We study a harmonically confined atomic gas which is subjected to an additional external potential such as an optical lattice. Using a linear response formulation, we determine the response of the gas to a small, time-dependent displacement of the harmonic trap and derive a simple exact relation showing that the centre-of-mass position of the atomic cloud is directly related to the global optical conductivity of the system. We demonstrate the usefulness of this approach by calculating the optical conductivity of bosonic atoms in an optical lattice. In the Mott insulating phase, there is clear evidence of an optical Mott gap, providing a proof-of-principle demonstration that the global optical conductivity gives high-quality information about the excitations of strongly correlated quantum gases.
We study a harmonically confined atomic gas which is subjected to an additional external potential such as an optical lattice. Using a linear response formulation, we determine the response of the gas to a small, time-dependent displacement of the harmonic trap and derive a simple exact relation showing that the centre-of-mass position of the atomic cloud is directly related to the global optical conductivity of the system. We demonstrate the usefulness of this approach by calculating the optical conductivity of bosonic atoms in an optical lattice. In the Mott insulating phase, there is clear evidence of an optical Mott gap, providing a proof-of-principle demonstration that the global optical conductivity gives high-quality information about the excitations of strongly correlated quantum gases.
We measure the conductivity of neutral fermions in a cubic lattice. A uniform force is applied at a single frequency by periodic displacement of the trapping potential, and the current response is observed though the global displacement of atoms. In the linear response regime, the steady-state ratio between current and force gives the ac conductivity. The tensor properties of the conductivity reveal temporal and spatial symmetries of the sample. Similarly to optical conductivity commonly measured in materials with reflectivity, exact sum rules relate dynamical measurements to thermodynamic properties. We explore the effect of lattice depth, temperature, interaction strength, and atom number on conductivity. Using a relaxation-time approximation, we extract the transport time of current. Our work enables a direct comparison between cold-atom experiments and conductivity studies of materials.
We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.
In this thesis, we observe and characterize the current response of neutral fermions to a periodic applied force, thereby obtaining their conductivity. The experiment takes place in a 3D optical lattice subject to weak harmonic confinement, where a quantum gas microscope enables high-resolution fluorescence imaging of atoms pinned to lattice sites. Using micron-scale periodic displacements of an underlying harmonic potential to provide the oscillating uniform force, we measure the global current response of the atoms up to frequencies sufficient to characterize intraband transport, but well below the bandgap. We observe that the current response scales linearly with the forcing, providing experimental verification that data is taken in the linear response regime. The resulting conductivity spectra are analyzed and fit using five different models, from which a broadening parameter and the spectral weight of the response may be obtained. Broadening of the current response spectrum provides a measure of the rate of dissipation, and increases with lattice depth, interaction strength, and density. This dissipation occurs purely due to fermion-fermion collisions, given the absence of phonons or impurities in our potentials. It is observed to require a finite lattice depth in order to break Galilean invariance, as well as to enable Umklapp scattering events, which play a significant role in the dynamics. Measured dissipation rates collapse onto the predictions of a kinetic theory under the wide range of conditions studied. The spectral weight of the conductivity spectrum predicts the impulse response of the global current. It satisfies a sum rule in the limit of small lattice depth, but diminishes as the depth increases, reflecting an increase in the band-averaged effective mass. Measured under varying temperatures, densities, interaction strengths, and lattice depths, the spectral weight is shown to collapse onto the predictions of a thermodynamic description of the system. Furthermore, it is shown to be unaffected by varying the strength of interactions between the fermions, illustrating a fundamental prediction for conductivity spectra. As our measurements approach a high-temperature regime, the inverse of the spectral weight is shown to approach T-linear behaviour.
Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around k=0. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.