Implementation of Cavity Squeezing of a Collective Atomic Spin

We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled rubidium-87 atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M.H.S., I.D.L., V.V., arXiv:0911.3936] through two orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical rubidium-87 hyperfine clock transition.Comment: 4 pages, 2 figures. To be published in Phys. Rev. Lett. Some additional details and clarified wording in response to referee comments. Figures and results unchange

Squeezing the Collective Spin of a Dilute Atomic Ensemble by Cavity Feedback

We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. L., M. H. S., and V. V., Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.Comment: 4 pages, 2 figures. Minor revision. To appear in Phys. Rev.

An Aharonov-Bohm interferometer for determining Bloch band topology

The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular $\pi$ Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.Comment: 5+5 page

Dynamic optical superlattices with topological bands

We introduce an all-optical approach to producing high-flux synthetic magnetic fields for neutral atoms or molecules by designing intrinsically time-periodic optical superlattices. A single laser source, modulated to generate two frequencies, suffices to create dynamically modulated interference patterns which have topological Floquet energy bands. In particular, we propose a simple laser setup that realizes a tight-binding model with uniform flux per plaquette and well-separated Chern bands. Our method relies only on the particles' scalar polarizability and far detuned light.Comment: 5 pages main text + 2 pages supplementary material; published versio

One- and two-axis squeezing of atomic ensembles in optical cavities

The strong light-matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown in [Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence from spontaneous emission and cavity decay, we find roughly the same level of squeezing for the two schemes scaling as (NC)^(1/2) where C is the single atom cooperativity and N is the total number of atoms. When compared to an ideal squeezing operation, we find that for specific initial states, a dissipative version of the one-axis scheme attains higher fidelity than the unitary one-axis scheme or the two-axis scheme. However, the unitary one-axis and two-axis schemes perform better for general initial states.Comment: 13 pages, 6 figure