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We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ( 40 K), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 TF . Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons.The achievement of Bose-Einstein condensation in atomic vapors [1] has given great impetus to efforts to realize superfluidity in dilute fermionic alkali gases. While conditions of quantum degeneracy have been obtained in potassium (, the lowest achievable temperatures to date have been limited to around 0.2T F [3]. Although this limit is essentially technical in nature, it appears likely that it will be necessary to utilize a strong pairing mechanism yielding superfluid transition temperatures close to this value.Even in high-T c superconductors, the typical critical temperatures are of the order of 10 −2 T F . In the context of strong-coupling superconductivity there has been much work on constructing minimal models to study the crossover from the seminal BCS theory [4] for conventional superconductivity to the Bose-Einstein condensation of tightly bound pairs, passing through nonperturbative regimes in T c /T F [5,6]. In this letter, we treat explicitly a short range quasibound resonant state by extending the theory given in Refs. [7] to predict the existence of a Feshbach resonance superfluidity in a gas of fermionic potassium atoms. This system has an ultrahigh critical phase transition temperature in close proximity to the Fermi temperature. This is a novel regime for quantum fluids, as illustrated in Fig. 1 where our system and others which exhibit superfluidity or BEC are compared.The seminal Bardeen-Cooper-Schrieffer (BCS) theory [4] of superconductivity applied to a dilute gas considers binary interactions between particles in two distinguishable quantum states, say | ↑ and | ↓ . For a uniform system, the fermionic field operators may be Fourierexpanded in a box with periodic boundary conditions giving wavevector-k dependent creation and annihilation operators a † kσ and a kσ for states |σ . At low energy, the binary scattering processes are assumed to be completely characterized by the s-wave scattering length a in terms of a contact quasipotential U = 4πh 2 an/m, where n is the number density. The Hamiltonian describing such a system is given bywhere ǫ k =h 2 k 2 /2m is the kinetic energy, m is the mass, and the constraint k 4 = k 1 + k 2 − k 3 gives momentum conservation.

The spectral purity of an oscillator is central to many applications, such as detecting gravity waves, defining the second, ground-state cooling and quantum manipulation of nanomechanical objects, and quantum computation. Recent proposals suggest that laser oscillators which use very narrow optical transitions in atoms can be orders of magnitude more spectrally pure than present lasers. Lasers of this high spectral purity are predicted to operate deep in the 'bad-cavity', or superradiant, regime, where the bare atomic linewidth is much less than the cavity linewidth. Here we demonstrate a Raman superradiant laser source in which spontaneous synchronization of more than one million rubidium-87 atomic dipoles is continuously sustained by less than 0.2 photons on average inside the optical cavity. By operating at low intracavity photon number, we demonstrate isolation of the collective atomic dipole from the environment by a factor of more than ten thousand, as characterized by cavity frequency pulling measurements. The emitted light has a frequency linewidth, measured relative to the Raman dressing laser, that is less than that of single-particle decoherence linewidths and more than ten thousand times less than the quantum linewidth limit typically applied to 'good-cavity' optical lasers, for which the cavity linewidth is much less than the atomic linewidth. These results demonstrate several key predictions for future superradiant lasers, which could be used to improve the stability of passive atomic clocks and which may lead to new searches for physics beyond the standard model.

We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the F 1, m f 21 hyperfine state of 87 Rb. The ratio of these is 7.4͑2.6͒ which agrees with the theoretical factor of 3! and demonstrates that condensate atoms are less bunched than noncondensate atoms.[S0031-9007(97)03611-9] PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Pj, 42.50.Dv The onset of Bose-Einstein condensation (BEC) is defined by the sudden accumulation of many bosons in a single quantum state. The symmetry property of bosons is such that if a gas is indeed composed of many identical bosons all occupying the same single-particle state, the gas will exhibit a collection of correlation properties known as coherence. While most early experiments on dilute-gas BEC [1-3] have shown good quantitative agreement with the simple physical model of macroscopic occupation of a single state, no dilute-gas experiment explicitly addressed the issue of coherence in the condensate until the striking observation by Andrews et al. [4] of first-order coherence in a sodium condensate. In this paper we describe collision-rate measurements that probe the higher-order coherence properties of thermal and Bose-condensed rubidium atoms [5]. In particular, the coherence of the BEC ground state is contrasted with the chaotic fluctuations of the ultracold noncondensed states.The correlation properties of degenerate samples of ideal bosons have already been extensively studied in the context of quantum optics [6]. In fact, the close analogies between the macroscopically occupied state of a laser beam (characterized as a "coherent state") and that of a Bose condensate have prompted the use of the term "atom laser" to describe some aspects of BEC [7]. Quantum optics teaches that a laser beam is described by a quantum field that exhibits both (i) "first-order coherence," meaning that a measurement of the phase of the field at one point in space and time may be used to predict the phase of the field at some other point [8] and (ii) "higher-order coherences," meaning in essence that the intensity fluctuations in a coherent sample are suppressed relative to those in a thermal sample with the same mean intensity.The analog of intensity fluctuations in a beam of photons is density fluctuations in a gas of atoms. For example, Fig. 1(a) shows the calculated [9] three-body correlation function for a gas of thermal (i.e., noncondensed) bosons. Note that there is an enhanced probability for finding three bosons close together. The same physics accounts for short-time photon bunching in a thermal light beam (the Hanbury-Brown-Twiss effect [10]), for the two-atom bunching that has been observed in beams of ultracold (but not condensed) atoms [11], and for three-pion correla...

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order 10 −12 W is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude.PACS numbers: 42.50. Nn, 06.30.6v, 37.10.Jk, 37.30.+i, 46.62.Eh Time and frequencies are the quantities that we can measure with the highest accuracy by far. From this fact derives the importance of clocks and frequency standards for many applications in technology and fundamental science. Some applications directly relying on atomic clocks are GPS, synchronization of data and communication networks, precise measurements of the gravitational potential of the earth, radio astronomy, tests of theories of gravity, and tests of the fundamental laws of physics.With the advent of octave spanning optical frequency combs [1,2] it has become feasible to use atomic transitions in the optical domain to build atomic clocks. Optical clocks based on ions [3] and ultracold neutral atoms confined in optical lattices [4] have recently demonstrated a precision of about 1 part in 10 15 at one second and a total fractional uncertainty of 10 −16 [4] or below [3], surpassing the primary cesium microwave standards [5,6].The state-of-the-art optical atomic clocks do not achieve the full stability that is in principle afforded by the atomic transitions on which they are founded. These transitions could have natural line-Qs of order 10 18 , exceeding the fractional stability of the clocks by a factor of ∼ 100. The main obstacle that prevents us from reaping the full benefit of the ultra-narrow clock transitions is the linewidth of the lasers used to interrogate these transitions. These lasers are stabilized against carefully designed passive high-Q cavities and achieve linewidths < 1 Hz, making them the most stable coherent sources of radiation. It is mainly the thermal noise of the reference cavity mirrors that prevent a further linewidth reduction [7] and substantially reducing this noise is hard [8].An elegant solution to these problems would be to directly extract light emitted from the ultra-narrow clock transition [9]. That light could then be used as an optical phase reference, circumventing the need for an ultra stable reference cavity. Unfortunately, the fluorescence light emitted on a clock transition is too weak for practical applications. For instance, for 10 6 fully inverted 87 Sr atoms the power of the spontaneously emitted light is of the order of 10 −16 W.The key observation that motivates this work is that if we could coerce the ensemble of atoms to emit the energy stored in them collectively rather than individually, the resulting power of order 10 −...

The burgeoning field of Bose-Einstein condensation in dilute alkali and hydrogen gases has stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems 1,2 . The recent experiments offer the possibility for exploring fundamental properties of low temperature physics in a very controllable and accessible way. One current goal of experimenters in this field is to observe superfluid-like behavior in these trapped Bose gases, analogous to persistent currents in superfluid liquid helium, which flow without observable viscosity, and electric currents in superconductors, which flow without observable resistance. These "super" properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay due to thermal relaxation 3 . Here we solve the time-dependent Gross-Pitaevskii equation of motion of the condensate involving two hyperfine atomic states and show how to generate, with extremely high fidelity, topological modes such as vortices that open the door to the study of superfluidity in these new systems. Our approach is inspired by recent experiments investigating a trapped condensate with two strongly coupled internal states 4,5 . We show how the interplay between the internal and motional dynamics can be utilized to prepare the condensate in a variety of interesting configurations.Since 1995, when Bose-Einstein condensation in a dilute atomic gas was first observed 6−8 , experimenters have sought a method to create a vortex in this system. In a typical experiment, around one million atoms are trapped in a magnetic harmonic potential and cooled below the critical temperature so that condensation occurs into the lowest energy quantized mode. In the usual case, this ground state has no circulation. One proposed scheme for preparing the condensate in a vortex mode 9−17 is to distort the confining potential and mechanically rotate the trap during the cooling process. In this way, the lowest energy mode may be engineered to be circulating about the axis of symmetry. Such an approach is in direct analogy with experiments on vortices in superfluid helium-the asymmetry of the harmonic trap for the atomic gas plays the role of surface roughness of a rotating vessel. Although conceptually this method appears promising for vortex generation in a trapped gas, so far technical difficulties have precluded its successful implementation.Instead of having the system condense into a vortex mode, an alternative approach is to allow the atoms to condense into the usual ground state and then dynamically generate the vortex from the non-rotating condensate. Several theoretical proposals have been made along these lines which utilize the interaction between the atoms and a specific laser field consisting of a beam of photons with non-zero orbital angular momentum 18−20 .The method we present here makes use of both of the techniques mentioned-mechanical rotation and the coupling of internal states using an el...

Atomtronics focuses on atom analogs of electronic materials, devices and circuits. A strongly interacting ultracold Bose gas in a lattice potential is analogous to electrons in solid-state crystalline media. As a consequence of the band structure, cold atoms in a lattice can exhibit insulator or conductor properties. P-type and N-type material analogs can be created by introducing impurity sites into the lattice. Current through an atomtronic wire is generated by connecting the wire to an atomtronic battery which maintains the two contacts at different chemical potentials. The design of an atomtronic diode with a strongly asymmetric current-voltage curve exploits the existence of superfluid and insulating regimes in the phase diagram. The atomtronic analog of a bipolar junction transistor exhibits large negative gain. Our results provide the building blocks for more advanced atomtronic devices and circuits such as amplifiers, oscillators and fundamental logic gates.