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Register a new userExploring universal and non-universal regimes of trimers from three-body interactions in one-dimensional lattices
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We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbour two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $Uleq-2t$ and positive $V>0$ a large trimer is stabilized, which persists as $Vrightarrow infty$, while both attractive $Uleq0$ and $Vleq0$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $Vrightarrow -infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V>>t$, $U<-2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.
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Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle exchanges when there are hard-core three-body interactions in one-dimension. We call this new exchange symmetry the traid group and demonstrate that it has abelian and non-abelian representations that are neither bosonic nor fermionic, and which also transform differently under particle exchanges than braid group anyons. We show that generalized exchange statistics occur because, like hard-core two-body interactions in two dimensions, hard-core three-body interactions in one dimension create defects with co-dimension two that make configuration space no longer simply-connected. Ultracold atoms in effectively one-dimensional optical traps provide a possible implementation for this alternate manifestation of anyonic physics.
We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with the recent experimental observation of two-magnon dynamics [Nature 502, 76 (2013)]. The two interacting particles can undergo independent- and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk seep of bosons is found to be exactly three times of the ones of fermions/HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.
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We show that there are effective three- and higher-body interactions generated by the two-body collisions of atoms confined in the lowest vibrational states of a 3D optical lattice. The collapse and revival dynamics of approximate coherent states loaded into a lattice are a particularly sensitive probe of these higher-body interactions; the visibility of interference fringes depend on both two-, three-, and higher-body energy scales, and these produce an initial dephasing that can help explain the surprisingly rapid decay of revivals seen in experiments. If inhomogeneities in the lattice system are sufficiently reduced, longer timescale partial and nearly full revivals will be visible. Using Feshbach resonances or control of the lattice potential it is possible to tune the effective higher-body interactions and simulate effective field theories in optical lattices.
It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law $propto t^{-2}$ in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour $propto t^{-2}$ is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour.
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