We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.

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The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing.

We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two regions of differing band topologies gives rise to topological edge states confined in a dielectric slab that propagate around sharp corners without backscattering. Three-dimensional finite-difference time-domain calculations show these edges to be confined in the out-of-plane direction by total internal reflection. Such nanoscale photonic crystal architectures could enable strong interactions between photonic edge states and quantum emitters.

We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers. DOI: 10.1103/PhysRevLett.103.245301 PACS numbers: 67.85.Àd, 03.75.Mn, 05.30.Jp, 75.10.Jm Ultracold atoms trapped in optical lattices represent a new frontier for the investigation of many-body physics [1,2]. The existence of novel physics at decreasing energy scales drives the quest for lower temperatures in the atomic Mott insulator. Insulating Mott shells form at a temperature T $ 0:2U, where U is the interaction energy. At the lower temperature T $ zJ, where J is the tunneling amplitude and z is the number of nearest neighbors, the conducting layers become superfluid and the system enters a quantum insulator state [3]. At the even colder temperature scale T $ J 2 =U, superexchange-stabilized phases can exist in the two-component Mott insulator; this is the regime of quantum magnetism [4]. Various proposals [5,6] have focused on the realization of quantum spin Hamiltonians in this regime. Detection of superexchange-driven phase transitions in these systems remains a major goal of ultracold atomic physics. Perhaps the most important barrier to experimental detection of such a phase transition is the requirement of temperatures well below 1 nK [4]. Additional cooling methods [7][8][9][10] will be needed to reach this very interesting temperature scale. However, it is clear that to assess current methods and to validate future cooling techniques, low-temperature thermometry of the Mott insulator is needed.Thermometry of systems in the Mott insulating state has remained a challenge [3,[11][12][13][14]. In this Letter, we discuss and demonstrate a simple and direct method of thermometry using a magnetic field gradient which works in the two-component Mott insulator.The theory behind this method of thermometry is straightforward. The system under consideration is an ensemble of atoms in a mixture of two hyperfine states loaded into a three-dimensional optical lattice in the presence of a weak magnetic field gradient. The two states have different magnetic moments, and are thus pulled towards opposite sides of the trapped sample by the gradient. At zero temperature, the spins will segregate completely, and a sharp domain wall will exist between the two spin domains (a small width due to superexchange coupling is typically negligible). This system has the same bulk physics as the single-compo...

We demonstrate a new cooling method in which a time-varying magnetic field gradient is applied to an ultracold spin mixture. This enables preparation of isolated spin distributions at positive and negative effective spin temperatures of ±50 picokelvin. The spin system can also be used to cool other degrees of freedom, and we have used this coupling to cool an apparently equilibrated Mott insulator of rubidium atoms to 350 picokelvin. These are the lowest temperatures ever measured in any system. The entropy of the spin mixture is in the regime where magnetic ordering is expected.

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.

We have observed Bragg scattering of photons from quantum degenerate 87 Rb atoms in a threedimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wavefunction whose position and momentum width is Heisenberg-limited. The spatial coherence of the wavefunction leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.