Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Abstract

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases – due to their repulsion – the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

Pump-probe spectroscopy of Bose polarons: Dynamical formation and coherence

“…We remark that a saturation trend at long timescales being in turn suggestive of the thermalization tendency of the system occurs also for other observables. These include, for instance, the dynamical structure factor (Appendix B) as well as entropic measures [104,105] such as the von-Neumann entropy [61,99,106] quantifying the degree of entanglement (results not shown for brevity).…”

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

“…We solve the time-dependent many-boson Schrödinger equation presented in Eq. (1) using the MCTDHB method 36,39,40,49,57,58,61,[65][66][67][68][69][70][71][72][73][73][74][75][76][77][78][79][80][81][82] . The method is well documented and applied in the literature 59 .…”

Correlation Dynamics of Dipolar Bosons in 1D Triple Well Optical Lattice

“…i=1 that build up the permanents are time-dependent fully variationally optimized quantities. MCTDHB theory is established as the most efficient way to solve the time-dependent many-body problems of interacting bosons accurately and has been applied for a wide set of problems [39,[43][44][45][46][47][48][49][50][51][52][53][54]. In the limit of M → ∞, the set of permanents {| n; t } spans the complete N boson Hilbert space.…”

“…The corresponding dynamics is simulated in the first principle by solving the time-dependent Schrödinger equation using MCTDHB method [37][38][39]. It is a general many-body method capable of addressing our system properly and its implementation in the MCTDH-X package [40][41][42] has been successfully employed in several earlier works [39,[43][44][45][46][47][48][49][50][51][52][53][54]. We explore the transition from SF to MI phase by analyzing the normalized first-and second-order Glauber's correlation function and dynamics of Shannon information entropy.…”