Abstract
We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which takes place in momentum space. The contact interaction affects the evolution of the relative momentum k of a pair of interacting rotors in a non-analytic way. Consequently the evolution operator U is exciting large relative momenta with amplitudes which decay only as a power law 1/k4. This is in contrast to the center-of-mass momentum K for which the amplitudes excited by U decay superexponentially fast with K. Therefore dynamical localization is preserved for the center-of-mass momentum, but destroyed for the relative momentum for any nonzero strength of interaction.
Highlights
The quantum kicked rotor (QKR) model is a canonical model to explore quantum chaos[1,2]
For the experimental realization in ref. 6, this interaction of Bose-Einstein condensate (BEC) atoms persists at all times - in contrast to the kick potential, and in contrast to the theoretical studies discussed above, which
A δ(x) interaction is long-ranged in momentum space, and can have a qualitatively strong impact on dynamical localization (DL) for interacting ultracold atoms
Summary
We consider two bosons moving on a ring [0, 2π) with δ-function interaction and periodic kicking potential. We start by computing the wave function of the two bosons system with δ-function interaction It can be represented in a center of mass and relative coordinates frame - (y1, y2), where y1 =x1 +x2, y2 =x1 −x2. The wave function should be invariant under permutation x1↔x2 and only symmetric functions (φφfMu22n((λyyc22/t)) i o==2n)eφφii2s22K((c−π0oφ)y.n22(Ft)yirn2ao +urmeo 2autπlhsl)oeaawtpne0edd:ri.φφoT22d((hy+iec2n)0b =)to h=uφenφ2d(d2yea(2r−r +iyv[0] a4c)to,πivbn)e.udItiitstiiitasosnnwdaoφenrr1t(tihviysa1yn)tmioφvt2mei(nyheg2at)rtshi=caatfjuuφthnm1e(cyptc1i:eoφ+nn2t′eφ(2r+2π′o()0fyφ)m22)−(a=ys2sφa−+2′n(φd−22′rπ0(e))−l,ai≡tytiv2f)e2o.φlmTlo2h′ow(em+swet0anh)vt=aaet do not decouple completely, due to the boundary conditions. With these boundary conditions it is easy to compute the wave function φ2 (see Supplementary material for more details): φ2 (y2 ).
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