ultracold atoms, ions and molecules supply unheard of chances of keep an eye on of quantum many physique structures and novel chances of purposes to quantum info processing and quantum metrology. really interesting is the opportunity of utilizing ultracold atoms in lattices to simulate condensed subject or maybe excessive power physics.
This booklet offers an entire and entire evaluate of ultracold lattice gases as quantum simulators. It opens up an interdisciplinary box concerning atomic, molecular and optical physics, quantum optics, quantum info, condensed topic and excessive strength physics. The e-book comprises a few introductory chapters on uncomplicated ideas and techniques, after which makes a speciality of the physics of spinor, dipolar, disordered, and annoyed lattice gases. It stories intimately the physics of synthetic lattice gauge fields with ultracold gases. The final a part of the ebook covers simulators of quantum desktops. After a short direction in quantum details idea, the implementations of quantum computation with ultracold gases are mentioned, in addition to our present knowing of condensed subject from a quantum info point of view.
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Extra info for Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems
Example text
23) The linear terms in δ φˆ vanish provided φ fulfills the famous (stationary) Gross–Pitaevskii equation, μφ = − 2 2m ∇2x φ + gφ∗ φφ . 23) can easily be diagonalized in the homogenous case by using the Fourier and Bogoliubov transforms. In the non-homogeneous case, such as in a trap, the diagonalization is typically technically much more involved. The corresponding eigenmodes describe quasiparticles, in the sense that creation of such quasiparticles is a superposition of the creation of a real particle and the annihilation of a real particle accompanied by the creation of two condensate particles.
The gas exhibits, however, a novel type of order: the Berezinskii–Kosterlitz–Thouless (BKT) phase. In one dimension the BEC is destroyed by phase fluctuations even at T = 0. 2 Bose–Einstein condensation in a trap As we have seen in the previous section, the existence of BEC depends in the first place on the density of states. , 1987, Bagnato and Kleppner, 1991). Let us consider here radially Quantum phase transitions symmetric traps with potentials V (x) ∝ expression: n( ) = 2π |x|s . The density of states is given now by the d dd x 23 dd pδ( − p2 /2m − V (x)) ∝ d ( d−2 2 +s) .
2000)). If the laser is red-detuned (Δ < 0), the atoms are attracted towards the regions of high intensity corresponding to the potential minima. Conversely, a blue-detuned laser (Δ > 0) pushes the atoms out of these regions since the potential minima are at the positions of minimum intensity. e. photon absorption and spontaneous emission processes, a large detuning is required because the photon scattering rate, which is proportional to the imaginary part of the polarizability, scales as I(r)/Δ2 .
