Controllable finite-momenta dynamical quasicondensation in the periodically driven one-dimensional Fermi-Hubbard model

Abstract

In the strongly interacting limit of the Hubbard model localized double-occupancies form effective hardcore bosonic excitations, called a doublons, which are long-lived due to energy conservation. Using timedependent density-matrix renormalisation group we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analysing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an η-quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon-hopping and doublon-repulsion are strongly renormalised by the drive, breaking the η−SU(2) symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrate that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering non-equilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.

Analytical solution for the steady states of the driven Hubbard model

“…Floquet theory can be used to understand how periodic driving can modify the parameters of the system and create additional terms on top of the undriven Hamiltonian. This renormalization results in an effective Hamiltonian which on transient scales can, for example, favor superconducting prethermal states [12][13][14][15][16][17][18][19][20][21][22][23][24][25], suppress wave-packet spreading and induce dynamical localization in a many-body bosonic gas [26], control spin-charge separation in a fermionic system [27], or stabilize exotic spinliquid states in frustrated systems [28].…”

Lieb's Theorem and Maximum Entropy Condensates

“…Whilst the equilibrium properties of the Hubbard model on unbalanced lattices are well known, the system's response to external forces such as a periodic driving field is not. This is especially true in comparison to the extensive theoretical efforts on balanced, hypercubic lattices to engineer driven Hamiltonians which guide the system into ordered, prethermal phases whilst transiently mitigating the deleterious Floquet heating [11,12,13,14,15,16] which is almost always inevitable -with only a few exceptions known [17,18]. These efforts to realise such correlated prethermal states of matter are motivated by the opportunities arising from the realisation of coherently driven electronic systems in solid-state material experiments [19,20,21].…”

$η$ Pairing of Light-Emitting Fermions: Nonequilibrium Pairing Mechanism at High Temperatures

“…The η-pairing states exhibit an off-diagonal long-range order [4], giving a rare example of fermionic superfluidity that is an exact eigenstate. However, since they cannot be the ground state of the Hubbard model except for the limiting case of an infinite attractive interaction [1,5], η pairing requires nonequilibrium situations such as adiabatic state preparation [6,7], laser irradiation [8][9][10][11], periodic driving [12][13][14][15][16], and tailored dissipative processes [17][18][19][20][21][22].…”