1D Optical Lattice Research Articles

Direct Tunneling Delay Time Measurement in an Optical Lattice

We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nanometers excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics.

Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low light intensity limit we illustrate the simulations in a system of atoms in a Mott-insulator state in a 2D optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.

Detecting the Chern number of topological Weyl semimetals in 3D optical lattices

We propose a realistic scheme to directly probe the Chern number of topological Weyl semimetals in optical lattices. The Weyl semimetal states can be realized with ultracold fermionic atoms trapped in three-dimensional optical lattices, and are topologically characterized by kz-dependent Chern number, where kz is the out-of-plane quasimomentum. We demonstrate with numerical simulations that this characteristic topological invariant can be extracted from the shift of the hybrid Wannier center in the optical lattice, based on the particle pumping approach. Through in situ measurement of atomic density, the topological properties of the Weyl semimetal states are then directly revealed.

An efficient quantum light–matter interface with sub-second lifetime

Quantum repeater holds the promise for scalable long-distance quantum communication. Towards a first quantum repeater based on memory-photon entanglement, significant progresses have made in improving performances of the building blocks. Further development is hindered by the difficulty of integrating key capabilities such as long storage time and high memory efficiency into a single system. Here we report an efficient light-matter interface with sub-second lifetime by confining laser-cooled atoms with 3D optical lattice and enhancing the atom-photon coupling with a ring cavity. An initial retrieval efficiency of 76(5)% together with an 1/e lifetime of 0.22(1) s have been achieved simultaneously, which already support sub-Hz entanglement distribution up to 1000 km through quantum repeater. Together with an efficient telecom interface and moderate multiplexing, our result may enable a first quantum repeater system that beats direct transmission in the near future.

Bound states and Cooper pairs of molecules in 2D optical lattices bilayer

We investigate the formation of Cooper pairs, bound dimers and the dimer‐dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two‐molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non‐zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer‐dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS‐BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.

Matter-wave propagation in optical lattices: geometrical and flat-band effects

The geometry of optical lattices can be engineered, allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of matter-wave propagation as a function of the lattice geometry. To address this issue, we investigated, theoretically, the quantum transport of noninteracting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square lattice has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Possible realizations of those dynamical phenomena are discussed.

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.

Critical point of a rotating Bose–Einstein condensates in optical lattice

In this paper, we have considered the critical point (critical atoms’ number and the corresponding critical temperature) of rotating condensate bosons trapped in optical lattices. Our system is formed by loading three dimensional harmonically trapped boson atoms into a 1D (axial direction) or 2D (radial direction) optical lattice. The system subjected to rotating with angular velocity Ω around to the axial direction z-axis. We employ the semiclassical approximation to calculate the critical point. Effects of the optical lattice depth, direction (axial or radial) and the rotation rate on the critical point are investigated using the semiclassical approximation. The calculated results showed that the temperature dependence of the critical point is changed in an optical lattice and depends crucially on the rotation rate. The effect of the finite size for one-dimensional optical lattice case, as required by experiment, is discussed. The outcome results furnish useful qualitatively theoretical results for the future Bose–Einstein condensation experiments in such traps.

Statistical Transmutation in Floquet Driven Optical Lattices.

We show that interacting bosons in a periodically driven two dimensional (2D) optical lattice may effectively exhibit fermionic statistics. The phenomenon is similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a driven lattice develops the moat shape, i.e., a minimum along a closed contour in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic quasiparticles. The statistical transmutation is achieved by the Chern-Simons flux attachment similar to the fractional quantum Hall case. We show that the velocity distribution of the released bosons is a sensitive probe of the fermionic nature of their stationary Floquet state.

Four-Dimensional Quantum Hall Effect with Ultracold Atoms

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.

Coherent Addressing of Individual Neutral Atoms in a 3D Optical Lattice.

We demonstrate arbitrary coherent addressing of individual neutral atoms in a 5×5×5 array formed by an optical lattice. Addressing is accomplished using rapidly reconfigurable crossed laser beams to selectively ac Stark shift target atoms, so that only target atoms are resonant with state-changing microwaves. The effect of these targeted single qubit gates on the quantum information stored in nontargeted atoms is smaller than 3×10^{-3} in state fidelity. This is an important step along the path of converting the scalability promise of neutral atoms into reality.

On-chip optical lattice for cold atom experiments.

An atom-chip-based integrated optical lattice system for cold and ultracold atom applications is presented. The retroreflection optics necessary for forming the lattice are bonded directly to the atom chip, enabling a compact and robust on-chip optical lattice system. After achieving Bose-Einstein condensation in a magnetic chip trap, we load atoms directly into a vertically oriented 1D optical lattice and demonstrate Landau-Zener tunneling. The atom chip technology presented here can be readily extended to higher dimensional optical lattices.

Detection of a single lithium atom in a magneto-optical trap

We report fluorescence detection of a single 7Li atom in a magneto-optical trap (MOT). We use a double MOT system, which allows us to control the loading rate of the second MOT by simply turning on or off the first MOT and to use a modest magnetic field gradient of 46 G/cm. A single atom is trapped for longer than 100 s. The fluorescence from the trapped atoms is imaged onto an electron-multiplying charge-coupled device with a unit magnification factor by a pair of aspheric lenses. The numerical aperture of the objective lens is 0.22 with a collecting efficiency of 1.3%. Accumulated fluorescence is extracted by integrating the signal over a region of interest of 500×350 μm2. For a 200-ms exposure time, the fluorescence count from a single atom is 8.8×103 and the background count from scattered MOT beams is 6.8 × 104. We actively stabilize the trap beam power to reduce the noise and the measured noise is two times the statistical noise. Overall signal-to-noise ratio of the single-atom detection is 37/√ Hz. We also describe a modification of the system that is adapted to an experimental configuration for quantum manipulation of single atoms in a 1D optical lattice.

Polarizability of ultracold molecules in the rovibrational ground state of

We study, both theoretically and experimentally, the dynamical polarizability of molecules in the rovibrational ground state of . Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability for wave numbers up to 20 000 . Our calculations are compared to experimental results at () as well as at (). Here, we discuss the measurements at . The ultracold Rb2 molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than are observed. In addition, the dynamical polarizability for the state is calculated. We provide simple analytical expressions that reproduce the numerical results for for all vibrational levels of as well as . Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at is of interest, since here, ultrastable high power lasers are available.

Site-resolved imaging of fermionic ^{6}Li in an optical lattice.

We demonstrate site-resolved imaging of individual fermionic ^{6}Li atoms in a single layer of a 3D optical lattice. To preserve the density distribution during fluorescence imaging, we simultaneously cool the atoms with 3D Raman sideband cooling. This laser cooling technique, demonstrated here for the first time for ^{6}Li atoms, also provides a pathway to rapid low-entropy filling of an optical lattice. We are able to determine the occupation of individual lattice sites with a fidelity >95%, enabling direct, local measurement of particle correlations in Fermi lattice systems. This ability will be instrumental for creating and investigating low-temperature phases of the Fermi-Hubbard model, including antiferromagnets and d-wave superfluidity.

Study on the clock-transition spectrum of cold 171Yb ytterbium atoms

We present a detailed study of the clock-transition spectrum of cold 171Yb ytterbium atoms in a 1D optical lattice. A typical clock-transition spectrum with a carrier-sideband structure is observed. After minimizing the power broadening effect and compensating the stray magnetic field, the carrier linewidth is narrowed to about 16 Hz for a 60 ms interrogation time. By increasing the interrogation time to 150 ms, the linewidth is further reduced to 6.8 Hz. By applying the bias magnetic field parallel to the clock-laser polarization, a two-peak spectrum corresponding to two π transitions is obtained. Finally, spin polarization of atoms to a single desired Zeeman sublevel of the ground state is also demonstrated. The presented results will be very useful for developing better optical lattice clocks.

Thermalization of strongly interacting bosons after spontaneous emissions in optical lattices

We study the out-of-equilibrium dynamics of bosonic atoms in a 1D optical lattice, after the ground-state is excited by a single spontaneous emission event, i.e. after an absorption and re-emission of a lattice photon. This is an important fundamental source of decoherence for current experiments, and understanding the resulting dynamics and changes in the many-body state is important for controlling heating in quantum simulators. Previously it was found that in the superfluid regime, simple observables relax to values that can be described by a thermal distribution on experimental time-scales, and that this breaks down for strong interactions (in the Mott insulator regime). Here we expand on this result, investigating the relaxation of the momentum distribution as a function of time, and discussing the relationship to eigenstate thermalization. For the strongly interacting limit, we provide an analytical analysis for the behavior of the system, based on an effective low-energy Hamiltonian in which the dynamics can be understood based on correlated doublon-holon pairs.

Experimental research on loading strontium bosons into the optical lattice operating at the “magic” wavelength

The optical lattice clock with neutral atoms occupies an outstanding position in the research field of atomic clocks, demonstrating the great potential of its performance (like the uncertainty and the stability). At present, the optical lattice clock has realized a 10-18 level of its uncertainty. In this paper, we present the realization of loading bosonic atoms 88Sr (strontium, alkaline-earth metals) into a one-dimensional (1D) optical lattice in our laboratory. The optical lattice where the atoms are trapped can make the energy level shift, called Stark shift. But there is the special optical lattice operating at the “magic” wavelength for clock transitions (5s2) 1S0-(5s5p) 3P0, which can make the same Stark light-shift for both of them, indicating a zero light-shift relative to the clock. In our experiment, Sr atoms are cooled in a two-stage cooling and its temperature can be as low as 2 μK. Then these cold atoms are confined in the Lamb-Dicke region by the lattice laser output from an amplified diode laser operating at the “magic” wavelength, 813 nm. Experimentally, it is straightforward to provide 850 mW of lattice power focused to a 38 μm beam radius. After the cold atoms have trapped in the optical lattice, the lifetime of atoms in 1D optical lattice is measured to be 270 ms. The temperature and the number are about 3.5 μK and 1.2×105 respectively. Besides, effects of the power of the lattice laser on both the number and temperature are analyzed. The number changes linearly with the laser power, while there is no obvious influence on the temperature by the power. This original and special approach for atoms trapped in the optical lattice can provide a long interrogation time for probing the clock transition. Furthermore, it may be the foundation for developing our optical lattice clock of strontium atoms.

Adiabatic loading of rotating bosons into 1D optical lattice

In this paper, the entropy-temperat ure curves are investigated for rotating boson gases in a 1D optical lattice with transverse harmonic connement. Regimes at which the atomic sample can be signicantly heated or cooled by adiabatically changing the lattice depth and the rotation rate are demonstrated. The suggested approach, which is the semiclassical approximation, includes the correction due to thenite size effect. The obtained results show that the entropy{temperat ure curves have a monotonically increasing nature for this system, in agreement with the standard thermodynamic arguments. Forxed temperature, entropy always increases with the increasing of the rotation rate or optical potential depth.

Dynamical preparation of laser-excited anisotropic Rydberg crystals in 2D optical lattices

We describe the dynamical preparation of anisotropic crystalline phases obtained by laser-exciting ultracold Alkali atoms to Rydberg p-states where they interact via anisotropic van der Waals interactions. We develop a time-dependent variational mean field ansatz to model large, but finite two-dimensional systems in experimentally accessible parameter regimes, and we present numerical simulations to illustrate the dynamical formation of anisotropic Rydberg crystals.