By Monika Aidelsburger
This paintings experiences at the new release of man-made magnetic fields with ultracold atoms in optical lattices utilizing laser-assisted tunneling, in addition to at the first Chern-number size in a non-electronic system.
It starts off with an advent to the Hofstadter version, which describes the dynamics of charged debris on a sq. lattice subjected to powerful magnetic fields. This version indicates power bands with non-zero topological invariants known as Chern numbers, a estate that's on the foundation of the quantum corridor impact. the most a part of the paintings discusses the belief of analog structures with ultracold impartial atoms utilizing laser-assisted-tunneling suggestions either from a theoretical and experimental viewpoint. Staggered, homogeneous and spin-dependent flux distributions are generated and characterised utilizing two-dimensional optical super-lattice potentials. also their topological houses are studied through the statement of bulk topological currents.
The experimental options offered right here supply a distinct environment for learning topologically non-trivial structures with ultracold atoms.
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Additional resources for Artificial Gauge Fields with Ultracold Atoms in Optical Lattices
According to Floquet theory this evolution can be described by an effective time-independent Floquet Hamiltonian Hˆ F as given in Eq. 11). 34) n=0 where the lowest two orders are given by 1 T ˆ Hˆ F(0) = H (t)dt, T 0 T t2 −i Hˆ (t2 ), Hˆ (t1 ) dt1 dt2 . 36) Higher orders of the Magnus expansion scale as 1/ωn , such that in the high frequency limit the effective time-independent Hamiltonian is well approximated by the lowest Hˆ F(0) . The explicit form of the effective time-averaged order of the expansion Hˆ F Hamiltonian depends on the time interval chosen for the integration, [0, T ] and [t0 , t0 +T ] respectively.
The static term of the Hamiltonian contains diverging components proportional to ω. Similar to the method described above we perform a unitary transformation. However, this time it further involves the timeperiodic part of the Hamiltonian Vˆ (t) [45, 46] and is defined according to 1 αωt Pˆ α + i |ψ M (t) = Rˆ M (t) |ψ(t) , with Rˆ M (t) = exp i α t Vˆ (t )dt . 37) This transformation leads to the new Hamiltonian Hˆ M (t) = Rˆ M Hˆ (t) Rˆ †M − i Rˆ M dt Rˆ †M . 39) with the corresponding micro-motion operator ˆ ˆ ei M M (t) ≡ ei K M (t) Rˆ M (t).
71) m For a driving frequency ω = / the micro-motion is associated with a constant drift in momentum space with δk(t) = ωt/a. Hence, if the system is initially prepared in the ground state of the unperturbed lattice with V0 = 0 and = 0, the momentum distribution travels across the Brillouin zone while the corresponding amplitudes remain unchanged. In Fig. 3b we illustrate the evolution for a state |ψ(t) using Eqs. 71), where |G S is again the ground state in the unperturbed lattice. After each period of the driving T the momentum components travelled across the Brillouin zone once.