Realization of a Floquet-Engineered Moat Band for Ultracold Atoms.

We experimentally engineer a moatlike dispersion in a system of weakly interacting bosons. By periodically modulating the amplitude of a checkerboard optical lattice, the two lowest isolated bands are hybridized such that the single particle energy displays a continuum of nearly degenerate minima that lie along a circle in reciprocal space. The moatlike structure is confirmed by observing a zero group velocity at nonzero quasimomentum and we directly observe the effect of the modified dispersion on the trajectory of the center of mass position of the condensate. We measure the lifetime of condensates loaded into different moat bands at different quasimomenta and compare to theoretical predictions based on a linear stability analysis of Bogoliubov excitations. We find that the condensate decay increases rapidly as the quasimomentum is decreased below the radius of the moat minimum, and argue that such dynamical instability is characteristic of moatlike dispersions, including spin-orbit coupled systems. The ground state of strongly interacting bosons in such degenerate energy landscapes is expected to be highly correlated, and our work represents a step toward realizing fractional quantum Hall-like states of bosons in an optical lattice.

Tunable Three-Body Loss in a Nonlinear Rydberg Medium.

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wave function and analytical estimates based on Fermi's golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

Which Way Does Stimulated Emission Go?

Is it possible to form an image using light produced by stimulated emission? Here we study light scatter off an assembly of excited chromophores. Due to the Optical Theorem, stimulated emission is necessarily accompanied by excited state Rayleigh scattering. Both processes can be used to form images, though they have different dependencies on scattering direction, wavelength and chromophore configuration. Our results suggest several new approaches to optical imaging using fluorophore excited states.

Exotic Photonic Molecules via Lennard-Jones-like Potentials.

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a Förster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multibody interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in two dimensions preferentially arrange themselves in a line configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

Quantum Interference between Photons from an Atomic Ensemble and a Remote Atomic Ion.

Many remote-entanglement protocols rely on the generation and interference of photons produced by nodes within a quantum network. Quantum networks based on heterogeneous nodes provide a versatile platform by utilizing the complementary strengths of the differing systems. Implementation of such networks is challenging, due to the disparate spectral and temporal characteristics of the photons generated by the different quantum systems. Here, we report on the observation of quantum interference between photons generated from a single ion and an atomic ensemble. The photons are produced on demand by each source located in separate buildings, in a manner suitable for quantum networking. Given these results, we analyze the feasibility of hybrid ion-ensemble remote entanglement generation.

Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit.

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them, by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength ( λ / 2 ) and arises from the nonlinear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark-state spin composition. We investigate adiabaticity requirements, and shape our time-dependent light fields to respect these requirements. We apply this framework to show that a λ / 4 -spaced lattice can be synthesized using realistic experimental parameters. As an example, we discuss mechanisms that limit lifetimes in these lattices, explore candidate systems with their limitations, and study adiabatic loading into the ground band of these lattices.

Optical Lattice with Torus Topology.

We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed high resolution imaging techniques. We numerically study the feasibility of this proposal by calculating the tunneling strengths for atoms in the torus lattice. To illustrate the nontrivial role of topology in atomic dynamics on the torus, we study the quantized superfluid currents and fractional quantum Hall (FQH) states on such a structure. For FQH states, we numerically investigate the robustness of the topological degeneracy and propose an experimental way to detect such a degeneracy. Our scheme for torus construction can be generalized to surfaces with higher genus for exploration of richer topological physics.

Dark State Optical Lattice with a Subwavelength Spatial Structure.

We report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10 nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44 ms, nearly 10^{5} times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

Optimization of photon storage fidelity in ordered atomic arrays.

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number N a like ∼ ( log N a ) 2 ∕ N a 2 , and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.

Anomalous Broadening in Driven Dissipative Rydberg Systems.

We observe interaction-induced broadening of the two-photon 5s-18s transition in ^{87}Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly 2 orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with blackbody induced population in nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.

Synthetic magnetic fields for ultracold neutral atoms.

Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation-a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall effect in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, which is evident from the appearance of vortices in our Bose-Einstein condensate. Our approach uses a spatially dependent optical coupling between internal states of the atoms, yielding a Berry's phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems. With a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.

Controlled exchange interaction between pairs of neutral atoms in an optical lattice.

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.

Precision measurement of transition matrix elements via light shift cancellation.

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Pulsed Sisyphus scheme for laser cooling of atomic (anti)hydrogen.

We propose a laser cooling technique in which atoms are selectively excited to a dressed metastable state whose light shift and decay rate are spatially correlated for Sisyphus cooling. The case of cooling magnetically trapped (anti)hydrogen with the 1S-2S-3P transitions by using pulsed ultraviolet and continuous-wave visible lasers is numerically simulated. We find a number of appealing features including rapid three-dimensional cooling from ∼1 K to recoil-limited, millikelvin temperatures, as well as suppressed spin-flip loss and manageable photoionization loss.

Differential light-shift cancellation in a magnetic-field-insensitive transition of 87rb.

The precise measurement of transition frequencies of trapped atomic samples is susceptible to inaccuracy arising from the inhomogeneous differential shift of the relevant energy levels in the presence of the trapping fields. We demonstrate near-complete cancellation of the differential ac Stark shift ("light shift") of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in ^{87}Rb atoms trapped in an optical lattice. Up to 95(2)% of the differential light shift is cancelled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology.

Absolute transition frequencies and quantum interference in a frequency comb based measurement of the (6,7)Li D lines.

Optical frequencies of the D lines of (6,7)Li were measured with a relative accuracy of 5 × 10⁻¹¹ using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1 MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for 6Li and 7Li are 10052.837(22) MHz and 10053.435(21) MHz. The splitting isotope shift is 0.599(30) MHz, in reasonable agreement with recent theoretical calculations.

Phases of a two-dimensional bose gas in an optical lattice.

Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

Competition between Factors Determining Bright versus Dark Atomic States within a Laser Mode.

We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the J = 1 to J' = 0 system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to in situ calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.

Realization of a stroboscopic optical lattice for cold atoms with subwavelength spacing.

Optical lattices are typically created via the ac Stark shift and are limited by diffraction to periodicities ⩾ λ/2, where λ is the wavelength of light used to create them. Lattices with smaller periodicities may be useful for many-body physics with cold atoms and can be generated by stroboscopic application of a phase-shifted lattice with subwavelength features. Here we demonstrate a λ/4-spaced lattice by stroboscopically applying optical Kronig-Penney-like potentials which are generated using spatially dependent dark states. We directly probe the periodicity of the λ/4-spaced lattice by measuring the average probability density of the atoms loaded into the ground band of the lattice. We measure lifetimes of atoms in this lattice and discuss the mechanisms that limit the applicability of this stroboscopic approach.

Coherent optical nanotweezers for ultracold atoms.

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultracold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work allows for subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.