We report the first in situ observation of density fluctuations on the scale of the thermal de Broglie wavelength in an ultracold gas of bosons. Bunching of $^{87}$Rb atoms in a quasi two-dimensional system is observed by single-atom imaging using a quantum gas microscope. Compared to a classical ensemble, we observe a 30 percent enhancement of the second-order correlation function. We show the spatial and thermal dependence of these correlations. The reported method of detecting in situ correlations can be applied to interacting many-body systems and to the study of critical phenomena near phase transitions.
We propose an experimental setup to efficiently measure the dynamic structure factor of ultracold quantum gases. Our method uses the interaction of the trapped atomic system with two different cavity modes, which are driven by external laser fields. By measuring the output fields of the cavity the dynamic structure factor of the atomic system can be determined. Contrary to previous approaches the atomic system is not destroyed during the measurement process.
Electron lattice potentials for ultracold atoms using circular Rydberg orbitals
Max-Planck Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Joint Quantum Centre (JQC) Durham-Newcastle, Department of Chemistry, Durham University（杜伦大学化学系）；Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart（斯图加特大学第五物理研究所及综合量子科学技术中心）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）
We present a general model allowing "quantum simulation" of one-dimensional Dirac models with 2- and 4-component spinors using ultracold atoms in driven 1D tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, Zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.
We theoretically study the low-energy scattering of ultracold atoms by a dielectric nanosphere of silica glass levitated in a vacuum. The atom and dielectric surface interact via dispersion force of which strength sensitively depends on the polarizability, dielectric function, and geometry. For cesium and rubidium atoms, respectively, we compute the atom-surface interaction strength, and characterize the stationary scattering states by taking adsorption of the atoms onto the surface into account. As the energy of the incoming atoms is lowered, we find that differences between quantum and class…
We demonstrate novel implementations of high-precision optical magnetometers which allow for spatially-selective and spatially-resolved in situ measurements using cold atomic clouds. These are realised by using shaped dispersive probe beams combined with spatially-resolved balanced homodyne detection. Two magnetometer sequences are discussed: a vectorial magnetometer, which yields sensitivities two orders of magnitude better compared to a previous realisation and a Larmor magnetometer capable of measuring absolute magnetic fields. We characterise the dependence of single-shot precision on the …
Atomic quantum gases in optical lattices serve as a versatile testbed for important concepts of modern condensed-matter physics. The availability of methods to characterize strongly correlated phases is crucial for the study of these systems. Diffraction techniques to reveal long-range spatial structure, which may complement \emph{in situ} detection methods, have been largely unexplored. Here we experimentally demonstrate that Bragg diffraction of neutral atoms can be used for this purpose. Using a one-dimensional Bose gas as a source of matter waves, we are able to infer the spatial ordering …
We present a direct measurement of the density profile of a two-dimensional Mott Insulator formed by ultracold atoms in an optical lattice. High resolution absorption imaging is used to probe the "wedding-cake" structure of a trapped gas as it crosses the boundary from a unit-filled Mott insulating phase to the superfluid phase at finite temperature. Detailed analysis of images yields measurements of temperature and local compressibility; for the latter we observe a strong suppression deep in the Mott-insulating phase, which is recovered for the superfluid and normal phases. Furthermore, we me…
We use single or few Cs atoms as thermometer for an ultracold, thermal Rb cloud. Observing the thermometer atoms' thermalization with the cold gas using spatially resolved fluorescence detection, we find an interesting situation, where a fraction of thermometer atoms thermalizes with the cloud while the other fraction remains unaffected. We compare release-recapture measurements of the thermometer atoms to Monte-Carlo simulations while correcting for the non-thermalized fraction, and recover the cold cloud's temperature. The temperatures obtained are verified by independent time-of-flight meas…
We demonstrate that a dispersive imaging technique based on the Faraday effect can measure the atom number in a large, ultracold atom cloud with a precision below the atom shot noise level. The minimally destructive character of the technique allows us to take multiple images of the same cloud, which enables sub-atom shot noise measurement precision of the atom number and allows for an in situ determination of the measurement precision. We have developed a noise model that quantitatively describes the noise contributions due to photon shot noise in the detected light and the noise associated w…
We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-light images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local density approximation rema…
We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists of superimposing two laser light fields with the same wavelength, but with opposite circular polarizations, where the phase and the amplitude of each light field are individually controlled. We find that the polarization-synthesized beam reaches a degree of polarization of 99.99%, which is mainly limited by static spatial variations of the polarization state over the beam profile. We also find that the depolarization caused by temporal fluctuations …
We demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by an imaging process. A {\em in situ} imaging technique is used to acquire repeated images of an ultracold gas confined in a shallow optical lattice. The backaction induced by these position measurements modifies the coherent quantum tunneling of atoms within the lattice. By smoothly varying the rate at which spatial information is extracted from the atomic ensemble, we observe the continuous crossover from the 'weak measurement regime' where position measurements have little infl…
In this letter, we propose how to measure the quantized nonlinear transport using two-dimensional ultracold atomic Fermi gases in a harmonic trap. This scheme requires successively applying two optical pulses in the left and lower half-planes and then measuring the number of extra atoms in the first quadrant. In ideal situations, this nonlinear density response to two successive pulses is quantized, and the quantization value probes the Euler characteristic of the local Fermi sea at the trap center. We investigate the practical effects in experiments, including finite pulse duration, finite ed…
Single-shot images are the standard readout of experiments with ultracold atoms -- the tarnished looking glass into their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here, we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in …
We propose a novel scheme for confining atoms to optical lattices by engineering a spatially-inhomogeneous hopping matrix element in the Hubbard-model (HM) description, a situation we term off-diagonal confinement (ODC). We show, via an exact numerical solution of the boson HM with ODC, that this scheme possesses distinct advantages over the conventional method of confining atoms using an additional trapping potential, including the presence of incompressible Mott phases at commensurate filling and a phase diagram that is similar to the uniform HM. The experimental implementation of ODC will t…
The ultracold molecular conversion rate occurring in an adiabatic ramp through a Fano-Feshbach resonance is studied and compared in two statistical models. One model, the so-called stochastic phase space sampling (SPSS)[E.Hodby et al., PRL.94 120402(2005)] evaluates the overlap of two atomic distributions in phase space by sampling atomic pairs according to a phase-space criterion. The other model, the chemical equilibrium theory(ChET)[S.Watabe and T.Nikuni, PRA.77 013616(2008)] considers atomic and molecular distributions in the limit of the chemical and thermal equilibrium. The present study…
We study collisions in an optically trapped, pure sample of ultracold Cs$_2$ molecules in various internal states. The molecular gas is created by Feshbach association from a near-degenerate atomic gas, with adjustable temperatures in the nanokelvin range. We identify several narrow loss resonances, which point to the coupling to more complex molecular states and may be interpreted as Feshbach resonances in dimer-dimer interactions. Moreover, in some molecular states we observe a surprising temperature dependence in collisional loss. This shows that the situation cannot be understood in terms …
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interacti…
More than 30 years ago, Thouless introduced the concept of a topological charge pump that would enable the robust transport of charge through an adiabatic cyclic evolution of the underlying Hamiltonian. In contrast to classical transport, the transported charge was shown to be quantized and purely determined by the topology of the pump cycle, making it robust to perturbations. On a fundamental level, the quantized charge transport can be connected to a topological invariant, the Chern number, first introduced in the context of the integer quantum Hall effect. A Thouless quantum pump may theref…
We propose a novel realization of Kondo physics with ultracold atomic gases. It is based on a Fermi sea of two different hyperfine states of one atom species forming bound states with a different species, which is spatially confined in a trapping potential. We show that different situations displaying Kondo physics can be realized when Feshbach resonances between the species are tuned by a magnetic field and the trapping frequency is varied. We illustrate that a mixture of ${}^{40}$K and ${}^{23}$Na atoms can be used to generate a Kondo correlated state and that momentum resolved radio frequen…
We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the …
{The Continuous Spontaneous Localization (CSL) theory alters the Schrödinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $λ$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predic…
The experimental realisation of large scale many-body systems has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. In order to work with these emerging physical platforms, new technologies for state identification are required. In this work, we present first steps towards efficient experimental quantum field tomography. We employ our procedure to capture ultracold atomic systems using atom chips, a setup that allows for the quantum simulation of static and dynamical properties of interacting quantum …
We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature. We compare our equation of state with an equation of state measured by the Tokyo group, that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well describe…
Ultracold polar molecules are an ideal platform for studying many-body physics with long-range dipolar interactions. Experiments in this field have progressed enormously, and several groups are pursuing advanced apparatus for manipulation of molecules with electric fields as well as single-atom-resolved in situ detection. Such detection has become ubiquitous for atoms in optical lattices and tweezer arrays, but has yet to be demonstrated for ultracold polar molecules. Here we present a proposal for the implementation of quantum gas microscopy for polar molecules, and specifically discuss a tec…
Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of strongly-correlated systems near the ground state. Cold atoms in optical lattices, in particular, represent a paradigmatic system, for which the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. In this paper, we describe our approach to study quantum criticality of cesium atoms in a two-dimensional lattice based on in situ density measurements. Our research…
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in-situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analogue of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lo…
An experimental group at Beijing[Yueyang Zhai, ${\it et. al.}$, Phys. Rev. A ${\bf 87}$, 063638 (2013)] introduced the method of standing-wave pulse sequence for efficiently preparing ultracold bosonic atoms into a specific excited band in a 1-dimensional optical lattice. Here, we report a theoretical extension of their work to the problem of 1-dimensional bichromatic superlattice. We find that varying the lattice parameters leads to the so-called Dirac point where a pair of excited bands crosses. This paper thus discusses ${\it simultaneously}$ the efficient excitation of the wave packet to t…
Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate (BEC), offers various aspects of advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, …
As the temperature of a many-body system approaches absolute zero, thermal fluctuations of observables cease and quantum fluctuations dominate. Competition between different energies, such as kinetic energy, interactions or thermodynamic potentials, can induce a quantum phase transition between distinct ground states. Near a continuous quantum phase transition, the many-body system is quantum critical, exhibiting scale invariant and universal collective behavior \cite{Coleman05Nat, Sachdev99QPT}. Quantum criticality has been actively pursued in the study of a broad range of novel materials \ci…
We present a numerical study of the dynamic response of a confined superfluid Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the full Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigar-shaped $^6$Li gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potentia…
We measure the temporal pair correlation function $g^{(2)}(τ)$ of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed {\it in situ} using a local, time-resolved single-atom sensitive probing technique. Third and fourth order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement and highlighting the role of interactions. Our results promote temporal correlations as new observables to study the dynamics of ultracold quantum ga…
Ultracold atoms in optical lattices offer a great promise to generate entangled states for scalable quantum information processing owing to the inherited long coherence time and controllability over a large number of particles. We report on the generation, manipulation and detection of atomic spin entanglement in an optical superlattice. Employing a spin-dependent superlattice, atomic spins in the left or right sites can be individually addressed and coherently manipulated by microwave pulses with near unitary fidelities. Spin entanglement of the two atoms in the double wells of the superlatti…
We report the anomalous Dyakonov-Perel' spin relaxation in ultracold spin-orbit coupled $^{40}$K gas when the coupling between $|9/2,9/2\ >$ and $|9/2,7/2\ >$ states (atcing as the effective Zeeman magnetic field) is much stronger than the spin-orbit coupled field. Both the transverse and longitudinal spin relaxations are investigated with small and large spin polarizations. It is found that with small spin polarization, the transverse (longitudinal) spin relaxation is divided into four (two) regimes: the normal weak scattering regime, the anomalous Dyakonov-Perel'-like regime, the anomalous E…
We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the $s$-wave scattering length. The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms. This observation, together with a finite-temperature analysis and the known first resonance, allows the most accurate demonstration to date of the discrete scaling behavior at the heart of Efimov physics. For the system of three identical boson…
Spectral moment sum rules are presented for the inhomogeneous many-body problem described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous many-body problem like strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering like a charge density wave or a spin density wave. We also show …
Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose--Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall become…
Solid state systems derive their richness from the interplay between interparticle interactions and novel band structures that deviate from those of free particles. Strongly interacting systems, where both of these phenomena are of equal importance, exhibit a variety of theoretically interesting and practically useful phases. Systems of ultracold atoms are rapidly emerging as precise and controllable simulators, and it is precisely in this strongly interacting regime where simulation is the most useful. Here we demonstrate how to hybridize Bloch bands in optical lattices to introduce long-rang…
We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a new class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically and semiclassically in both situations and show that the quantum correlations are maintained in the separated p…
We study a novel millimetre-scale magnetic trap for ultracold atoms, in which the current carrying conductors can be situated outside the vacuum region, a few mm away from the atoms. This design generates a magnetic field gradient in excess of \SI{1000}{G/cm} at a distance of \SI{2}{mm} from the conductors. We perform electromagnetic and thermo-mechanical characterisation using Finite Element Methods (FEM). The predicted behaviour has been verified by electrical and thermal measurements on a prototype, but has not been implemented on an apparatus with cold atoms. Operating this trap at the hig…
The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realization of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the mere laser excitation of ultracold gases ca…
We experimentally investigate the dynamics of spin solitary waves (magnetic solitons) in a harmonically trapped, binary superfluid mixture. We measure the in-situ density of each pseudospin component and their relative local phase via an interferometric technique we developed, and as such, fully characterise the magnetic solitons while they undergo oscillatory motion in the trap. Magnetic solitons exhibit non-dispersive, dissipationless long-time dynamics. By imprinting multiple magnetic solitons in our ultracold gas sample, we engineer binary collisions between solitons of either same or oppo…
We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small sub-volumes of a weakly interacting ultracold atomic 1D cloud are studied using \textit{in situ} absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the \textit{quantum quasicondensate} regime, the ratio of chemical potential to thermal energy is $μ/ k_B T\simeq4$, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a non-local analysis at varia…
Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments whereas in cold-gases systems, time-of-flight and in-situ absorption imaging are the standard observation techniques. However, none of these methods allow the in-situ detection of spatially resolved correlation functions at the single-particle level. Here we give a more detailed account of recent advances in the detection of correlation functions using in-situ fluorescence imaging of ultracold…
By a novel reciprocal space analysis of the measurement, we report a calibrated in situ observation of the bunching effect in a 3D ultracold gas. The calibrated measurement with no free parameters confirms the role of the exchange symmetry and the Hanbury Brown-Twiss effect in the bunching. Also, the enhanced fluctuations of the bunching effect give a quantitative measure of the increased isothermal compressibility. We use 2D images to probe the 3D gas, using the same principle by which computerized tomography reconstructs a 3D image of a body. The powerful reciprocal space technique presented…
