We present a theoretical analysis of BeatNote Superlattices (BNSLs), a recently demonstrated technique for generating periodic trapping potentials for ultracold atomic clouds, with arbitrarily large lattice spacings while maintaining interferometric stability. By combining two optical lattices with slightly different wavelengths, a beatnote intensity pattern is formed, generating, for low depths, an effective lattice potential with a periodicity equal to the wavelength associated to the difference between the wave vectors of the two lattices. We study the range of lattice depths and wavelengths under which this approximation is valid and investigate its robustness against perturbations. We present a few examples where the use of BNSLs could offer significant advantages in comparison to well-established techniques for the manipulation of ultracold atomic gases. Our results highlight the potential of BNSLs for quantum simulation, atom interferometry, and other applications in quantum technologies.
We present a theoretical analysis of BeatNote Superlattices (BNSLs), a recently demonstrated technique for generating periodic trapping potentials for ultracold atomic clouds, with arbitrarily large lattice spacings while maintaining interferometric stability. By combining two optical lattices with slightly different wavelengths, a beatnote intensity pattern is formed, generating, for low depths, an effective lattice potential with a periodicity equal to the wavelength associated to the difference between the wave vectors of the two lattices. We study the range of lattice depths and wavelengths under which this approximation is valid and investigate its robustness against perturbations. We present a few examples where the use of BNSLs could offer significant advantages in comparison to well-established techniques for the manipulation of ultracold atomic gases. Our results highlight the potential of BNSLs for quantum simulation, atom interferometry, and other applications in quantum technologies.
We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.
In this thesis I report the realization of a large spacing optical lattice exploiting the beat-note of two retro-reflected laser beams with slightly different wavelengths i.e 1064 nm and 1013 nm. The resulting potential, in addition to a very fast modulation, exhibits a slow periodicity that provides an optical potential for the atoms that behaves like an effective lattice with 10 micrometers of separation between lattice sites. \nI studied theoretically the band structure of the new lattice and I performed numerical simulations in order to obtain predictions of the energy gap as a function of the lattice depth in different configurations. \nRegarding my experimental contribution, I have complitely designed and assembled the setup for the stabilization of the intensity and the frequency of the laser sources. In particular, for the stabilization of the relative frequencies of the two lasers, I develope a technique that allows to lock the two frequencies to the same optical cavity. \nThanks to the high control of the residual forces on the sample and the capability to cancel the interatomic interactions using magnetic Feshbach resonaces, we have managed to observe spatial Bloch oscillations of condensates, measuring the atom number in each well. The observed dynamics exhibits a coherence up to 1 s that correponds to a sensitivity of the order of 5 times10^-5 g with a spatial resolution of ten microns. We characterized experimentally the frequency and the amplitude of the oscillations for different value of the force and the results show a very good agreement with theoretical simulations. \nTo our knowledge the sensitivity acquired in this work is the higher reported in litterature in the measurement of small forces (<< g) using a trapped atom interferometer. The main limitations to the coherence time and the precision of the measurements are related to the limited control we have in the way we tune the external force, i.e, optically. \nThe simplicity of the Bloch oscillation interferometer and the creation of a large spacing periodic potential open interesting perspective in the measurements of small and local forces with trapped condensates and can be useful for the investigation of Casimir-Polder forces or deviations of the \ngravitational law at short distances. \nIn the first half of my PhD I participated to another project: we studied the behaviour of an ultra-cold mixture of two different internal states of potassium. In particular regimes of interaction the cloud tends to collapse but, at high density, many-body effects occur and stabilize the mixture to a fixed volume. In free space it doesn't collapse or expand and it behaves like a liquid droplet. We have characterized the time evolution and the equilibrium properties of the droplets and we have peformed experimental studies on the collisional dynamics between two droplets. Good agreement with theoretical analysis confirm our control on the system and open interesting perspective for the studies of their excitation spectrum and superfluid behaviour.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations between the spin of adjacent atoms are realisable with optical lattices forming arrays of double-well potentials. We study the creation of a lattice containing a spin-encoded Bell-pair in each double-well, and show that resilient, highly-entangled many-body states are realisable using lattice manipulations. We show that the creation of cluster-like states encoded on Bell-pairs can be achieved using these systems, and we provide measurement networks that allow the execution of quantum algorithms while maintaining intact the resilience of the system. Finally, we investigate the possibility to create a diatomic molecular state and simulate Fermi systems via the excitation to Rydberg levels of ground-state atoms trapped in optical lattices. We develop a method based on symbolical manipulations to compute the interaction parameters between highly-excited electrons, and evaluate them for different electronic configurations. We use these parameters to investigate the existence of diatomic molecular states with equilibrium distances comparable to typical lattice spacings. Considering the possibility to excite atoms trapped in an optical lattice to Rydberg levels such that the electronic cloud of neighbouring atoms overlap, we propose a model describing their interactions and compute its parameters. If such systems were realised, they would allow the simulation of Fermi systems at a temperature much below the Fermi temperature, thus enabling the observation of quantum phenomena hitherto inaccessible with current technology.
Optical superlattice has a wide range of applications in the study of ultracold atom physics. Especially, it can be used to trap and manipulate thousands of atom pairs in parallel which constitutes a promising system for quantum simulation and quantum computation. In the present work, we report on a high-power optical superlattice formed by a 532-nm and 1064-nm dual-wavelength interferometer with a short lattice spacing of 630 nm. The short-term fluctuation (in 10 seconds) of the relative phase between the short lattice and the long lattice is measured to be 0.003π, which satisfies the needs for performing two-qubit gates among neighboring lattice sites. We further implement this superlattice in a 87Rb experiment with a quantum gas microscope of single-site resolution, where the high-power 532-nm laser is necessary for pinning atoms in the short lattice during imaging, providing a unique platform for engineering quantum states.
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
This thesis contains theoretical research on ultracold quantum gases in spatially periodic potentials, featuring high-frequency periodic driving, long-range interactions, or both. The largest part features deep potentials where the behaviour of the gas is well-described by quantum lattice models. The periodic driving is then integrated out to obtain effective time-independent descriptions. One project investigates emergent long-range interactions in a stationary, weak, spatially periodic potential, where a lattice theory is not appropriate.In two short introductory chapters, the topics of ultracold atoms, optical lattice potentials, periodic driving, and long-range interactions, are sketched, without attempting to give a complete overview. Some experimentally relevant length and energy scales are given, but the main focus is on deriving and constructing theoretical descriptions of ultracold gases in various spatially and/or temporally periodic potentials.The first project presented, is focused on how the single-particle spectrum of a Bose gas in a non-separable two-dimensional square lattice is affected by high-frequency periodic driving; the most striking conclusion is that under suitable circumstances, it develops two inequivalent minima, leading to finite-momentum Bose-Einstein condensation. Perturbative calculations indicate that local interactions induce spontaneous time-reversal symmetry breaking (TRSB) in such a system.The second project investigates the interplay between kinetic frustration and long-range interactions in fermionic gases. Both a mean-field approximation and exact diagonalisations predict that such a system, studied in the more specific realisation of a weakly interacting dipolar fermionic gas in a 2D triangular lattice, also leads to spontaneous TRSB. Furthermore, a density wave could form at quarter filling, where the Fermi surface is perfectly nested. Perhaps more interesting yet, a spatially inhomogeneous TRSB pattern is predicted, confined to the low-density sublattice that emerges in the density wave.The third project revolves around the question of supersolidity in the presence of a gauge field. Applying the Bogolyubov approximation to a variation of the extended Bose-Hubbard model, indicates that combining an artificial staggered magnetic field in a 2D square lattice with nearest-neighbour density-density interactions, not only leads to a supersolid with staggered vortices, but also induces an inhomogeneous distribution of the associated currents around the elementary plaquette.In the fourth project, a one-dimensional Bose gas with strong local interactions in a weak lattice at incommensurate densities is shown to feature excitations corresponding to excess or deficit particles. The excitations interact repulsively at long distances, in spite of the fact that the underlying atoms themselves do not. As a consequence, the incommensurability of the density with the lattice can drive a transition to a density wave and even a supersolid.The four above-mentioned research projects combine bosonic and fermionic gases, weak and strong interactions, perturbative and mean-field approximations, effective field theories and exact diagonalisations. The main overall conclusion is that long-range interactions and high-frequency periodic driving lead to a very diverse range of fascinating phenomena in ultracold lattice gases.