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arXiv:1505.05150 · Physical Review Letters

Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta

Lev Vidmar, J. P. Ronzheimer, Michael Schreiber, S. Braun, Sean S. Hodgman, S. Langer, Fabian Heidrich‐Meisner, Immanuel Bloch, Ulrich Schneider

Published Oct 19, 2015• 93 citations
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Abstract

Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta ±(π/2)(ℏ/d) in the momentum distribution function.

DOI
10.1103/physrevlett.115.175301

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Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta ±(π/2)(ℏ/d) in the momentum distribution function.
Long-range order in quantum many-body systems is usually associated with equilibrium situations.Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case.We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d.After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice.Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta Æðπ=2Þðℏ=dÞ in the momentum distribution function.
Abstract Quasicondensation in one dimension is known to occur for equilibrium systems of hard-core bosons (HCBs) at zero temperature. This phenomenon arises due to the off-diagonal long-range order in the ground state, characterized by a power-law decay of the one-particle density matrix g 1 ( x , y ) ∼ | x − y | − 1 / 2 —a well-known outcome of Luttinger liquid theory. Remarkably, HCBs, when allowed to freely expand from an initial product state (i.e. characterized by initial zero correlation), exhibit quasicondensation and demonstrate the emergence of off-diagonal long-range order during nonequilibrium dynamics. This phenomenon has been substantiated by numerical and experimental investigations in the early 2000s. In this work, we revisit the dynamical quasicondensation of HCBs, providing a fully analytical treatment of the issue. In particular, we derive an exact asymptotic formula for the equal-time one-particle density matrix by borrowing ideas from the framework of quantum Generalized Hydrodynamics. Our findings elucidate the phenomenology of quasicondensation and of dynamical fermionization occurring at different stages of the time evolution, as well as the crossover between the two.
We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of non-interacting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with one of non-interacting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.
We develop an exact approach to study the quench dynamics of hard-core bosons initially in thermal equilibrium in one-dimensional lattices. This approach is used to study the sudden expansion of thermal states after confining potentials are switched off. We find that a dynamical fermionization of the momentum distribution occurs at all temperatures. This phenomenon is studied for low initial site occupations, for which the expansion of the cloud is self-similar. In this regime, the occupation of the natural orbitals allows one to distinguish hard-core bosons from noninteracting fermions. We also study the free expansion of initial Mott insulating domains at finite temperature and show that the emergence of off-diagonal one-body correlations is suppressed gradually with increasing temperature. Surprisingly, the melting of the Mott domain is accompanied by an effective cooling of the system. We explain this phenomenon analytically using an equilibrium description based on an emergent local Hamiltonian.
We study the ground-state properties and nonequilibrium dynamics of hard-core bosons confined in one-dimensional lattices in the presence of an additional periodic potential (superlattice) and a harmonic trap. The dynamics is analyzed after a sudden switch-on or switch-off of the superlattice potential, which can bring the system into insulating or superfluid phases, respectively. A collapse and revival of the zero-momentum peak can be seen in the first case. We study in detail the relaxation of these integrable systems towards equilibrium. We show how after relaxation time averages of physical observables, like the momentum distribution function, can be predicted by means of a generalization of the Gibbs distribution.