Bespoke magnetic field design for a magnetically shielded cold atom interferometer.

Quantum sensors based on cold atoms are being developed which produce measurements of unprecedented accuracy. Due to shifts in atomic energy levels, quantum sensors often have stringent requirements on their internal magnetic field environment. Typically, background magnetic fields are attenuated using high permeability magnetic shielding, with the cancelling of residual and introduction of quantisation fields implemented with coils inside the shield. The high permeability shield, however, distorts all magnetic fields, including those generated inside the sensor. Here, we demonstrate a solution by designing multiple coils overlaid on a 3D-printed former to generate three uniform and three constant linear gradient magnetic fields inside the capped cylindrical magnetic shield of a cold atom interferometer. The fields are characterised in-situ and match their desired forms to high accuracy. For example, the uniform transverse field, Bx, deviates by less than 0.2% over more than 40% of the length of the shield. We also map the field directly using the cold atoms and investigate the potential of the coil system to reduce bias from the quadratic Zeeman effect. This coil design technology enables targeted field compensation over large spatial volumes and has the potential to reduce systematic shifts and noise in numerous cold atom systems.

A portable magneto-optical trap with prospects for atom interferometry in civil engineering.

The high precision and scalable technology offered by atom interferometry has the opportunity to profoundly affect gravity surveys, enabling the detection of features of either smaller size or greater depth. While such systems are already starting to enter into the commercial market, significant reductions are required in order to reach the size, weight and power of conventional devices. In this article, the potential for atom interferometry based gravimetry is assessed, suggesting that the key opportunity resides within the development of gravity gradiometry sensors to enable drastic improvements in measurement time. To push forward in realizing more compact systems, techniques have been pursued to realize a highly portable magneto-optical trap system, which represents the core package of an atom interferometry system. This can create clouds of 107 atoms within a system package of 20 l and 10 kg, consuming 80 W of power.This article is part of the themed issue 'Quantum technology for the 21st century'.

Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants.

Singly ionized ytterbium, with ultranarrow optical clock transitions at 467 and 436 nm, is a convenient system for the realization of optical atomic clocks and tests of present-day variation of fundamental constants. We present the first direct measurement of the frequency ratio of these two clock transitions, without reference to a cesium primary standard, and using the same single ion of 171Yb+. The absolute frequencies of both transitions are also presented, each with a relative standard uncertainty of 6×10(-16). Combining our results with those from other experiments, we report a threefold improvement in the constraint on the time variation of the proton-to-electron mass ratio, µ/µ=0.2(1.1)×10(-16) yr(-1), along with an improved constraint on time variation of the fine structure constant, α/α=-0.7(2.1)×10(-17) yr(-1).

Interferometry with Bose-Einstein condensates in microgravity.

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

Long-range interacting many-body systems with alkaline-earth-metal atoms.

Alkaline-earth-metal atoms can exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the (3)P(0) - (3)D(1) transition of the triplet manifold. In the case of bosonic strontium, which we discuss here, this transition has a wavelength of 2.6 µm and a dipole moment of 4.03 D, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states (3)P(0) and (3)D(1). This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tunable disorder and anisotropy. We derive the many-body master equation, investigate the dynamics of excitation transport, and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with long-range interactions. As such, they represent an alternative to current related efforts employing Rydberg gases, atoms with large magnetic moment, or polar molecules.

Bose-Einstein condensation in microgravity.

Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Collisions of dark solitons in elongated Bose-Einstein condensates.

We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.

Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices?

Mixtures of bosonic and fermionic atoms in optical lattices provide a promising arena to study strongly correlated systems. In experiments realizing such mixtures in the quantum-degenerate regime the temperature is a key parameter. We investigate the intrinsic heating and cooling effects due to an entropy-preserving raising of the optical lattice, identify the generic behavior valid for a wide range of parameters, and discuss it quantitatively for the recent experiments with 87Rb and 40K atoms. In the absence of a lattice, we treat the bosons in the Hartree-Fock-Bogoliubov-Popov approximation, including the fermions in a self-consistent mean-field interaction. In the presence of the full three-dimensional lattice, we use a strong coupling expansion. We find the temperature of the mixture in the lattice to be always higher than for the pure bosonic case, shedding light onto a key point in the analysis of recent experiments.

Exact solution of strongly interacting quasi-one-dimensional spinor Bose gases.

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta repulsion. The eigenfunctions are constructed from the wave functions of noninteracting spinless fermions, based on Girardeau's Fermi-Bose mapping. We show that the spinor bosons behave like a compound of noninteracting spinless fermions and noninteracting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.

Magnetically tuned spin dynamics resonance.

We present the experimental observation of a magnetically tuned resonance phenomenon in the spin mixing dynamics of ultracold atomic gases. In particular, we study the magnetic field dependence of spin conversion in F=2 (87)Rb spinor condensates in the crossover from interaction dominated to quadratic Zeeman dominated dynamics. We discuss the observations in the framework of spin dynamics as well as matter wave four wave mixing. Furthermore, we show that the validity range of the single mode approximation for spin dynamics is significantly extended at high magnetic field.

Ultracold heteronuclear molecules in a 3D optical lattice.

We report on the creation of ultracold heteronuclear molecules assembled from fermionic 40K and bosonic 87Rb atoms in a 3D optical lattice. Molecules are produced at a heteronuclear Feshbach resonance on both the attractive and the repulsive sides of the resonance. We precisely determine the binding energy of the heteronuclear molecules from rf spectroscopy across the Feshbach resonance. We characterize the lifetime of the molecular sample as a function of magnetic field and measure lifetimes between 20 and 120 ms. The efficiency of molecule creation via rf association is measured and is found to decrease as expected for more deeply bound molecules.

Tuning of heteronuclear interactions in a degenerate Fermi-Bose mixture.

We demonstrate tuning of interactions between fermionic 40K and bosonic 87Rb atoms by Feshbach resonances and access the complete phase diagram of the harmonically trapped mixture from phase separation to collapse. On the attractive side of the resonance, we observe a strongly enhanced mean-field energy of the condensate due to the mutual mean-field confinement, predicted by a Thomas-Fermi model. As we increase heteronuclear interactions beyond a threshold, we observe an induced collapse of the mixture. On the repulsive side of the resonance, we observe vertical phase separation of the mixture in the presence of the gravitational force, thus entering a completely unexplored part of the phase diagram of the mixture. In addition, we identify the 515 G resonance as p wave by its characteristic doublet structure.

Localization of bosonic atoms by fermionic impurities in a three-dimensional optical lattice.

We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular, we study the dependence of this transition on the fermionic (40)K impurity concentration by a comparison to the corresponding superfluid to Mott-insulator transition in a pure bosonic (87)Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a simple mean-field argument, which indicates that disorder-related effects play a significant role.

Interaction-driven dynamics of 40K- 87Rb Fermion-Boson gas mixtures in the large-particle-number limit.

We have studied effects of interspecies attraction in a Fermi-Bose mixture over a large regime of particle numbers in the 40K-87Rb system. We report on the observation of a mean-field driven collapse at critical particle numbers of 1.2 x 10(6) 87Rb atoms in the condensate and 7.5 x 10(5) 40K atoms consistent with mean-field theory for a scattering length of aFB = -284a(0). For large overcritical particle numbers, we see evidence for revivals of the collapse. Part of our detailed study of the decay dynamics and mechanisms is a measurement of the (87Rb- 87Rb- 40K) three-body loss coefficient K3 = (2.8 +/- 1.1) x 10(-28) cm6/s, which is an important parameter for dynamical studies of the system.

Soliton trains in Bose-Fermi mixtures.

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.

Dynamics of F=2 spinor Bose-Einstein condensates.

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of 10(-12) cm(3) s(-1) for spin-changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10(-13) cm(3) s(-1) for hyperfine-changing collisions. We observe polar behavior in the F=2 ground state of 87Rb, while we find the F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.

Bose-Einstein condensation in dilute atomic gases.

Bose-Einstein condensation is one of the most curious and fascinating phenomena in physics. It lies at the heart of such intriguing processes as superfluidity and superconductivity. However, in most cases, only a small part of the sample is Bose-condensed and strong interactions are present. A weakly interacting, pure Bose-Einstein condensate (BEC) has therefore been called the "holy grail of atomic physics". In 1995 this grail was found by producing almost pure BECs in dilute atomic gases. We review the experimental development that led to the realization of BEC in these systems and explain how BECs are now routinely produced in about 25 laboratories worldwide. The tremendous experimental progress of the past few years is outlined and a number of recent experiments show the current status of the field. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00114-001-0277-8.