The pairing of fermions lies at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state, and the quest for superconductors with high critical temperature equates to a search for systems with strong pairing mechanisms. Ultracold atomic Fermi gases present a highly controllable model system for studying strongly interacting fermions. Tunable interactions (through Feshbach collisional resonances) and the control of population or mass imbalance among the spin components provide unique opportunities to investigate the stability of pairing-and possibly to search for exotic forms of superfluidity. A major controversy has surrounded the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly (that is, at unitarity). Here we present the phase diagram of a spin-polarized Fermi gas of (6)Li atoms at unitarity, experimentally mapping out the superfluid phases versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization; this is the signature of a first-order superfluid-to-normal phase transition, and disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully paired superfluid to a partially polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.

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Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.PACS numbers: 03.75.Lm, 64.60.My The characteristic feature of Bose-Einstein condensation is the accumulation of a macroscopic number of particles in the lowest quantum state. Condensate fragmentation, the macroscopic occupation of two or more quantum states, is usually prevented by interactions [1], but may happen in spinor condensates [2,3]. However, multiple condensates may exist in metastable situations. Let's assume that an equilibrium condensate has formed in one quantum state, but now we modify the system allowing for one even lower state. How does the original condensate realize that it is in the wrong state and eventually migrate to the true ground state of the system? What determines the time scale for this equilibration process? This is the situation which we experimentally explore in this paper using a double-well potential.The process we study is relevant for at least four different questions.(1) The description of the formation of the condensate is a current theoretical frontier and requires finite-temperature quantum kinetic theories. There are still discrepancies between theoretical predictions and experimental results [4,5]. Our double-well system has the advantage of being an almost closed system (little evaporation) with well defined initial conditions and widely adjustable time scales (through the height of the barrier). (2) Spinor condensates show rich ground states and collective excitations due to the multi-component order parameter [2]. Several groups have observed longlived metastable configurations [6,7,8,9] and speculated about transport of atoms from one domain to another via the thermal cloud [6,8]. The double-well potential allows us to characterize such distillation processes in their simplest realization. (3) The incoherent transport observed here in a double well-potential imposes stringent limitations on future experiments aiming at the observation of coherent transport in Josephson junctions [10,11,12]. (4) Our observation of condensate growth in one potential well due to the addition of thermal atoms realizes the key ideas of proposals on how to achieve a continuous atom laser [13] which is different from the experiment where condensates were replenished with transported condensates [14]. The whole system has equilibrated. V denotes the height of the potential barrier between the two wells, which is measured with respect to the bottom of the left well, and ∆U the trap depth difference between the two wells.The scheme of the experiment is shown in Fig....

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to approximately 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 µm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.PACS numbers: 03.75. Dg, 39.20.+q, 03.75.Lm Demonstrating atom interferometry with particles confined by magnetic [1,2,3,4] and optical [5] microtraps and waveguides would realize the matter wave analog of optical interferometry using fiber-optic devices. Current proposals for confined-atom interferometers rely on the merger and separation of two potential wells to coherently divide atomic wavepackets [6,7,8]. This type of division differs from previously demonstrated atomic beam splitters. To date, atomic beams and vapors have been coherently diffracted into different momentum states by mechanical [9,10] and optical [11] gratings, and Bose-Einstein condensates have been coherently delocalized over multiple sites in optical lattices [12,13,14,15,16,17]. Atom interferometers utilizing these beam splitting elements have been used to sense accelerations [12,18] and rotations [19,20], monitor quantum decoherence [21], characterize atomic and molecular properties [22], and measure fundamental constants [18,23].In this Letter, we demonstrate a trapped-atom interferometer with gaseous Bose-Einstein condensates confined in an optical double-well potential. Condensates were coherently split by deforming an initially single-well potential into two wells separated by 13 µm. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the atoms from the separated potential wells [17,24]. This recombination method avoids deleterious mean field effects [25,26] and detects applied phase shifts on a single realization of the experiment, unlike in-trap recombination schemes [6,7,8].The large separation between the split potential wells allowed the phase of each condensate to evolve independently and either condensate to be addressed individually. An ac Stark phase shift was applied to either condensate by temporarily turning off the optical fields generating its potential well. The spatial phase of the resulting matter wave interference pattern shifted linearly with the applied phase shift and was independent of the time of its application. This verified the phase sensitivity of the interferometer and the independent phase evolution of the separated condensates. The measured coherence time of the separated condensates was 5 ms.The present work demonstrates a trapped-atom interferometer with two interfering paths. This geometry has the flexibility to measure either highly localized...

Doubly quantized vortices were topologically imprinted in |F = 1 23 Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.PACS numbers: 03.75. Kk, 03.75.Lm, 67.90.+z Quantum fluids, like superfluid He, electrons in a superconductor or a Bose-Einstein condensate of atoms, are described by a macroscopic wavefunction. This requires the flow field to be irrotational, and gives rise to superfluidity and quantized circulation [1]. Atoms in a BoseEinstein condensate, for example, can only circulate with angular momentum equal to integer multiple ofh, in the form of a quantized vortex [2].Vortices are excited states of motion and therefore energetically unstable towards relaxation into the motional ground state, where the condensate is at rest. However, quantization constrains the decay: a vortex in BoseEinstein condensates cannot simply fade away or disappear, it is only allowed to move out of the condensate or annihilate with another vortex of opposite circulation. Vortex decay and metastability, due to inhibition of decay, have been a central issue in the study of superfluidity [3,4,5,6,7,8]. In almost pure Bose-Einstein condensates, vortices with lifetimes up to tens of seconds have been observed [9,10,11].Giving a Bose-Einstein condensate angular momentum per particle larger thanh can result in one multiplyquantized vortex with large circulation or, alternatively, in many singly-quantized vortices each with angular momentumh. The kinetic energy of atoms circulating around the vortex is proportional to the square of the angular momentum; therefore the kinetic energy associated with the presence of a multiply-quantized vortex is larger than the kinetic energy of a collection of singlyquantized vortices carrying the same angular momentum. A multiply-quantized vortex can decay coherently by splitting into singly-quantized vortices and transferring the kinetic energy to coherent excitation modes, a phenomenon called dynamical instability which is driven by atomic interactions [5,12,13,14], and not caused by dissipation in an external bath. Observations of arrays of singly-quantized vortices in rapidly rotating condensates [10,11] indirectly suggests that the dynamical instability leads to fast decay of multiply-quantized vortices. However, the existence of stable multiply-quantized vortices in trapped Bose-Einstein condensates has been predicted with a localized pinning potential [12] or in a quartic potential [15]. Stable doubly-quantized vortices were observed in superconductors in presence of pinning forces [16] and in superfluid 3 He-A which has a multicomponent order parameter [17]. Recently, formation of a multiply-quantized vortex in a Bose-Einstein condensate has been demonstrated using topological phases [18,19], and surprisingly long lifetime of a "giant" vortex core has been report...