Shallow Optical Lattice Research Articles

Phases and coherence of strongly interacting finite bosonic systems in shallow optical lattice

We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between short-range contact interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth. For the dipolar interaction, the many-body features become more distinct and true Mott state can appear even in a shallow lattice. Whereas, for incommensurate fraction of particles, incomplete localization happens that exhibits distinct features in the measure of two-body coherence.

Matter-wave gap solitons and vortices of dense Bose–Einstein condensates in Moiré optical lattices

Optical lattices provide a key enabling and controllable platform for exploring new physical phenomena and implications of degenerate quantum gases both in the quantum and nonlinear regimes. Based on the Gross–Pitaevskii/nonlinear Schrödinger equation with competing cubic–quintic nonlinearity, we show, numerically and theoretically, the nonlinear localization of dense Bose–Einstein condensates (BECs) in a novel two-dimensional twisted periodic potential called Moiré optical lattices which, in essence, build a bridge between the perfect optical lattices and aperiodic ones. Our theory reveals that the Moiré optical lattices display a wider second gap and flat-band feature, and support two kinds of localized matter-wave structures like gap solitons and topological states (gap vortices) with vortex charge s=1, all populated inside the finite gaps of the linear Bloch-wave spectrum. We demonstrate, by means of linear-stability analysis and direct perturbed evolutions, that these localized structures have wide stability regions, paving the way for studying flat-band and Moiré physics in shallow optical lattices and for finding robust coherent matter waves therein. The twisted periodic structures can be readily implemented with currently available optical-lattice technique in BECs and nonlinear optics experiments where the results predicted here are observable.

Emergent Mott insulators at noninteger fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground-state properties of an ultracold-atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersed in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system to be in a self-bound superfluid phase, with its particle density distribution manifesting a self-concentrated structure. However, in a relatively deep optical lattice, the attractive interaction can drive the system, leading to the Mott-insulator phase even though the global filling factor is not an integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott insulators, with their effective density manifesting a devil's-staircase structure with respect to the strength of the attractive interaction. A detailed estimation of the relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups.

Subrecoil Clock-Transition Laser Cooling Enabling Shallow Optical Lattice Clocks.

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the μK regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ^{1}S_{0}-^{3}P_{0} clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the 10^{-19} level.

Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice

We study the dynamics of a one-dimensional Bose gas at unit filling in both shallow and deep optical lattices and obtain the dynamic structure factor \bm{S(k,\omega)}𝐒(𝐤,𝛚) by monitoring the linear response to a weak probe pulse. We introduce a new procedure, based on the time-dependent variational Monte Carlo method (tVMC), which allows to evolve the system in real time, using as a variational model a Jastrow-Feenberg wave function that includes pair correlations. Comparison with exact diagonalization results of \bm{S(k,\omega)}𝐒(𝐤,𝛚) obtained on a lattice in the Bose-Hubbard limit shows good agreement of the dispersion relation for sufficiently deep optical lattices, while for shallow lattices we observe the influence of higher Bloch bands. We also investigate non-linear response to strong pulses. From the power spectrum of the density fluctuations we obtain the excitation spectrum, albeit broadened, by higher harmonic generation after a strong pulse with a single low wave number. As a remarkable feature of our simulations we furthermore demonstrate that the full excitation spectrum can be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.

Ultraslow light realization using an interacting Bose\u2013Einstein condensate trapped in a shallow optical lattice

In this article, we propose an experimentally feasible scheme for the ultraslow light realization based on the optomechanically induced transparency (OMIT) phenomenon using a hybrid optomechanical system consisting of a one-dimensional Bose–Einstein condensate trapped in a shallow optical lattice considering the nonlinear effect of atom-atom interaction. It is shown how the system can switch from the normal mode splitting to the OMIT regime by manipulation of the s-wave scattering frequency of atomic collisions when the cavity is pumped at a fixed rate. Then, it is shown that an ultraslow light with a time delay more than 150 ms corresponding to a group velocity about 1 mm/s is achievable by controlling the optical lattice depth as well as the strength of atom-atom interaction and the number of atoms. Importantly, such an ultraslow light is detectable in the output of the cavity since it occurs in the frequency region of coupling-probe detuning where the reflection coefficient of the cavity is maximum.

Floquet Engineering Hz-Level Rabi Spectra in Shallow Optical Lattice Clock.

Quantum metrology with ultrahigh precision usually requires atoms prepared in an ultrastable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultracold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive a shallow ^{87}Sr optical lattice clock. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz linewidth. With careful comparison between the theory and experiment, we demonstrate that the Rabi frequency and the Bloch bands can be tuned, simultaneously and independently. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phases of matter by engineering exotic spin orbit couplings.

Experimental observation of quantum tunneling in shallow optical lattice

For a one-dimensional optical lattice clock built in the horizontal direction, when the stability and uncertainty of the system reach the order of 10<sup>–18</sup> or more, the clock frequency shift caused by the quantum tunneling effect becomes not negligible. In the shallow optical lattice, the quantum tunneling effect will cause the clock transition spectrum to be significantly broadened. So, in this paper the quantum tunneling phenomenon in the shallow optical lattice is studied, laying a foundation for the evaluation of uncertainty of <sup>87</sup>Sr atomic optical lattice clock system. In this experiment, on the platform of one-dimensional <sup>87</sup>Sr atomic optical lattice clock, the narrow-linewidth <sup>1</sup>S<sub>0</sub>(<inline-formula><tex-math id="M4">\begin{document}$ \left|g \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M4.png"/></alternatives></inline-formula>)→<sup>3</sup>P<sub>0</sub>(<inline-formula><tex-math id="M5">\begin{document}$ \left|e \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M5.png"/></alternatives></inline-formula>) transition (that is, the clock transition) is excited by an ultra-stable and ultra-narrow linewidth 698 nm laser, and the distribution of strontium atoms in a specific quantum state is prepared. In the deep optical lattice, after the cold <sup>87</sup>Sr atoms in preparation reach a <inline-formula><tex-math id="M6">\begin{document}$ \left|e,{n}_{z}=1 \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M6.png"/></alternatives></inline-formula> state, the lattice depth of the optical lattice is adiabatically reduced. Then, the carrier-sideband resolved clock transition spectral line is detected in the shallow optical lattice. The obvious splitting of the carrier spectral line is observed from the clock transition spectral line, which indicates that the strontium atom has an obvious quantum tunneling phenomenon between the adjacent lattice sites of the optical lattice. In addition, when the lattice potential lattice depth is reduced, owing to the incommensurability of lattice light wavelength (813 nm) and clock laser wavelength (698 nm), the tunneling of atoms between adjacent lattice points will lead to spin-orbit coupling effect. Owing to the exceptionally long lifetime (120(3) s) of <sup>3</sup>P<sub>0</sub> state, it can not only suppress the decoherence, but also reduce the atomic loss rate caused by spontaneous emission. This has a natural advantage for studying the spin-orbit coupling of fermions. Therefore, the understanding of quantum tunneling mechanism in optical lattice is not only conducive to improving the uncertainty of the <sup>87</sup>Sr atomic optical lattice clock, but also lays the foundation for observing the spin-orbit coupling effect of fermions on this platform.

Engineering Quantum States of Matter for Atomic Clocks in Shallow Optical Lattices.

We investigate the effects of stimulated scattering of optical lattice photons on atomic coherence times in a state-of-the art ^{87}Sr optical lattice clock. Such scattering processes are found to limit the achievable coherence times to less than 12s (corresponding to a quality factor of 1×10^{16}), significantly shorter than the predicted 145(40)s lifetime of ^{87}Sr's excited clock state. We suggest that shallow, state-independent optical lattices with increased lattice constants can give rise to sufficiently small lattice photon scattering and motional dephasing rates as to enable coherence times on the order of the clock transition's natural lifetime. Not only should this scheme be compatible with the relatively high atomic density associated with Fermi-degenerate gases in three-dimensional optical lattices, but we anticipate that certain properties of various quantum states of matter-such as the localization of atoms in a Mott insulator-can be used to suppress dephasing due to tunneling.

Effective spin-spin interactions in bilayers of Rydberg atoms and polar molecules

We show that indirect spin-spin interactions between effective spin-1/2 systems can be realized in two parallel 1D optical lattices loaded with polar molecules and/or Rydberg atoms. The effective spin can be encoded into low-energy rotational states of polar molecules or long-lived states of Rydberg atoms, tightly trapped in a deep optical lattice. The spin-spin interactions can be mediated by Rydberg atoms, placed in a parallel shallow optical lattice, interacting with the effective spins by charge-dipole (for polar molecules) or dipole-dipole (for Rydberg atoms) interaction. Indirect XX, Ising and XXZ interactions with interaction coefficients $J^{\bot}$ and $J^{zz}$ sign varying with interspin distance can be realized, in particular, the $J_{1}-J_{2}$ XXZ model with frustrated ferro-(antiferro-)magnetic nearest (next-nearest) neighbor interactions.

Synthetic gauge fields for lattices with multi-orbital unit cells: routes towards a π-flux dice lattice with flat bands

We propose a general strategy for generating synthetic magnetic fields in complex lattices with non-trivial connectivity based on light–matter coupling in cold atomic gases. Our approach starts from an underlying optical flux lattice in which a synthetic magnetic field is generated by coupling several internal states. Starting from a high-symmetry optical flux lattice, we superpose a scalar potential with a super- or sublattice period in order to eliminate links between the original lattice sites. As an alternative to changing connectivity, the approach can also be used to create or remove lattice sites from the underlying parent lattice. To demonstrate our concept, we consider the dice lattice geometry as an explicit example, and construct a dice lattice with a flux density of half a flux quantum per plaquette, providing a pathway to flat bands with a large band gap. While the intuition for our proposal stems from the analysis of deep optical lattices, we demonstrate that the approach is robust even for shallow optical flux lattices far from the tight-binding limit. We also provide an alternative experimental proposal to realise a synthetic gauge field in a fully frustrated dice lattice based on laser-induced hoppings along individual bonds of the lattice, again involving a superlattice potential. In this approach, atoms with a long-lived excited state are trapped using an ‘anti-magic’ wavelength of light, allowing the desired complex hopping elements to be induced in a specific laser coupling scheme for the dice lattice geometry. We conclude by comparing the complexity of these alternative approaches, and advocate that complex optical flux lattices provide the more elegant and easily generalisable strategy.

One-dimensional repulsive Fermi gas in a tunable periodic potential

By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the Tonks-Girardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.

Thermally activated phase slips of one-dimensional Bose gases in shallow optical lattices

We study the decay of superflow via thermally activated phase slips in one-dimensional Bose gases in a shallow optical lattice. By using the Kramers formula, we numerically calculate the nucleation rate of a thermally activated phase slip for various values of the filling factor and flow velocity in the absence of a harmonic trapping potential. Within the local density approximation, we derive a formula connecting the phase-slip nucleation rate with the damping rate of a dipole oscillation of the Bose gas in the presence of a harmonic trap. We use the derived formula to directly compare our theory with the recent experiment done by the LENS group [L. Tanzi, et al., Sci. Rep. {\bf 6}, 25965 (2016)]. From the comparison, the observed damping of dipole oscillations in a weakly correlated and small velocity regime is attributed dominantly to thermally activated phase slips rather than quantum phase slips.

Quantum phase transition in a shallow one-dimensional optical lattice

In this article the extended Bose-Hubbard model describing ultra-cold atoms confined in a shallow, one-dimensional optical lattice is introduced and studied by the exact diagonalization approach. All parameters of the model are related to the only relevant parameter controlled experimentally -- the depth of the optical potential. Changes in a shape of the insulating lobe in the phase diagram of the system are explored and the value of the critical tunneling for which the system undergoes the phase transition (from the insulating to the superfluid phase) is predicted. It is shown that the value of critical tunneling is substantially affected by the presence of the tunnelings to distant sites of the optical lattice. The results may have some importance in upcoming experiments on quantum quench through phase transition points.

Observation of coherent quench dynamics in a metallic many-body state of fermionic atoms.

Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarized fermions is prepared along with a Bose-Einstein condensate in a shallow three-dimensional optical lattice. After a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons, we observe long-lived coherent oscillations in the fermionic momentum distribution, with a period that is determined solely by the Fermi-Bose interaction energy. Our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalized fermionic quantum states and for quantum metrology.

Infinite density for cold atoms in shallow optical lattices

Infinite densities are non-normalizable quasi-probability distributions that can describe the long-time properties of systems when ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. Their experimental observation has remained elusive so far. We here perform semiclassical Monte Carlo simulations of cold atoms in dissipative optical lattices with realistic parameters. We show that the momentum infinite density, as well as its scale invariance, should be observable in shallow potentials. We further evaluate the momentum autocorrelation function both in the stationary and nonstationary, aging regime.

Dynamics of correlations in shallow optical lattices

We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor ${n}_{0}$, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at $q=0$. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.

Bosonic Hard-Rods in One Dimensional Optical Lattices

Diffusion Monte Carlo simulations on the subject of bosonic hard rods trapped in one dimensional optical lattices are presented. The existence of Mott Insulator phases for integer fillings is deduced from the behavior of the energy per particle as a function of the density. The analysis of the pair distribution functions and structure factors suggest the existence of fluid-like phases for shallow optical lattices that evolve to solid-like arrangements when the confinement is deep enough.

Anomalous Spatial Diffusion and Multifractality in Optical Lattices

The transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We develop a projector operator method able to derive, in this case, a generalized Smoluchowski equation for the position variable. We show that this explicitly non-markovian equation can be written as a systematic expansion involving higher-order derivatives. We use the latter to compute arbitrary moments of the spatial distribution and analyze their multifractal properties.

Wave-function-renormalization effects in resonantly enhanced tunneling

We study the time evolution of ultracold atoms in an accelerated optical lattice. For a Bose-Einstein condensate with a narrow quasimomentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a steplike structure. In this regime we establish a connection between the wave-function-renormalization parameter $Z$ introduced by P. Facchi, H. Nakazato, and S. Pascazio [Phys. Rev. Lett. 86, 2699 (2001)] to characterize nonexponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force.