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Quasimomentum Cooling and Relaxation in a Strongly Correlated Optical Lattice

David Chen, Carolyn Meldgin, Philip Russ, Erich J. Mueller, Brian DeMarco

Published Mar 26, 2015• 0 citations
OpenAlex

Abstract

A key challenge for optical lattice experiments focused on simulating models of strongly correlated electronic solids has been achieving lower temperatures. Although cooling of lattice-well vibrational states has been demonstrated, the motion of atoms through the lattice, characterized by their quasimomentum, has not been cooled directly. Furthermore, quasimomentum equilibration, which is necessary for cooling, has remained unexplored. Here, we use quasimomentum-selective stimulated Raman transitions to directly measure rethermalization rates and cool quasimomentum for a bosonic lattice Hubbard gas. The measured relaxation rate is consistent with a short-range, two-particle scattering model without free parameters at high lattice depths, despite an apparent violation of the Mott-Ioffe-Regel (MIR) bound. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides, and the cooling method we have developed is applicable to any species, including fermionic atoms.

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A key challenge for optical lattice experiments focused on simulating models of strongly correlated electronic solids has been achieving lower temperatures. Although cooling of lattice-well vibrational states has been demonstrated, the motion of atoms through the lattice, characterized by their quasimomentum, has not been cooled directly. Furthermore, quasimomentum equilibration, which is necessary for cooling, has remained unexplored. Here, we use quasimomentum-selective stimulated Raman transitions to directly measure rethermalization rates and cool quasimomentum for a bosonic lattice Hubbard gas. The measured relaxation rate is consistent with a short-range, two-particle scattering model without free parameters at high lattice depths, despite an apparent violation of the Mott-Ioffe-Regel (MIR) bound. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides, and the cooling method we have developed is applicable to any species, including fermionic atoms.
This thesis describes experiments focused on investigating out-of-equilibrium phenomena in the Bose-Hubbard Model and exploring novel cooling techniques for ultracold gases in optical lattices. In the first experiment, we study quenches across the Mott-insulator-to-superfluid quantum phase transition in the 3D Bose-Hubbard Model. The quench is accomplished by continuously tuning the ratio of the Hubbard energies. We observe that the degree of excitation is proportional to the fraction of atoms that cross the phase boundary, and that the amount of excitations and energy produced during the quench have a power-law dependence on the quench rate. These phenomena suggest an excitation process analogous to the mechanism for defect generation in non-equilibrium classical phase transitions. This experiment constitutes the first observation of the Kibble-Zurek mechanism in a quantum quench. We have reported our findings in Ref. [1]. In a second experiment, published in Ref. [2], we investigate dissipation as a method for cooling a strongly interacting gas. We introduce dissipation via a bosonic reservoir to a strongly interacting bosonic gas in the Mott-insulator regime of a 3D spin-dependent optical lattice. The lattice atoms are excited to a higher energy band using laser-induced Bragg transitions. A weakly interacting superfluid comprised of atoms in a state that does not experience the lattice potential acts as a dissipative bath that interacts with the lattice atoms through collisions. We measure the resulting bath-induced decay using the atomic quasimomentum distribution, and we compare the decay rate with predictions from a weakly interacting model with no free parameters. A competing intrinsic decay mechanism arising from collisions between lattice atoms is also investigated. The presence of intrinsic decay can not be accommodated within a non-interacting framework and signals that strong interactions may play a central role in the lattice-atom dynamics. The intrinsic decay process we observe may negatively impact the success of cooling via dissipation because a fraction of intrinsic decay events can deposit a large amount of energy into the lattice gas. In a third experiment, we develop and carry out the first demonstration of cooling an atomic quasimomentum distribution. Our scheme, applied in a proof-of-principle experiment to 3D Bose-Hubbard gas in the superfluid regime, involves quasimomentum-selective Raman transitions. This experiment is motivated by the search of new cooling techniques for lattice-trapped gases. Efficient cooling exceeding heating rates is achieved by iteratively removing high quasimomentum atoms from the lattice. Quasimomentum equilibration, which is necessary for cooling, is investigated by directly measuring rethermalization rates after bringing the quasimomentum distribution of the gas out of equilibrium. The measured relaxation rate is consistent at high lattice depths with a short-range, two-particle scattering model without free parameters, despite an apparent violation of the Mott-Ioffe-Regel bound. Our results may have implications for models of unusual transport phenomena in materials with strong interactions, such as heavy fermion materials and transition metal oxides. The cooling method we have developed is applicable to any species, including fermionic atoms. Our results are available in Ref. [3]
"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."
Optical lattices have emerged as ideal simulators for Hubbard models of strongly correlated materials, such as the high-temperature superconducting cuprates. In optical lattice experiments, microscopic parameters such as the interaction strength between particles are well known and easily tunable. Unfortunately, this benefit of using optical lattices to study Hubbard models comes with one clear disadvantage: the energy scales in atomic systems are typically nanokelvin compared with kelvin in solids, with a correspondingly miniscule temperature scale required to observe exotic phases such as d -wave superconductivity. The ultra-low temperatures necessary to reach the regime in which optical lattice simulation can have an impact—the domain in which our theoretical understanding fails—have been a barrier to progress in this field. To move forward, a concerted effort is required to develop new techniques for cooling and, by extension, techniques to measure even lower temperatures. This paper will be devoted to discussing the concepts of cooling and thermometry, fundamental sources of heat in optical lattice experiments, and a review of proposed and implemented thermometry and cooling techniques.
We use 40K atoms trapped in a cubic optical lattice to simulate the Fermi-Hubbard model. The work in this thesis focuses on investigating dynamics in the Fermi-Hubbard model and developing techniques for engineering Hamiltonians beyond the minimal Hubbard model. We discussed three experiments. In the first, we investigated the transport properties of a Fermi lattice gas by directly measuring the transport lifetime at various interaction strengths and temperatures. The resistivity is inferred from the measured transport lifetime. We observe anomalous transport behavior, which is analogous to bad-metal behavior in strongly correlated electronic materials. The second experiment presents the first realization of correlated, density-dependent tunneling in a Fermi-Hubbard optical lattice model by applied Raman laser fields. This correlated tunneling involves spin-flips and the generation of doublons, which have been observed experimentally. We also confirmed that the amplitude of correlated tunneling is suppressed when neighboring lattice sites are unoccupied. The last experiment explores the possibility to introduce long-range interactions for fermions trapped in optical lattices via Rydberg-dressed states. We developed a novel velocity-selective spectroscopy method to measure the transition between the 5P_1/2 and Rydberg states via electromagnetically induced transparency. This measurement is a first step toward inducing Rydberg-dressed interactions in optical lattices.
We use a momentum-space hole-burning technique implemented via stimulated Raman transitions to measure the momentum relaxation time for a gas of bosonic atoms trapped in an optical lattice. By changing the lattice potential depth, we observe a smooth crossover between relaxation times larger and smaller than the bandwidth. The latter condition violates the Mott-Ioffe-Regel bound and indicates a breakdown of the quasiparticle picture. We produce a simple kinetic model that quantitatively predicts these relaxation times. Finally, we introduce a cooling technique based upon our hole-burning technique.
Electrical current in conventional metals is carried by electrons that retain their individual character. Bad metals, such as the normal state of some high-temperature superconductors, violate this scenario, and the complete picture for their behavior remains unresolved. Here, we report phenomena consistent with bad-metal behaviour in an optical-lattice Hubbard model by measuring the transport lifetime for a mass current excited by stimulated Raman transitions. We demonstrate incompatibility with weak-scattering theory and key characteristics of bad metals: anomalous resistivity scaling consistent with T-linear behavior, the onset of incoherent transport, and the approach to the Mott-Ioffe-Regel limit. Our work demonstrates a direct method for determining the transport lifetime, which is critical to theory but difficult to measure in materials, and exposes minimal ingredients for bad-metal behavior.