Relaxation Dynamics of a Fermi Gas in an Optical Superlattice

Abstract

This paper comprises an experimental and theoretical investigation of the time evolution of a Fermi gas following fast and slow quenches of a one-dimensional optical double-well superlattice potential. We investigate both the local tunneling in the connected double wells and the global dynamics towards a steady state. The local observables in the steady-state resemble those of an equilibrium state, whereas the global properties indicate a strong non-equilibrium situation. One of the grand goals of condensed matter physics is the dynamic control of the quantum properties of materials. The target is the creation of new functionality as well as the dynamic change in between different phases. Recently, great experimental progress has been made in this direction [1]. Examples are photo-induced phase transitions as in the insulator-to-metal transitions, fast demagnetization and magnetization control, or the generation of Josephson plasmons (which are typically present in superconducting phases) in non-superconducting stripedorder cuprates [2]. However, the underlying dynamical mechanisms are often far from being understood, since many different processes in the form of phononic relaxation channels are present in the solid state.Recent progress towards understanding nonequilibrium physics in the solid state has been complemented by advances in ultracold atomic physics. Atomic quantum gases are excellent systems in which to study quantum dynamics [3, 4] because of the clean preparation, wide tunability and long coherence times. In particular, different dynamical processes can be well separated and timescales for the real-time detection of dynamics are experimentally favourable. The fastest relevant energy scale, the Fermi energy, is on the order of 10kHz and can be well resolved. So far, experimental progress in the probing and understanding of dynamical phenomena in optical lattices has been mostly focused on bosonic systems where, for example, interaction quenches have been studied [3][4][5][8][9][10][11][12][13][14]. With fermionic gases in optical lattices, interaction quenches [15][16][17][18] and spin dynamics have been investigated [19,20].In this paper we investigate experimentally and theoretically the time evolution of a Fermi gas in a bichromatic optical lattice which is imposed along one dimension of the gas, following a sudden or a slow quench of the lattice potential. We initially prepare a patterned density distribution in the optical lattice and measure the relaxation of both local and non-local observables towards a steady-state.Experimentally [21], we start from a non-interacting degenerate gas of N = 1.2(2)·10 5 40 K atoms in each of the two lowest hyperfine spin states |F = 9/2, m F = −9/2 and |F = 9/2, m F = −7/2 in a dipole trap with trapping frequencies ω x = 2π × 38 Hz, ω y = 2π × 66 Hz and ω z = 2π ×376 Hz. The scattering length between the two components is set to zero by means of a Feshbach resonance. The gas has a temperature of (0.3±0.1) T F where k B T F = E F is the Fermi energy of the ga...

Equilibration via Gaussification in Fermionic Lattice Systems

“…So far it is, however, unclear why this dephasing tends to happen so rapidly. In fact, experiments often observe equilibration after very short times which are independent of the system size [5,12], while even the best theoretical bounds for general initial states of concrete systems diverge exponentially [2,11]. This discrepancy poses the challenge of precisely identifying the equilibration time, which constitutes one of the main open questions in the field [1][2][3].…”

Finite-temperature charge transport in the one-dimensional Hubbard model

“…The interest in the one-dimensional (1D) version of the model arises because of the existence of an exact solution based on the Bethe ansatz [4] and its relevance for quasi-1D materials [5][6][7][8][9], nanostructures [10][11][12] and realizations with ultracold atomic gases in optical lattices [3,13]. A recent optical-lattice experiment has investigated the non-equilibrium charge transport in the twodimensional Hubbard model [14].…”

Two Fermions in a Double Well: Exploring a Fundamental Building Block of the Hubbard Model

“…A promising approach to answer these questions is to use ultracold atoms trapped in periodic potentials as quantum simulators of the Hubbard model [2][3][4][5][6][7][8]. Such experiments have been performed both in large-and small-scale systems.…”

“…The paradigmatic example for this approach is the Hubbard model, which reduces the physics of a quantum many-body system to tunneling of particles between adjacent sites and interactions between particles occupying the same site. While this model captures essential properties of electrons in a crystalline solid and provides a microscopic explanation for the existence of Mott-insulating and antiferromagnetic phases, many questions about this Hamiltonian -such as whether it can explain d-wave superfluidity -are still unanswered [1].A promising approach to answer these questions is to use ultracold atoms trapped in periodic potentials as quantum simulators of the Hubbard model [2][3][4][5][6][7][8]. Such experiments have been performed both in large-and small-scale systems.…”