We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan's contact to the momentum C/q. Bragg spectroscopy of ultracold 6Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the f-sum rule, which is found to improve the accuracy of the structure factor measurement.

We have studied the transition from two to three dimensions in a low temperature weakly interacting 6Li Fermi gas. Below a critical atom number N(2D) only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above N(2D) the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

We use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of 87 Rb atoms prepared in the internal states |1 ≡ |F = 1, mF = −1 and |2 ≡ |F = 2, mF = 1 for the precision measurement of the interspecies scattering length a12 with a relative uncertainty of 1.6 × 10 −4 . We show that in a cigar-shaped trap the three-dimensional (3D) dynamics of a component with a small relative population can be conveniently described by a one-dimensional (1D) Schrödinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio a12/a11, where a11 is the intraspecies scattering length of a highly populated component 1, and is largely decoupled from the scattering length a22, the total atom number and loss terms. By fitting numerical simulations of the coupled Gross-Pitaevskii equations to the recorded temporal evolution of the axial width we obtain the value a12 = 98.006(16) a0, where a0 is the Bohr radius. Our reported value is in a reasonable agreement with the theoretical prediction a12 = 98.13(10) a0 but deviates significantly from the previously measured value a12 = 97.66 a0 [1] which is commonly used in the characterisation of spin dynamics in degenerate 87 Rb atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length a22 = 95.44(7) a0 which also deviates from the previously reported value a22 = 95.0 a0 [1]. We characterise two-body losses for the component 2 and obtain the loss coefficients γ12 = 1.51(18) × 10 −14 cm 3 /s and γ22 = 8.1(3) × 10 −14 cm 3 /s.

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Abstract. We propose the use of periodic arrays of permanent magnetic films for producing magnetic lattices of microtraps for confining, manipulating and controlling small clouds of ultracold atoms and quantum degenerate gases. Using analytical expressions and numerical calculations we show that periodic arrays of magnetic films can produce one-dimensional (1D) and two-dimensional (2D) magnetic lattices with non-zero potential minima, allowing ultracold atoms to be trapped without losses due to spin flips. In particular, we show that two crossed layers of periodic arrays of parallel rectangular magnets plus bias fields, or a single layer of periodic arrays of square-shaped magnets with three different thicknesses plus bias fields, can produce 2D magnetic lattices of microtraps having nonzero potential minima and controllable trap depth. For arrays with micron-scale periodicity, the magnetic microtraps can have very large trap depths (∼0.5 mK for the realistic parameters chosen for the 2D lattice) and very tight confinement.

We present measurements of the binding energies of 6 Li p-wave Feshbach molecules formed in combinations of the |F = 1/2, mF = +1/2 (|1 ) and |F = 1/2, mF = −1/2 (|2 ) states. The binding energies scale linearly with magnetic field detuning for all three resonances. The relative molecular magnetic moments are found to be 113 ± 7 µK/G, 111 ± 6 µK/G and 118 ± 8 µK/G for the |1 −|1 , |1 −|2 and |2 −|2 resonances, respectively, in good agreement with theoretical predictions. Closed channel amplitudes and the size of the p-wave molecules are obtained theoretically from full closed-coupled calculations.

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.

The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(kF a), where kF is the Fermi wave-vector and a is the s-wave scattering length, and the temperature T /TF , where TF is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature. [1][2][3]. Universal systems should satisfy two requirements: firstly, the gas must be dilute enough that the mean interparticle spacing n −1/3 greatly exceeds the range of the interaction potential r 0 , and, secondly, the interactions, characterized by the s-wave scattering length, a, should be sufficiently strong that a greatly exceeds n −1/3 . All Fermi systems that satisfy these requirements will behave identically on a scale given by the average particle separation, independent of the details of the interaction potential. Recent theoretical work by Tan [4][5][6] and others [7][8][9][10][11] has identified several exact relations applicable to Fermi systems in the universal regime. The central parameter in these relations is a quantity called the contact I, which forms a link between microscopic and macroscopic system properties.Contact quantifies the likelihood of finding two interacting fermions with very small separation and is closely linked to the pair-correlation function [4]. In strong analogy with the phase diagram of the Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid crossover of two-component Fermi gases [12], I depends upon two parameters: the dimensionless interaction strength 1/(k F a), where k F is the Fermi wavevector, and the relative temperature T /T F , where T F is the Fermi temperature. Previous theoretical [7,13] and experimental [14][15][16] work has investigated the interaction dependence of the contact, and a number of recent studies have calculated the temperature dependence of the contact [13,[17][18][19]. To date however, there have been no measurements of this latter dependence.In this letter, we report the first measurements of the temperature dependence of the contact using Bragg spectroscopy of a 6 Li Fermi gas at unitarity. Bragg spectroscopy allows for quantitative measurements of the static structure factor S(k) which is directly proportional to the contact at high momenta. We extract the first and second moments from our Bragg spectra and use these to obtain the dynamic structure factor S(k, ω) and from this S(k) and the contact. Our results are in good agreement with theoretical predictions and indicate that pair-correlations at high momenta persist well above the critical temperature for superfluidity.Tan's exact relations for Fermi gases near the ...