We suggest two experimental methods for probing both short- and long-range spin correlations of atoms in optical lattices using superlattice potentials. The first method involves an adiabatic doubling of the periodicity of the underlying lattice to probe neighboring singlet (triplet) correlations for fermions (bosons) by the occupation of the resulting vibrational ground state. The second method utilizes a time-dependent superlattice potential to generate spin-dependent transport by any number of prescribed lattice sites, and probes correlations by the resulting number of doubly occupied sites. For experimentally relevant parameters, we demonstrate how both methods yield large signatures of antiferromagnetic correlations of strongly repulsive fermionic atoms in a single shot of the experiment. Lastly, we show how this method may also be applied to probe $d$-wave pairing, a possible ground-state candidate for the doped repulsive Hubbard model.
We suggest two experimental methods for probing both short- and long-range spin correlations of atoms in optical lattices using superlattice potentials. The first method involves an adiabatic doubling of the periodicity of the underlying lattice to probe neighboring singlet (triplet) correlations for fermions (bosons) by the occupation of the resulting vibrational ground state. The second method utilizes a time-dependent superlattice potential to generate spin-dependent transport by any number of prescribed lattice sites, and probes correlations by the resulting number of doubly occupied sites. For experimentally relevant parameters, we demonstrate how both methods yield large signatures of antiferromagnetic correlations of strongly repulsive fermionic atoms in a single shot of the experiment. Lastly, we show how this method may also be applied to probe d-wave pairing, a possible ground-state candidate for the doped repulsive Hubbard model.
We previously proposed [K. G. L. Pedersen, B. M. Andersen, G. M. Bruun, O. F. Sylju\aa{}sen, and A. S. S\o{}rensen, Phys. Rev. A 84, 041603 (2011)] a method to utilize a temporally dependent superlattice potential to mediate spin-selective transport and thereby probe long- and short-range magnetic correlations in optical lattices. Specifically, this can be used for detecting antiferromagnetic ordering in repulsive fermionic optical lattice systems, but more generally it can serve as a means of directly probing correlations among the atoms by measuring the mean value of an observable, the number of double occupied sites. Here we provide a detailed investigation of the physical processes that limit the effectiveness of this ``conveyer belt method.'' Furthermore, we propose a simple way to improve the procedure, resulting in an essentially perfect (error-free) probing of the magnetic correlations. These results shows that suitably constructed superlattices constitute a promising way of manipulating atoms of different spin species as well as probing their interactions.
We suggest a simple experimental method for probing antiferromagnetic spin correlations of two-component Fermi gases in optical lattices. The method relies on a spin selective Raman transition to excite atoms of one spin species to their first excited vibrational mode where the tunneling is large. The resulting difference in the tunneling dynamics of the two spin species can then be exploited, to reveal the spin correlations by measuring the number of doubly occupied lattice sites at a later time. We perform quantum Monte Carlo simulations of the spin system and solve the optical lattice dynamics numerically to show how the timed probe can be used to identify antiferromagnetic spin correlations in optical lattices.
This dissertation summarizes my recent work regarding systems of strongly interacting fermionic atoms in optical lattices. This work addresses the combination of two experimental techniques that have been the subject of much recent research in ultracold atom physics. One is the use of optical lattices, which provide a means to realize diverse interaction configurations within a clean, controllable system. The other is the use of magnetically tunable Feshbach resonances to control the strength of the interatomic interaction. Together, these techniques offer the possibility of an experimental realization of many important model Hamiltonians of condensed matter physics, and may also lead to the discovery of new physics. Recent study of this system has shown that strong interactions near Feshbach resonance will lead to the population of multiple lattice bands, and that collisions between atoms on neighboring sites cannot be neglected. These effects lead to a complicated Hamiltonian, but one which can be simplified to an effective single-band model equivalent to the generalized Hubbard model (GHM), which is an extension of the Hubbard model that includes correlated hopping terms. My main results concern the study of this model. The strong correlations between the particles make it difficult to definitively determine the many body physics of the GHM. As a first approach to understanding the GHM in optical lattices, I focus mainly on cases where the problem is greatly simplified by allowing interactions among only small groups of lattice sites. This restriction can be implemented in experiments using an optical superlattice potential. Our results include a proposed scheme (based on double-well superlattices) to empirically verify that the GHM describes this system and to directly measure the various parameters of this model. Other results include exact solutions on four-site square plaquettes, which demonstrate that d-wave excitations can occur in the low-energy states. By using a superlattice to give an array of weakly coupled plaquettes, one can thus produce a d-wave superfluid state. This is of relevance to the study of high-Tc superconductors, although I note certain key differences between the sort of d-wave superfluid described here and that of the superconductors.
This thesis reports on the microscopic investigation of antiferromagnetic order in Hubbard chains, realized with ultracold repulsively interacting fermions in an optical lattice. Extending a quantum gas microscope on spin resolution opened the possibility to Access the full charge and spin statistics of a strongly correlated fermionic many body system. Using this technique, we measured antiferromagnetic correlations over distances up to three lattice sites. Starting with a repulsive degenerate two component mixture of 6Li atoms trapped in a single plane of a vertical lattice, we loaded the Atoms into one-dimensional tubes of a transverse optical superlattice. By adiabatically ramping up the lattice potential along the tubes, we isentropically entered the strongly correlated regime of the one-dimensional Fermi-Hubbard Hamiltonian. We spatially separated the two spin states into opposite sites of local double wells orthogonal to the direction of the lattice before single atom and site sensitive imaging. In this way we extracted the spin information of every single lattice site and were able to evaluate spin-spin correlations. The two component degenerate gases were produced with sub-Poissonian atom number fluctuations by magnetically driven evaporative cooling in vicinity of a Feshbach resonance, used to set the scattering length. The dependence of antiferromagnetic correlations on the driving superexchange coupling was experimentally investigated by varying the interparticle scattering length before loading the atoms into the optical lattice. Taking advantage of the underlying trapping potential of the optical lattice, which shaped the filling and the entropy of the gases, the influence of density excitations and different entropies on spin correlations was observed. By post-selecting the Hubbard chains based on their average filling and local atom number fluctuations, spin correlations corresponding to 58% of the zero temperature predictions in the Heisenberg regime were measured. By comparing the obtained antiferromagnetic correlations to Quantum-Monte-Carlo predictions for our System the lowest measured entropy per particle could be stated as s = 0.51(4)kB, clearly below the critical value of s = ln(2)kB, which is required to form longer ranged correlations. Below this critical entropy, in contrast to local density fluctuations, these spin correlations strongly depend on the entropy of the system. In the future, such a spin thermometer can be used to benchmark novel cooling techniques, which are required to enter the temperature regime of d-wave superconducting states. The access to the full particle and spin statistics will enable us to read out multi-point correlation functions, which characterize such exotic states of matter.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.