In this thesis I report a microscope system for fluorescence imaging of ultra-cold ytterbium atoms trapped in a two-dimensional optical lattice with single-site resolution.Having a rich variety of isotopes, ytterbium atoms trapped in two-dimensional optical lattices are a promising tool to study many-body quantum phenomena resulting from strongly interacting systems.In particular, quantum simulators using fermionic atoms are useful for studying the Fermi-Hubbard model, which is expected to be the key to elucidate the mechanism of high temperature superconductors.In order to observe atoms trapped in an optical lattice, a large number of photons is required to obtain a well resolved image.In contrast with to the conventional method of lasercooling the atoms while observing their fluorescence, in this experiment a deep potential was created using a combination of a shallow ground-state and a deep excited-state potentials, which confines the heated atoms during the imaging process.The resulting quantum gas microscope was able to resolve individual lattice sites in an optical lattice with a 544 nm spacing.And I'm not happy with all the analyses that go with just the classical theory, because nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.
In this thesis I report a microscope system for fluorescence imaging of ultra-cold ytterbium atoms trapped in a two-dimensional optical lattice with single-site resolution.Having a rich variety of isotopes, ytterbium atoms trapped in two-dimensional optical lattices are a promising tool to study many-body quantum phenomena resulting from strongly interacting systems.In particular, quantum simulators using fermionic atoms are useful for studying the Fermi-Hubbard model, which is expected to be the key to elucidate the mechanism of high temperature superconductors.In order to observe atoms trapped in an optical lattice, a large number of photons is required to obtain a well resolved image.In contrast with to the conventional method of lasercooling the atoms while observing their fluorescence, in this experiment a deep potential was created using a combination of a shallow ground-state and a deep excited-state potentials, which confines the heated atoms during the imaging process.The resulting quantum gas microscope was able to resolve individual lattice sites in an optical lattice with a 544 nm spacing.And I'm not happy with all the analyses that go with just the classical theory, because nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.
We report a high-resolution microscope system for imaging ultracold ytterbium atoms trapped in a two-dimensional optical lattice. By using the ultraviolet strong transition combined with a solid immersion lens and high-resolution optics, our system resolved individual sites in an optical lattice with a 544-nm spacing. Without any cooling mechanism during the imaging process, the deep potential required to contain the atoms was realized using a combination of a shallow ground-state and a deep excited-state potentials. The lifetime and limitations of this setup were studied in detail.
We demonstrate site-resolved imaging of individual bosonic atoms in a Hubbard-regime two-dimensional optical lattice with a short lattice constant of 266 nm. To suppress the heating by probe light with the 1 S 0 – 1 P 1 transition of the wavelength λ = 399 nm for high-resolution imaging and preserve atoms at the same lattice sites during the fluorescence imaging, we simultaneously cool atoms by additionally applying narrow-line optical molasses with the 1 S 0 – 3 P 1 transition of the wavelength λ = 556 nm. We achieve a low temperature of , corresponding to a mean oscillation quantum number along the horizontal axes of 0.22(4) during the imaging process. We detect, on average, 200 fluorescence photons from a single atom within a 400 ms exposure time, and estimate a detection fidelity of 87(2)%. The realization of a quantum gas microscope with enough fidelity for Yb atoms in a Hubbard-regime optical lattice opens up the possibilities for studying various kinds of quantum many-body systems such as Bose and Fermi gases, and their mixtures, and also long-range-interacting systems such as Rydberg states.
We demonstrate site-resolved imaging of individual bosonic 174Yb atoms in aHubbard-regime twodimensional optical lattice with a short lattice constant of 266 nm. To suppress the heating by probe light with the 1S0- 1P1 transition of the wavelength λ = 399 nmfor high-resolution imaging and preserve atoms at the same lattice sites during the fluorescence imaging, we simultaneously cool atoms by additionally applying narrow-line optical molasses with the 1S0 3P1 transition of the wavelength λ = 556 nm.We achieve a lowtemperature of T = 7.4(13) μK, corresponding to amean oscillationquantum number along the horizontal axes of 0.22(4) during the imaging process.Wedetect, on average, 200 fluorescence photons from a single atom within a 400 ms exposure time, and estimate a detection fidelity of 87(2)%. The realization of a quantum gas microscope with enough fidelity for Yb atoms in a Hubbard-regime optical lattice opens up the possibilities for studying various kinds of quantum many-body systems such as Bose and Fermi gases, and their mixtures, and also long-rangeinteracting systems such as Rydberg states.
This thesis describes the methods used to achieve single-atom and single-site resolved fluorescence imaging of a quantum gas of fermionic atoms held in an optical lattice. This kind of quantum gas microscopy has been previously applied to bosonic atoms in two experiments, and has allowed for extensive studies of many-body quantum systems. Here we detail methods to extend the techniques of quantum gas microscopy to fermionic species of atoms, opening the door to quantum simulation of electronic models of condensed matter physics. We prepare quantum degenerate gases of fermionic 40K through sympathetic cooling with a gas of \Rb. The gas prepared is trapped less than 1 mm away from a thin vacuum window, an experimental geometry which permits interrogation with a large Numerical Aperture microscope objective. The cloud is loaded into a 527 nm-period cubic optical lattice, ideal for quantum simulation of many-body models of fermionic particles such as the Hubbard model. The optical lattice is designed to allow for potential depths up to V/kB = 250 microKelvin, sufficient to strongly confine 40K atoms into individual lattice sites. EIT cooling --- a technique previously demonstrated in ion-trapping experiments --- is used to cool the fermionic atoms deeply towards the ground motional state of the lattice wells. We collect the photons scattered during continuous application of EIT cooling, while atoms are kept pinned in the lattice for many seconds. We strongly suppress all other sources of light with the use of a modulated cooling scheme and a spinning chopper wheel. Collecting the scattered light produced during 2 s of EIT cooling allows us to resolve single atoms in a fluorescence image. We demonstrate that the high resolution of our imaging apparatus also permits atom positions to be precisely identified on the length scale of the optical lattice. Thus we demonstrate the realisation of a quantum gas microscope for fermionic atoms, allowing for precise investigation of the ground states and dynamics of correlated quantum states of fermionic particles.
続紙 １ ) 京都大学 博 士(理 学) 氏名 柴田 康介 論文題目 High-sensitivity in situ imaging of atoms in an optical lattice with narrow optical transitions (狭線幅光学遷移を用いた光格子中の原子の高感度その場イメージング) (論文内容の要旨)Development of laser cooling techniques in recent decades has enabled us to study neutral atoms in a quite controlled way.Cold neutral atoms have been used as a platform to study intriguing quantum many-body phenomena such as Bose-Einstein condensation and Bardeen-Cooper-Schriefer-Bose-Einstein condensation crossover.The excellent controllability of a cold atom system allows us precise measurements with unprecedented accuracy, which provides wide applications, such as an atomic clock.Another important application of cold atoms is quantum information processing.Internal degrees of freedom of a trapped cold atom can be regarded as a well-defined quantum bit (qubit) and quantum gate operations are realized by moderate internal or external interaction.In such cold atom research, a probing method plays an important role.In fact, one of the advantages of cold atom research is the ability to "see" atoms directly by taking images of the atoms via resonant or near-resonant light to the atoms.Among various developments in probing techniques, high-sensitivity detection is of particular importance, especially in the study of a simple system of a few atoms.While high-sensitivity detection and imaging were demonstrated with alkaline metals, there has been increasing interest on a different kind of atomic species.One attractive atomic species is ytterbium.Ytterbium is an alkaline-earth-like-metal atom and has several unique features, such as the rich variety of isotopes of two fermions and five bosons, and the existence of long-lived metastable electronic states.These features offer various possibilities in quantum many-body physics research and are also advantageous to quantum information processing as well as precision measurement.Therefore, a high-sensitivity imaging of ytterbium atoms will bring about a significant development in cold atom research.Under these backgrounds, this thesis reports on the successful demonstration of highsensitivity in situ imaging of ytterbium atoms in a two-dimensional optical lattice.The applicant demonstrated fluorescence imaging of ytterbium atoms in an optical lattice using optical molasses with a narrow optical transition of the wavelength 556 nm ("green molasses"), providing the Doppler cooling limit temperature low enough compared to the typical optical lattice depths.The applicant successfully observed a spatial modulation of fluorescence intensity with a period of approximately 6 μm as a result of the interference between the lattice period of 266 nm and the period of the standing-wave optical molasses of 278 nm.This pattern indicates that the temperature was sufficiently lower than the lattice potential so that the atoms emitted fluorescent photons around the bottom of the lattice sites
Imagine a new generation of computers that dramatically surpasses the most powerful supercomputers, being able to tackle the most challenging of computational problems. These problems arise, for example, in quantum physics where the computational power required to model a many-particle system increases exponentially with the number of its constituents, and as a consequence the calculations become prohibitively time-consuming. Nobel laureate Richard Feynman proposed this new type of computer in the early 1980s: ‘Let the computer itself be built of quantum mechanical elements which obey quantum mechanical laws.’ Such a quantum simulator would allow researchers to tackle challenging problems in condensed-matter physics. In particular many-body fermionic quantum systems are very difficult to compute due to the antisymmetric nature of the wave function, and the resulting sign problem for quantum Monte Carlo methods. This is why a quantum simulator will be an excellent test bed to investigate phenomena and properties of strongly correlated fermionic quantum systems. A powerful experimental platform to realize a quantum simulator is laser-cooled atoms [1] held in an artificial crystal of light, generated by superimposing laser beams. The atoms are kept in this optical lattice similar to marbles in the hollows of an egg carton, and they can mimic the behaviour of electrons in a real crystal. These systems interface atomic physics with condensed matter physics in a new way, as the tools of atomic physics allow for exquisite control of many experimental parameters, which are often inaccessible in solid state experiments. In-situ imaging techniques [2] using ‘quantum-gas microscopes’ constitute a new approach to the study of many-body quantum systems in an optical lattice with unprecedented resolution at the single-particle and single-site level [3,4]. This new method is complementary to earlier optical lattice experiments measuring distributions in momentum space after a time-of-flight expansion. A quantum-gas microscope uses an optical imaging system (Fig. 1a) for collecting the fluorescence light of ultracold atoms in an optical lattice with high spatial resolution comparable to the lattice spacing of ≈ 500 nm. (a) Atoms in optical lattice atoms are imaged with a high-resolution microscope objective [4]. (b) Single-site addressing is achieved by focussing a laser beam through the microscope onto selected atoms, bringing them into resonance with microwave radiation which produces spin flips [12]. (c) and (d) Single-atom-resolved fluorescence images of bosonic Mottinsulators [4,9]. (e) Deterministically prepared atom distribution using single-site addressing [12]. (f) Direct observation of single-atom quantum walks [15]. Fluorescence imaging of atoms in a quantum-gas microscope has made it possible to directly observe bosonic Mott insulators with single-atom resolution [4–6], giving access to in-situ measurements of temperature and entropy distributions. Subsequently, ground-breaking experiments in many-body quantum dynamics have been performed, such as the first direct observation of correlation spreading after quenches of the system to lower lattice depths [7]. Other experiments include the quantum simulation of an antiferromagnetic spin-1/2 chain [8], the realization of algorithmic cooling [9], the direct measurement of correlations across the superfluid-to-Mott-insulator transition [10], or the observation of the ‘Higgs’ amplitude mode [11]. The high-resolution imaging system is also capable of optically addressing individual atoms with sub-diffraction-limited resolution. For this purpose, a laser beam is focussed though the microscope objective onto selected lattice sites, bringing the atoms into resonance with microwave radiation which produces spin flips [12,13]. The preparation of arbitrary atom distributions in the lattice not only opens perspectives for neutral-atom quantum information processing, but also allows the deterministic creation of specific out-of-equilibrium situations, and their ensuing system dynamics can be studied with single-atom resolution. Examples include the creation of spin impurities and the study of their dynamics in a many-body system [14], the observation of quantum walks [15] and magnon-bound states [16], and the measurement of entanglement entropy [17]. The technique used for single-site-resolved detection of individual atoms in the optical lattice is fluorescence imaging. It requires laser cooling of the atoms to sub-Doppler temperatures while detecting the fluorescence photons emitted during this process. A challenge is to achieve a low particle loss rate and to prevent the atoms from hopping between lattice sites. In the case of the first quantum-gas microscopes, this has been implemented with bosonic rubidium-87 atoms, and also recently for ytterbium-174. However, it has proven more challenging for fermionic alkaline species such as potassium-40 and lithium-6, as their low mass and small excited state hyperfine splitting-prevented standard sub-Doppler cooling from working. As a result, it took several years to extend the quantum-gas microscope technique to fermionic species, and in 2015 several groups have demonstrated single-atom-resolved imaging of fermions [18]. In these setups, the direct observation of band insulators [19], fermionic Mott insulators [20,21] and even antiferromagnetic correlations [22] has been reported most recently. These developments provide fascinating opportunities to study many-body fermionic quantum systems with single-particle access. The fermionic nature of the electron is vital to understanding a range of phenomena within solid-state physics, such as electron pairing in superconductivity, and quantum magnetism. In this context, the quantum simulator will allow, e.g. for direct measurement of ordered quantum phases and out-of-equilibrium dynamics, with access to quantities such as spin--spin correlation functions and the growth of many-body entanglement. The high-resolution imaging systems could also be used to project tailored time-varying light fields onto the atoms, allowing the removal of high-entropy regions by locally modifying the confining potential to attain very low-entropy states. Attaining these low-entropy many-particle states is one of the key challenges in our field. In summary, quantum-gas microscopes offer unprecedented access to many-body quantum systems, and they will allow us to gain an even deeper insight into the intriguing world of quantum physics that governs the properties of strongly correlated materials. Using a well-controlled quantum system to simulate other quantum systems could help resolve some of the most challenging problems scientists face in condensed matter physics and materials science, but it will also provide new insights in quantum chemistry, high-energy physics and biology. SK acknowledges funding from the EU (ERC FERMILATT, SIQS, QuProCs) and SUPA.