Trapped Atomic Gases Research Articles

Design and optimization of a 100 keV DC/RF ultracold electron source

An ultracold electron source based on near-threshold photoionization of a laser-cooled and trapped atomic gas is presented in this work. Initial DC acceleration to ∼10 keV and subsequent acceleration of the created bunches to 100 keV by RF fields makes the design suitable to serve as injector for accelerator-based light sources, single-shot ultrafast protein crystallography, applications in dielectric laser acceleration schemes, and potentially as an injector for free electron lasers operating in the quantum regime. This paper presents the design and properties of the developed DC/RF structure. It is shown that operation at a repetition frequency of 1 kHz is achievable and detailed particle tracking simulations are presented showing the possibility of achieving a brightness that can exceed conventional RF photosources.

Compact ultracold electron source based on a grating magneto-optical trap

The ultrafast and ultracold electron source, based on near-threshold photoionisation of a laser-cooled and trapped atomic gas, offers a unique combination of low transverse beam emittance and high bunch charge. Its use is however still limited because of the required cold-atom laser-cooling techniques. Here we present a compact ultracold electron source based on a grating magneto-optical trap (GMOT), which only requires one trapping laser beam that passes through a transparent accelerator module. This makes the technique more widely accessible and increases its applicability. We show the GMOT can be operated with a hole in the center of the grating and with large electric fields applied across the trapping region, which is required for extracting electron bunches. The calculated values of the applied electric field were found to agree well with measured Stark shifts of the laser cooling transition. The electron beams extracted from the GMOT have been characterised. Beam energies up to 10 keV were measured using a time-of-flight method. The normalised root-mean-squared transverse beam emittance was determined using a waist scan method, resulting in $\epsilon = 1.9 \rm{nm}$. The root-mean-squared transverse size of the ionisation volume is $30 \mu\rm{m}$ or larger, implying an electron source temperature in the few-10K range, $2-3$ orders of magnitude lower than conventional electron sources, based on photoemission or thermionic emission from solid state surfaces.

Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas

We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$. We predict Exciting temporal oscillations of the density distribution is a high-precision method for probing ultracold trapped atomic gases. Interaction effects in their many-body dynamics are particularly puzzling and counter-intuitive in one spatial dimension (1D) due to enhanced quantum correlations. We consider 1D quantum Bose gas in a parabolic trap at zero temperature and explain, analytically and numerically, how oscillation frequency depends on the number of particles, their repulsion and the trap strength. We identify the frequency with the energy difference between the ground state and a particular excited state. This way we avoided resolving the dynamical evolution of the system, simplifying the problem immensely. We find an excellent quantitative agreement of our results with the data from the Innsbruck experiment [Science 325, 1224 (2009)].

Superconductivity and superfluidity as universal emergent phenomena

Superconductivity (SC) or superfluidity (SF) is observed across a remarkably broad range of fermionic systems: in BCS, cuprate, iron-based, organic, and heavy-fermion superconductors, and superfluid helium-3 in condensed matter; in a variety of SC/SF phenomena in low-energy nuclear physics; in ultracold, trapped atomic gases; and in various exotic possibilities in neutron stars. The range of physical conditions and differences in microscopic physics defy all attempts to unify this behavior in any conventional picture. Here we propose a unification through the shared symmetry properties of the emergent condensed states, with microscopic differences absorbed into parameters. This, in turn, forces a rethinking of specific occurrences of SC/SF such as cuprate high-temperature superconductivity, which becomes far less mysterious when seen as part of a continuum of behavior shared by a variety of other systems.

Vortices and Dynamics in Trapped Bose-Einstein Condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.

Ultracold Electron Source for Single-Shot, Ultrafast Electron Diffraction

Ultrafast electron diffraction (UED) enables studies of structural dynamics at atomic length and timescales, i.e., 0.1 nm and 0.1 ps, in single-shot mode. At present UED experiments are based on femtosecond laser photoemission from solid state cathodes. These photoemission sources perform excellently, but are not sufficiently bright for single-shot studies of, for example, biomolecular samples. We propose a new type of electron source, based on near-threshold photoionization of a laser-cooled and trapped atomic gas. The electron temperature of these sources can be as low as 10 K, implying an increase in brightness by orders of magnitude. We investigate a setup consisting of an ultracold electron source and standard radio-frequency acceleration techniques by GPT tracking simulations. The simulations use realistic fields and include all pairwise Coulomb interactions. We show that in this setup 120 keV, 0.1 pC electron bunches can be produced with a longitudinal emittance sufficiently small for enabling sub-100 fs bunch lengths at 1% relative energy spread. A transverse root-mean-square normalized emittance of epsilon(x) = 10 nm is obtained, significantly better than from photoemission sources. Correlations in transverse phase-space indicate that the transverse emittance can be improved even further, enabling single-shot studies of biomolecular samples.

Simulated performance of an ultracold ion source

At present, the smallest spot size which can be achieved with state-of-the-art focused ion beam (FIB) technology is mainly limited by the chromatic aberrations associated with the 4.5 eV energy spread of the liquid-metal ion source. Here we numerically investigate the performance of an ultracold ion source which has the potential for generating ion beams which combine high brightness with small energy spread. The source is based on creating very cold ion beams by near-threshold photoionization of a laser-cooled and trapped atomic gas. We present ab initio numerical calculations of the generation of ultracold beams in a realistic acceleration field and including all Coulomb interactions, i.e., both space charge effects and statistical Coulomb effects. These simulations demonstrate that with existing technology reduced brightness values exceeding 105 A m−2 sr−1 V−1 are feasible at an energy spread as low as 0.1 eV. The estimated spot size of the ultracold ion source in a FIB instrument ranges from 10 nm at a current of 100 pA to 0.8 nm at 1 pA.

Resonantly paired fermionic superfluids

We present a theory of a degenerate atomic Fermi gas, interacting through a narrow Feshbach resonance, whose position and therefore strength can be tuned experimentally, as demonstrated recently in ultracold trapped atomic gases. The distinguishing feature of the theory is that its accuracy is controlled by a dimensionless parameter proportional to the ratio of the width of the resonance to Fermi energy. The theory is therefore quantitatively accurate for a narrow Feshbach resonance. In the case of a narrow s-wave resonance, our analysis leads to a quantitative description of the crossover between a weakly paired BCS superconductor of overlapping Cooper pairs and a strongly paired molecular Bose–Einstein condensate of diatomic molecules. In the case of pairing via a p-wave resonance, that we show is always narrow for a sufficiently low density, we predict a detuning-temperature phase diagram, that in the course of a BCS–BEC crossover can exhibit a host of thermodynamically distinct phases separated by quantum and classical phase transitions. For an intermediate strength of the dipolar anisotropy, the system exhibits a p x + i p y paired superfluidity that undergoes a topological phase transition between a weakly coupled gapless ground state at large positive detuning and a strongly paired fully gapped molecular superfluid for a negative detuning. In two dimensions the former state is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian vortex excitations familiar from fractional quantum Hall systems.

Pulsed Raman output coupler for an atom laser

We theoretically study a pulsed stimulated two-photon Raman outcoupler for an atom laser using a full three-dimensional description. A finite-temperature trapped Bose-condensed atomic gas is treated self-consistently by the Hartree-Fock-Bogoliubov equations. The model is closely related to a recent experiment on optical outcoupling [E. W. Hagley et al., Science 283, 1706 (1999)]. We analyze the momentum distribution of the output atoms and show how the output beam may be used as a probe of the quantum state for the trapped atomic gas and how it could be engineered and controlled in a nonlinear way.

Transition from collisionless to hydrodynamic behavior in an ultracold Fermi gas.

Relative motion in a two-component, trapped atomic gas provides a sensitive probe of interactions. By studying the lowest frequency excitations of a two-spin-state gas confined in a magnetic trap, we have explored the transition from the collisionless to the hydrodynamic regime. As a function of collision rate, we observe frequency shifts as large as 6% as well as a dramatic, nonmonotonic dependence of the damping rate. The measurements agree qualitatively with expectations for behavior in the collisionless and hydrodynamic limits and are quantitatively compared to a classical kinetic model.