Optical lattice experiments have proved to be a versatile tool for studying strongly correlated quantum systems. The motivation behind these experiments is to use the cold atoms to emulate a solid state system for which the Hamiltonian is analytically or numerically non-solvable. In our experiment, we construct a 3D simple cubic lattice system which realizes the Fermi-Hubbard model and provides us the opportunity to study the antiferromagnetic (AFM) insulator phase. In order to establish evaporative cooling in the optical lattice and to enlarge the size of the AFM phase, we implement a compensation potential additional to the standard lattice beam. In this thesis, I will present detailed steps to construct and calibrate the compensated 3D optical lattice system.
Optical lattice experiments have proved to be a versatile tool for studying strongly correlated quantum systems. The motivation behind these experiments is to use the cold atoms to emulate a solid state system for which the Hamiltonian is analytically or numerically non-solvable. In our experiment, we construct a 3D simple cubic lattice system which realizes the Fermi-Hubbard model and provides us the opportunity to study the antiferromagnetic (AFM) insulator phase. In order to establish evaporative cooling in the optical lattice and to enlarge the size of the AFM phase, we implement a compensation potential additional to the standard lattice beam. In this thesis, I will present detailed steps to construct and calibrate the compensated 3D optical lattice system.
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.
We use ultracold spin--1/2 atomic fermions (6Li) 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.
The next generation of 3D optical lattice experiments requires a new vacuum chamber design. In the past, a 3D optical lattice apparatus in our lab was used to create and observe antiferromagnetic (AFM) coorelations within a 6Li-based degenerate Fermi gas. In that experiment, implementing anti-trapping beams overlapped with the standard lattice beams allowed the potential landscape to be made smoother, in an effort to increase the spatial extent of the AFM phase. Nevertheless, preparing atoms to be even cooler, and further extending the region of interest requires newer solutions. One method is to use the anti-trapping beams in a slightly different manner. By utilizing a higher numerical aperture optical beam line for anti-trapping, finer adjustments can be made in the potential. Combined with digital-micromirror based holography techniques. the anti-trapping beams can be custom-shaped to carve even finer details into the optical lattice. With sufficient control over beamshaping, one could perform better entropy re-distribution within the atom cloud. In this way, the central AFM region can be made colder by pushing entropy out to the wings. In this thesis, I will detail the work done in analyzing and designing a new chamber to fulfill the previously mentioned features.
Strongly interacting many-body systems are of great interest in many areas of physics. Ultracold atoms in optical lattices are a powerful tool for creating and studying such systems. In this thesis, the construction and characterization of an 3D optical lattice for a ultra-cold Strontium apparatus is described. A 1064nm fiber amplified laser system is used to create three orthogonal pairs of standing waves that together form the 3D lattice. By delivering 4W of power to each arm of the lattice and focusing the beams to a beam radius of about 250 microns at the location of the atoms, we can create a 3D lattice with a maximum trap depth around 70 photon recoils.
A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom systems are of interest since cold atom experiments provide a control on model parameters. In this thesis, we use novel analytical and computational techniques to treat strongly interacting bosonic systems. Taking advantage of the very versatile quantum Monte Carlo Stochastic Green Function algorithm, we studied several interesting problems. First, we explore a recently developed new confining method for cold atoms on optical lattices. Atoms are confined via a hopping integral that decreases as a function of the distance from the center of the lattice. This method might lead to lower temperatures than existing diagonal confinement methods. Next, we study the ground state phase diagram of interacting bosons on a ring-shape lattice with a region of weak hopping integrals. The model, an extension of the well known Bose-Hubbard model, develops a novel local Mott phase in addition to the usual Mott and superfluid phases in the homogeneous system. This might provide a new insight to the description of atomtronics applications. Finally, we study the two species Bose Hubbard model in a two-dimensional lattice. This model presents novel phases due to the complexity associated with multiple species. Its phase diagram shows ordered and coexistence phases including a ferromagnetic phase separated phase with high entropy. This phase might be accessible experimentally. The novel phases found from our studies are linked to experiments on ultra-cold atoms trapped by laser beams.
The advancement in the eld of cold-atoms has generated a lot of interest in the condensed matter community. Cold-atom experiments can simulate clean, disor-der/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an ex-perimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advance-ment in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and anti-ferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem (entropy issues).
In this thesis, we have addressed the issue of the \cooling problem for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of cold-atoms and optical lat-tice potentials, and a brief review of the experimental work going on in the cold-atomic systems. Experimental limitations like \fermionic cooling problem have been discussed in some detail. Then we proposed a bilayer band-insulator model to circumvent the \entropy problem and simultaneously increasing the transi-tion temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean- eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter-1 : provides a general introduction to the ultra-cold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about cold-atom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many many-body Hamiltonians in experiments, which until now was just a theoretical tool to describe various many-body physics. In the end we give a brief idea for introducing disorder in the cold-atom experiments discuss the limitations of these experiments in realizing the \interesting super uid and anti-ferromagnetic phases of fermionic Hubbard model in optical lattices.
Chapter-2 : gives a brief idea of \Determinant Quantum Monte-Carlo (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how…