In this work, I present the experimental realization of two-dimensional state-dependent transport of cesium atoms trapped in a three-dimensional optical lattice. Leveraging the ability to state-dependently transport atoms, I demonstrate microwave photon mediated sideband cooling to the motional ground state along two dimensions. Once cooled down to the vibrational ground state, we use these atoms as sensitive probes to detect both magnetic ﬁeld gradients and optical ﬁeld inhomogeneities, by means of Ramsey interferometry. This enables us to perform Ramsey imaging of optical dipole traps, an essential technique which helps in the precise alignment of optical beams inside the vacuum cell.

In the ﬁrst part of the thesis, I introduce the main experimental apparatus of the Discrete Quantum Simulator (DQSIM) machine, as our experiment is known, with emphasis on the technical improvements over the past few years, such as increasing the atom ﬁlling in our optical lattice from double digits to a few thousand. Using these atoms as magnetic probes, I conﬁrm the expected magnetic shielding factor of about 2000 from the mu-metal shielding enclosing the vacuum cell. I ﬁnally discuss the control we have over the internal state of the atoms, with a measured Rabi frequency of Ω≈2π × 200 kHz.

In chapter 3, I introduce the concept of state-dependent transport, which forms the basis of most experiments planned with the DQSIM machine. I go on to discuss the polarization synthesizer, the technical backbone of the state-dependent optical lattices. The polarization synthesizer allows us to create any arbitrary polarization state of light, by independently controlling the phase and amplitude of each circular polarization component of a linearly polarized optical lattice beam. With two such polarization synthesizers implemented in the experiment, I report on the experimental realization of state-dependent transport in two dimensions. This is followed by the demonstration of microwave photon mediated ground state cooling in two dimensions, where we achieve a ground state population of about 95% along each dimension.

In the following chapter, I introduce the Ramsey spectroscopy technique, a mainstay of high precision experiments. Using Ramsey spectroscopy, I investigate some sources of dephasing in our experiment, from inhomogeneous magnetic ﬁelds to diﬀerential light shifts. Based on these Ramsey measurements, I show that we can achieve coherence times greater than a millisecond if we restrict the region of interest in our optical lattice. Exploiting the high precision Ramsey interferometry further, in chapter 5, I introduce a versatile technique for the precise in-vacuo reconstruction of optical potentials. This Ramsey imaging technique is used to image the four laser beams that form our three-dimensional lattice, helping us align them with micrometer precision. In the ﬁnal chapter, I summarize the work done in this thesis and discuss some future experiments that are planned for the DQSIM machine, from plane selection to two-dimensional quantum walks.