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Quantum Phases of Matter in Optical Lattices

Han Pu, Randall G. Hulet

Published Jun 30, 2015• 0 citations
OpenAlex

Abstract

Abstract : Ultracold atoms confined in optical lattice potentials provide an ideal platform to address some of the most outstanding questions in quantum many-body physics, that are difficult or impossible to study using conventional solid state systems. During this DARPA program, progressin several important directions has been made. We have developed cooling techniques suitable for a lattice system and cooled fermionic lithium atoms confined in a three-dimensional (3D) cubic lattice to unprecedented low temperatures, very close to the Neel temperature. We employed Bragg scattering of near-resonant light to observe the antiferromagnetic correlations. We have mapped the phase diagram overthe entire BEC-BCS crossover for a trapped 3D gas with imbalanced numbers of spin-up and spin-down atoms, and have also observed the crossover from a 1D to a 3D spin-imbalanced Fermi gas. We have investigated dynamics, rethermalization and out-of-equilibrium phenomena in strongly correlated lattice systems, as well as in disordered lattice systems. These studies greatly deepened our understanding of quantum phases of matter in lattice potentials.

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Abstract : Ultracold atoms confined in optical lattice potentials provide an ideal platform to address some of the most outstanding questions in quantum many-body physics, that are difficult or impossible to study using conventional solid state systems. During this DARPA program, progressin several important directions has been made. We have developed cooling techniques suitable for a lattice system and cooled fermionic lithium atoms confined in a three-dimensional (3D) cubic lattice to unprecedented low temperatures, very close to the Neel temperature. We employed Bragg scattering of near-resonant light to observe the antiferromagnetic correlations. We have mapped the phase diagram overthe entire BEC-BCS crossover for a trapped 3D gas with imbalanced numbers of spin-up and spin-down atoms, and have also observed the crossover from a 1D to a 3D spin-imbalanced Fermi gas. We have investigated dynamics, rethermalization and out-of-equilibrium phenomena in strongly correlated lattice systems, as well as in disordered lattice systems. These studies greatly deepened our understanding of quantum phases of matter in lattice potentials.
"This thesis presents research on a variety of dynamical phenomena in strongly correlated systems. We use 87Rb atoms trapped in a disordered optical lattice to realize the 3D Bose Hubbard model, with independently, dynamically tunable lattice depth and disorder strength. The equilibrium behavior of the Bose Hubbard and disordered Bose Hubbard models are understood, but there are many outstanding questions about dynamics. One area of interest is in dynamical behavior near quantum phase boundaries, such as the generation of quench-induced excitations in the presence of disorder. Another area concerns heat flow, relaxation, and thermalization. The primary focus of this thesis is driving a gas across a disorder-induced quantum phase transition from the Bose glass to the superfluid phase via quenching the disorder. We measured excitations generated during the quench and related them to crossing the equilibrium phase transition determined by quantum Monte Carlo simulations of the trapped system. The behavior we observe is reminiscent of the quantum Kibble Zurek mechanism, where the relaxation timescale diverges and local fluctuations are ""frozen"" into the system near the phase boundary. Understanding how disorder impacts the Kibble Zurek paradigm about behavior near a phase boundary provides insight into the dynamics of strongly interacting, disordered systems. The three other works discussed in this thesis concern relaxation and energy transfer in clean optical lattices. Understanding these dynamical properties of lattice gases is key to developing tools such as cooling in a lattice. In the first result, a gas comprised of two spin states was loaded into a spin-dependent optical lattice, such that one spin state experienced the lattice, and the other did not. We found that when the lattice gas was heated, energy transfer to the non-lattice gas did not occur at higher lattice depths due to the mismatch in the dispersion relations. In the second result, lattice atoms were excited to a higher band and found to decay to the ground state via two mechanisms. One decay channel involved generating excitations in the non-lattice atoms, while the other channel involved collisions between lattice atoms, where one atom decayed to the ground state and the other was excited to a higher band. The final result measured relaxation timescales by removing atoms with low quasimomentum and measuring rethermalization. The observed timescales are faster than the tunneling time and interaction time of the lattice. Proof-of-principle cooling was also demonstrated by removing atoms with higher quasimomentum and allowing the remaining atoms rethermalize to a cooler temperature."
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on the recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We discuss symmetry breaking, collective modes, and detection issues, e.g. in Bragg scattering. On the other hand, bosonic multiflavor ensembles allow for engineering of spin Hamiltonians which are interesting from a quantum computation point of view. Finally, we address the role of disorder in optical lattices. Fermionic atoms experience Anderson localization at sufficiently strong disorder. Interactions among the atoms induce a competing tendency towards delocalization. We present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.
Quantum simulation is emerging as an ambitious and active subfield of atomic physics. This thesis describes progress towards the goal of simulating condensed matter sys-tems, in particular the physics of the Fermi-Hubbard model, using ultracold Lithium atoms in an optical lattice. A major goal of the quantum simulation program is to observe phase transitions of the Hubbard model, into Néel antiferromagnetic phases and d-wave superfluid phases. Phase transitions are generally accompanied by a change in an underlying correlation in a physical system. Such correlations may be most amenable to probing by looking at fluctuations in the system. Experimental techniques for probing density and magnetization fluctuations in a variety of atomic Fermi systems are developed. The suppression of density fluctuations (or atom “shot noise”) in an ideal degenerate Fermi gas is observed by absorption imaging of time-of-flight expanded clouds. In-trap measurements of density and magnetization fluctuations are not easy to probe with absorption imaging, due to their extremely high attenuation. A method to probe
We use ultracold spin--1/2 atomic fermions (6^66Li) to realize the Hubbard model on a three-dimensional (3D) optical lattice. At relatively high temperatures and at densities near half-filling, we show that the gas forms a Mott insulator with unordered spins. To observe antiferromagnetic order that is predicted to occur at lower temperatures, we developed the compensated optical lattice method to evaporatively cool atoms in the lattice. This cooling has enabled the detection of short-range magnetic order by spin-sensitive Bragg scattering of light.