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arXiv:1708.01250 · Physical Review X

Band and Correlated Insulators of Cold Fermions in a Mesoscopic Lattice

Martin Lebrat, Pjotrs Grišins, Dominik Husmann, Samuel Häusler, Laura Corman, Thierry Giamarchi, Jean-Philippe Brantut, Tilman Esslinger

Published Mar 29, 2018• 81 citations
arXivHTMLPDF

Abstract

Experiments and simulations demonstrate local control over quantum-coherent transport by creating an insulating phase of ultracold atoms in a one-dimensional quantum wire, providing a novel test bed for nonequilibrium many-body physics.
DOI
10.1103/physrevx.8.011053

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Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave \nphysics has been immense. Among the many recent achievements there is \nthe miniaturization of atom traps, demonstration of the superfluid-Mott insulator \nquantum-phase transition in optical lattices and the experimental demonstration of \nthe BEC-BCS crossover in ultra-cold gases. \nMiniaturization of atom traps using micro-structured wires on a chip is one important \nstep towards an on-chip cold-atom device. These so-called \\atom chips" provide \nhigh control and versatility for trapping and guiding the ultra-cold atomic clouds. \nParticularly interesting is the use of these microchips to build mesoscopic devices \nfor cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. \nHowever, these mesoscopic devices require coherent transport of the atom cloud. A \ngeneral method to treat decoherence due to current fluctuations in multi-wire atomchip \ntraps is presented in the rst part of this thesis. The decoherence rate Γ shows a \nstrong dependence on the distance between the wire and the atom cloud, r0, scaling \nas Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a \nstrong dependence of the decoherence rate on the trap geometry is found. \n \nStudying many-body eects in ultra-cold quantum gases is another important \nresearch eld. Experiments using ultra-cold quantum gases in optical lattices have \ndemonstrated the superuid-Mott insulator quantum phase transition and manybody \nentanglement. Optical lattices are based on a periodic modulation of the light \nintensity, generated by retro-reected laser beams. Correlations of the atomic cloud \nbetween dierent lattice sites of the optical lattice play a central role in these manybody \nexperiments. The dierent phases of the superuid-Mott insulator system can \nbe characterized by the dierent behavior of the inter-lattice site correlations. There \nare several numerical methods such as Quantum Monte Carlo (QMC) simulations, \nDensity Matrix Renormalization Group (DMRG) simulations, exact-diagonalization, \nor the Gutzwiller ansatz, to investigate the dynamics of an ultra-cold gas in an optical \nlattice theoretically. The Gutzwiller method, corresponding to the mean-eld solution, \nallows for the treatment of large lattice sizes. Mean-eld approaches have proven \nto be very useful to describe many-body physics. However, diculties arise in the correct \ndescription of the behavior of the decay of inter-lattice site correlations. Based on \nthe Gutzwiller approach, we have developed a method which allows the successive inclusion \nof inter-lattice site correlations. Comparing the results for the particle-number \nuctuations and the correlation function obtained from pure Gutzwiller calculations, \nto calculations which perturbatively include short-range correlations and calculations \n \nusing \\quasi-exact methods", showed a considerable improvement relative to the pure \nGutzwiller results due to the inclusion of short-range correlations. \nMany-body eects do not only arise in periodic potentials, but become increasingly \nimportant at ultra-low temperatures. The formation of Bose-Einstein condensates \nrequires an overlap of the atom wavefunctions and, hence, the formation of \na single condensate wavefunction. Another example of a many-body state is the \nsuperuid-BCS state, commonly used as a description of superconductivity. Here, \nfermions in dierent hyperne states form Cooper pairs. Experiments with ultracold \nquantum gases enable a variation of the interparticle interaction, e.g. , by using \na Feshbach resonance. Using Feshbach resonances to tune the interaction strength \nhas enabled the experimental observation of the crossover from a superuid-BCS \nstate to a Bose-Einstein condensate of molecules. A useful way to characterize the \ndierent states of ultra-cold quantum gases is to investigate the particle-number uctuations. \nIn this thesis we suggest to divide the atomic cloud into bins and consider \nthe atom-number uctuations in these bins. We calculate the full counting statistics \nfor dierent physical systems of ultra-cold gases (e.g. bosonic gases, fermionic gases, \nand spin mixtures). In particular, we consider the BCS-state as a rst trial example \nto show that there is a strong variation in the particle-number statistics at the \ncrossover from a superuid-BCS state to a Bose-Einstein condensate of molecules.

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Chapter 4 extends the previous chapter by scaling up by a factor of ten the number of barriers in the quantum wire, thus forming a one-dimensional lattice site by site.For the first time in a cold-atom experiment, we characterize the appearance of an insulating phase via transport measurements, here visible as a conductance minimum at chemical potentials in the expected band gap of the infinite lattice.This length scaling gives insights on how the transmission of a finite lattice maps to band theory in the thermodynamic limit.We furthermore study the influence of non-uniformity, lattice height and temperature on the apparent transition between conductor and band insulator.-Chapter 5 reproduces the previous measurements on a mesoscopic lattice with stronger attractive interactions spanning the BCS and unitary regimes.Surprisingly, we observe the persistence of an insulating gap in the conductance, although one could expect superfluidity in the wire and the neighboring reservoirs to dominate transport properties.This behavior is attributed to the formation of a Luther-Emery liquid, a strongly correlated phase characteristic of the one-dimensional physics of the channel, for which we provide a detailed introduction.Numerical simulations based on Tomonaga-Luttinger theory support this interpretation.-Chapter 6 finally investigates transport in a short quantum point contact through a spin-dependent obstacle produced by an optical tweezer at frequencies close to the transitions of two different hyperfine states.The micron-wide footprint of the tweezer
Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave \nphysics has been immense. Among the many recent achievements there is \nthe miniaturization of atom traps, demonstration of the superfluid-Mott insulator \nquantum-phase transition in optical lattices and the experimental demonstration of \nthe BEC-BCS crossover in ultra-cold gases. \nMiniaturization of atom traps using micro-structured wires on a chip is one important \nstep towards an on-chip cold-atom device. These so-called \\atom chips" provide \nhigh control and versatility for trapping and guiding the ultra-cold atomic clouds. \nParticularly interesting is the use of these microchips to build mesoscopic devices \nfor cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. \nHowever, these mesoscopic devices require coherent transport of the atom cloud. A \ngeneral method to treat decoherence due to current fluctuations in multi-wire atomchip \ntraps is presented in the rst part of this thesis. The decoherence rate Γ shows a \nstrong dependence on the distance between the wire and the atom cloud, r0, scaling \nas Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a \nstrong dependence of the decoherence rate on the trap geometry is found. \n \nStudying many-body eects in ultra-cold quantum gases is another important \nresearch eld. Experiments using ultra-cold quantum gases in optical lattices have \ndemonstrated the superuid-Mott insulator quantum phase transition and manybody \nentanglement. Optical lattices are based on a periodic modulation of the light \nintensity, generated by retro-reected laser beams. Correlations of the atomic cloud \nbetween dierent lattice sites of the optical lattice play a central role in these manybody \nexperiments. The dierent phases of the superuid-Mott insulator system can \nbe characterized by the dierent behavior of the inter-lattice site correlations. There \nare several numerical methods such as Quantum Monte Carlo (QMC) simulations, \nDensity Matrix Renormalization Group (DMRG) simulations, exact-diagonalization, \nor the Gutzwiller ansatz, to investigate the dynamics of an ultra-cold gas in an optical \nlattice theoretically. The Gutzwiller method, corresponding to the mean-eld solution, \nallows for the treatment of large lattice sizes. Mean-eld approaches have proven \nto be very useful to describe many-body physics. However, diculties arise in the correct \ndescription of the behavior of the decay of inter-lattice site correlations. Based on \nthe Gutzwiller approach, we have developed a method which allows the successive inclusion \nof inter-lattice site correlations. Comparing the results for the particle-number \nuctuations and the correlation function obtained from pure Gutzwiller calculations, \nto calculations which perturbatively include short-range correlations and calculations \n \nusing \\quasi-exact methods", showed a considerable improvement relative to the pure \nGutzwiller results due to the inclusion of short-range correlations. \nMany-body eects do not only arise in periodic potentials, but become increasingly \nimportant at ultra-low temperatures. The formation of Bose-Einstein condensates \nrequires an overlap of the atom wavefunctions and, hence, the formation of \na single condensate wavefunction. Another example of a many-body state is the \nsuperuid-BCS state, commonly used as a description of superconductivity. Here, \nfermions in dierent hyperne states form Cooper pairs. Experiments with ultracold \nquantum gases enable a variation of the interparticle interaction, e.g. , by using \na Feshbach resonance. Using Feshbach resonances to tune the interaction strength \nhas enabled the experimental observation of the crossover from a superuid-BCS \nstate to a Bose-Einstein condensate of molecules. A useful way to characterize the \ndierent states of ultra-cold quantum gases is to investigate the particle-number uctuations. \nIn this thesis we suggest to divide the atomic cloud into bins and consider \nthe atom-number uctuations in these bins. We calculate the full counting statistics \nfor dierent physical systems of ultra-cold gases (e.g. bosonic gases, fermionic gases, \nand spin mixtures). In particular, we consider the BCS-state as a rst trial example \nto show that there is a strong variation in the particle-number statistics at the \ncrossover from a superuid-BCS state to a Bose-Einstein condensate of molecules.
In this thesis, both experimental studies and numerical simulations of ultracold atoms in optical potentials are presented in a collection of nine scientific papers. In particular, noise-induced transport in dissipative optical lattices and superfluid properties of Bose-Einstein condensates have been studied. Noise is usually regarded as a complication to most systems and as something that needs to be minimized. However, in a series of experiments at Umeå University, noise has been shown to play a key role for laser-cooled cesium atoms trapped in dissipative optical lattices. By using a combination of two dissipative optical lattices, where the relative spatial phase between them can be controlled, a so-called Brownian motor can be realized, where energy can be extracted from the inherent noise. In the experiment, this energy is used to control the transport of the laser-cooled atoms in real time and along pre-designed paths. This thesis also presents a way to characterize this system in terms of energy conversion efficiency and coherence of the transport, which may allow for a more straightforward comparison with other systems that rely on noise rectification. In the studies, it is also shown that the noise triggers a downward drift due to gravity, even though the optical potential should support the atoms. Further investigation of this might help to understand the underlying principles of laser cooling, as well as showing that the system might be suitable as a flexible test bed for statistical physics. In close relation to the experimental system, two numerical simulations are also presented, one in which different ways to induce asymmetries between two periodic potentials are investigated, and one in which a proposal for detecting quantum walks is explored. In the second part of the thesis, a work from the Joint Quantum Institute is presented, where a long-lived persistent current in a toroidal Bose-Einstein condensate, held in an all-optical trap, is created. The critical velocity of the superflow is measured in the presence of a tunable barrier. The system can be seen as a first realization of an elementary closed-loop atom circuit. Finally a theoretical study of the crossover between one- and two-dimensional systems is presented, in particular the transition between a two-dimensional superfluid to a one-dimensional Mott insulator is investigated.