Two-dimensional Quantum Gas Research Articles

An efficient method to generate near-ideal hollow beams of different shapes for box potential of quantum gases.

Ultracold quantum gases are usually prepared in conservative traps for quantum simulation experiments. The atomic density inhomogeneity, together with the consequent position-dependent energy and time scales of cold atoms in traditional harmonic traps, makes it difficult to manipulate and detect the sample at a higher level. These problems are partially solved by optical box traps made of blue-detuned hollow beams. However, generating a high-quality hollow beam with high light efficiency for the box trap is challenging. Here, we present a scheme that combines the fixed optics, including axicons and prisms, to pre-shape a Gaussian beam into a hollow beam with a digital micromirror device (DMD) to improve the quality of the hollow beam further, providing a nearly ideal optical potential of various shapes for preparing highly homogeneous cold atoms. The highest power-law exponent of potential walls can reach a value over 100, and the light efficiency from a Gaussian to a hollow beam is also improved compared to direct optical shaping by a mask or a DMD. Combined with a one-dimensional optical lattice, a nearly ideal two-dimensional uniform quantum gas with different geometrical boundaries can be prepared for exploring quantum many-body physics to an unprecedented level.

Expansion of a quantum gas in a shell trap

We report the observation of the controlled expansion of a two-dimensional (2D) quantum gas confined onto a curved shell-shaped surface. We start from the ellipsoidal geometry of a dressed quadrupole trap and introduce a novel gravity compensation mechanism enabling to explore the full ellipsoid. The zero-point energy of the transverse confinement manifests itself by the spontaneous emergence of an annular shape in the atomic distribution. The experimental results are compared with the solution of the three-dimensional Gross–Pitaevskii equation and with a 2D semi-analytical model. This work evidences how a hidden dimension can affect dramatically the embedded low-dimensional system by inducing a change of topology.

Effect of Two-Step Formosolv Fractionation on the Structural Properties and Antioxidant Activity of Lignin.

The formosolv fractionation process has been demonstrated to be an effective approach toward lignin recovery as an antioxidant from lignocellulosic biomass. In this study, four lignin fractions, FL-88%, FSL-70%, FIL-70% and FL-EtAc, were isolated from Phragmites australis biomass through two-step formosolv fractionation (88% formic acid delignification followed by 70% aqueous formic acid fractionation). To better understand the structural properties of the lignin obtained from this fractionation process, four isolated lignins were successfully characterized by gel permeation chromatography (GPC), Fourier transform infrared (FT-IR), two-dimensional heteronuclear single quantum coherence nuclear magnetic resonance (2D-HSQC NMR) spectroscopy, thermogravimetric analysis (TGA) and gas chromatograph-mass spectroscopy (GC/MS). It was found that lignin depolymerization via β-O-4 cleavage occurred via a formylation, elimination and hydrolysis mechanism, accompanied by a competitive condensation reaction. Noteworthily, two-step formosolv fractionation can produce specific lignin fractions with different ABTS and DPPH radical scavenging activities. The FL-EtAc fraction with low molecular weight (Mw = 2748 Da) and good homogeneity (PDI = 1.5) showed excellent antioxidant activity, compared with the other three isolated lignin fractions, even equal to that of commercial antioxidant BHT at the same concentration of 2.0 mg·mL−1. These findings are of great help for specific lignin from biomass as a natural antioxidant in the future.

Compressibility and the equation of state of an optical quantum gas in a box.

The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment was carried out in a nanostructured dye-filled optical microcavity. We observed signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.

Universal relations for dipolar quantum gases

We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential. We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function. These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement. For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction. We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.

Generating two-dimensional quantum gases with high stability**Project supported by the National Key R&D Program of China (Grant No. 2016YFA0301603), the National Natural Science Foundation of China (Grant No. 11874341), Anhui Initiative in Quantum Information Technologies, and Chinese Academy of Sciences.

Quantum gas microscopy has enabled the study on intriguing properties of ultracold atoms in optical lattices. It provides the cutting-edge technology for manipulating quantum many-body systems. In such experiments, atoms have to be prepared into a two-dimensional (2D) system for being resolved by microscopes with limited depth of focus. Here we report an experiment on slicing a single layer of the atoms trapped in a few layers of pancake-shaped optical traps to create a 2D system. This technique is implemented with a microwave “knife”, i.e., a microwave field with a frequency defined by the resonant condition with the Zeeman-shifted atomic levels related to a gradient magnetic field. It is crucial to keep a stable preparation of the desired layer to create the 2D quantum gas for future experimental applications. To achieve this, the most important point is to provide a gradient magnetic field with low noises and slow drift in combination with a properly optimized microwave pulse. Monitoring the electric current source and the environmental magnetic field, we applied an actively stabilizing circuit and realized a field drift of 0.042(3) mG/hour. This guarantees creating the single layer of atoms with an efficiency of 99.92(3)% while atoms are hardly seen in other layers within 48 hours, satisfying future experimental demands on studying quantum many-body physics.

Coulomb drag of excitons in Bose-Fermi systems

We develop a microscopic theory of the Coulomb drag effect in a hybrid system consisting of spatially separated two-dimensional quantum gases of degenerate electrons and dipolar excitons. We consider both the normal-phase and condensate regimes of the exciton subsystem and investigate the cross-mobility of the system being the kinetic coefficient, which couples the static electric field applied to the electron layer with the particle density current (flux) in the exciton subsystem. We study the temperature dependence of the cross-mobility and its dependence on the interlayer separation. We show that exciton-exciton interaction plays a dramatic role. If the exciton gas is in the normal phase, then the screening of interlayer interaction by the exciton subsystem results in an exponential damping of the cross-mobility with the decrease of temperature, while at low temperatures, the interactions result in a robust bosonic transport due to the emergence of the Bogoliubov quasiparticles.

First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas

Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose–Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose–Einstein condensation, true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases.

Exact two-body solutions and quantum defect theory of two-dimensional dipolar quantum gas

In this paper, we provide the two-body exact solutions of the two-dimensional (2D) Schrödinger equation with isotropic interactions. An analytic quantum defect theory is constructed based on these solutions and it is applied to investigate the scattering properties as well as two-body bound states of an ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves, which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.

Matter-wave Fourier optics with a strongly interacting two-dimensional Fermi gas

We demonstrate and characterize an experimental technique to directly image the momentum distribution of a strongly interacting two-dimensional quantum gas with high momentum resolution. We apply the principles of Fourier optics to investigate three main operations on the expanding gas: focusing, collimation and magnification. We focus the gas in the radial plane using a harmonic confining potential and thus gain access to the momentum distribution. We pulse a different harmonic potential to stop the rapid axial expansion which allows us to image the momentum distribution with high resolution. Additionally, we propose a method to magnify the mapped momentum distribution to access interesting momentum scales. All these techniques can be applied to a wide range of experiments and in particular to study many-body phases of quantum gases.

Spin dynamics in a two-dimensional quantum gas

We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. We show that the two clouds are anticorrelated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with nonlocal Einstein-Podolsky-Rosen entanglement.

A two-dimensional quantum gas in a magnetic trap

We present the first experimental realization of a two-dimensional quantum gas in a purely magnetic trap dressed by a radio frequency field in the presence of gravity. The resulting potential is extremely smooth and very close to harmonic in the two-dimensional plane of confinement. We fully characterize the trap and demonstrate the confinement of a quantum gas to two dimensions. The trap geometry can be modified to a large extent, in particular in a dynamical way. Taking advantage of this possibility, we study the monopole and the quadrupole modes of a two-dimensional Bose gas.

All-optical transport and compression of ytterbium atoms into the surface of a solid immersion lens

We present an all-optical method to load 174Yb atoms into a single layer of an optical trap near the surface of a solid immersion lens which improves the numerical aperture of a microscope system. Atoms are transported to a region 20 um below the surface using a system comprised by three optical dipole traps. The "optical accordion" technique is used to create a condensate and compress the atoms to a width of 120 nm and a distance of 1.8 um away from the surface. Moreover, we are able to verify that after compression the condensate behaves as a two-dimensional quantum gas.

The Berezinskii–Kosterlitz–Thouless transition in imbalanced 2D Fermi gases: The role of fluctuations

The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.

Two-dimensional quantum gas in a hybrid surface trap

We demonstrate a novel optical trapping scheme for ultracold atoms. Using a combination of evanescent wave, standing wave, and magnetic potentials we create a deeply 2D Bose-Einstein condensate (BEC) at a few microns from a glass surface. Using techniques such as broadband "white" light to create evanescent and standing waves, we realize a smooth potential with a trap frequency aspect ratio of 300:1:1 and long lifetimes. This makes the setup suitable for many-body quantum simulations and applications such as high precision measurements close to surfaces.

Conductivity Measurement of Helium Surface Electrons in the Coexistence of Adsorbed 2D Atomic Hydrogen Gas

Cold hydrogen atoms (H) are adsorbed on liquid helium surface to form two-dimensional (2D) quantum gas. Because of the boson nature of H atoms, when 2D H gas is cold and dense enough, it is expected to exhibit a transition to superfluid phase by Kosterlitz-Thouless mechanism. In order to sense the state of 2D H gas, we used helium surface electrons as a probe. Since the conductivity of surface electrons is sensitively influenced by collisions with its environment, such as He vapor atoms and ripplons, it is expected to detect the existence of H atoms on the same surface. We prepared a 2D mixture gas of H and electrons on a helium surface and measured the conductivity of the electrons. Strong magnetic field was applied to avoid chemical processes: electron attachment on H atom and H-H recombination. We employed pulse excited edge-magnetoplasmon (EMP) technique for the conductivity measurement. We show EMP spectrum under the influence of H atoms and discuss the potentiality of surface electrons for probing states of adsorbed 2D H gas.

Thermodynamic properties of a harmonically trapped, two-dimensional charged quantum gas in a magnetic field

We present exact analytical results for the thermodyanmic properties of a two-dimensional (2D), harmonically trapped charged quantum gas in a magnetic field. While our results are applicable to both Fermi and Bose gases, we focus our attention on trapped fermions owing to their relevant application in the density-functional theory of inhomogeneous Fermi systems. In particular, we test the Thomas–Fermi (or continuum) approximation (TFA) for the functional relation τ[ρ] using the exact ρ(r) and show that it reproduces the local and global properties of the exact kinetic energy density τ(r) surprisingly well. However, when we compare our exact results for various thermodynamic quantities with the TFA, we find that it misses several important features. These deviations are shown to be entirely due to the quantum mechanical properties of the system, which are not accounted for in the continuum approximation.

Physics of Hole Transport in Strained Silicon MOSFET Inversion Layers

A comprehensive quantum anisotropic transport model for holes was used to study silicon PMOS inversion layer transport under arbitrary stress. The anisotropic band structures of bulk silicon and silicon under field confinement as a twodimensional quantum gas are computed using the pseudopotential method and a six-band stress-dependent k.p Hamiltonian. Anisotropic scattering is included in the momentum-dependent scattering rate calculation. Mobility is obtained from the Kubo-Greenwood formula at low lateral field and from the fullband Monte Carlo simulation at high lateral field. Using these methods, a comprehensive study has been performed for both uniaxial and biaxial stresses. The results are compared with device bending data and piezoresistance data for uniaxial stress, and device data from strained Si channel on relaxed SiGe substrate devices for biaxial tensile stress. All comparisons show a very good agreement with simulation. It is found that the hole band structure is dominated by 12 wings, where mechanical stress, as well as the vertical field under certain stress conditions, can alter the energies of the few lowest hole subbands, changing the transport effective mass, density-of-states, and scattering rates, and thus affecting the mobility

Charged two-dimensional quantum gas in a uniform magnetic field at finite temperature

We present closed-form, analytical expressions for the thermodynamic properties of an ideal, two-dimensional (2D) charged Fermi or Bose gas in the presence of a uniform magnetic field of arbitrary strength. We consider both the homogeneous quantum gas (in which case our expressions are exact) and the inhomogeneous gas within the local-density approximation. Our results for the Fermi gas are relevant to the current-density-functional theory of low-dimensional electronic systems in magnetic fields. For a 2D charged Bose gas (CBG) in a homogeneous magnetic field, we show that the uniform system undergoes a sharp transition at a critical temperature ${T}_{c}^{\ensuremath{\star}},$ below which there is a macroscopic occupation of the lowest Landau level. An examination of the one-body density matrix, however, reveals the absence of long-range order, thereby indicating that the transition cannot be interpreted to a Bose-Einstein condensate. Nevertheless, for $Tl{T}_{c}^{\ensuremath{\star}}$ and weak magnetic fields, the system still exhibits magnetic properties which are practically indistinguishable from those of a condensed, superconducting CBG. We therefore conclude that while a condensate is a sufficient condition for the ideal CBG to exhibit a superconducting state, it may not be a necessary condition.