Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

Abstract

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0:77k B which is about twice as large as the entropy at the Néel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy. Experimental progress in the field of atomic quantum gases has led to a new approach to quantum many-body physics. In particular, the combination of quantum degenerate and strongly interacting Fermi gases [1,2] with optically induced lattice potentials [3] now allows the study of a centerpiece of quantum condensed matter physics, the Fermi-Hubbard model [4]. The high level of control over the atomic systems has led to the concept of quantum simulation, which for the case of the Fermi-Hubbard model is expected to provide answers to intriguing open questions of frustrated magnetism and d-wave superfluidity [5]. Recent experiments [6,7] have indeed demonstrated that the strongly correlated regime of the repulsive FermiHubbard model is experimentally accessible and the emergence of a Mott insulating state has been observed. In this Letter, we succeed in performing a quantitative simulation of the Fermi-Hubbard model using cold atoms. The level of precision of the experiment enables us to determine the entropy and the temperature of the system, and thereby to quantify the approach to the low temperature phases.The main challenge for the quantum simulation of the Fermi-Hubbard model is a further reduction in temperature. Here the lack of a quantitative thermometry method in the lattice is a key obstacle. For strongly correlated bosonic systems thermometry has recently been demonstrated by direct comparison with quantum Monte Carlo simulations [8] or by using the boundary of two spin polarized clouds [9]. In the fermionic case, previous methods to determine the temperature could be used only in limiting regimes of the Hubbard model, namely, the noninteracting [10,11] and zero-tunneling [6,12] regimes. However, intermediate interactions are most interesting for quantum simulation of the Fermi-Hubbard model and no reliable thermometry method has been available up to now.In both the metallic and Mott insulating regimes an accurate measurement of the double occupancy provides direct access to thermal excitations. We analyze the crossover from thermal creation of double occupancies to thermal depletion which is unique to a trapped system (see Fig. 1). The variability of the d...

Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

“…We plot the temperature as a function of ρ for various values of the total entropy per particle. Recent studies have shown that the entropy per particle (s) for a particular U can be estimated by fitting the doubleoccupancy measurements at different ρ to data from numerical simulations [8]. In Figs.…”

“…On the theoretical side, there is an ever-increasing demand for precise numerical results for the relevant parameters of the Hubbard model and for large enough system sizes, which could be used to interpret current experiments and also provide suggestions for future experiments [6][7][8][9][10][11]. For this model, especially for strong interactions, the present computations become particularly challenging as the temperature is lowered below the hopping amplitude.…”

Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model

“…In particular, the igh degree of control over the interaction parameters alows for using atomic systems as quantum simulators of eneric theoretical models [2]. Central to these efforts ies the possibility of observing quantum phase transiions (QPT).…”

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

“…Our calculations of the entropy per particle presented above helps us to generate temperature calibration curves which can be used to estimate the temperature of the system during experiments, as has already been done for fermions [32]. In Fig.…”