Dual-comb spectroscopy is an emerging new spectroscopic tool that exploits the frequency resolution, frequency accuracy, broad bandwidth, and brightness of frequency combs for ultrahigh-resolution, high-sensitivity broadband spectroscopy. By using two coherent frequency combs, dual-comb spectroscopy allows a sample's spectral response to be measured on a comb tooth-by-tooth basis rapidly and without the size constraints or instrument response limitations of conventional spectrometers. This review describes dual-comb spectroscopy and summarizes the current state of the art. As frequency comb technology progresses, dual-comb spectroscopy will continue to mature and could surpass conventional broadband spectroscopy for a wide range of laboratory and field applications.

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A Bose-Einstein condensate ͑BEC͒ is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii ͑GP͒ equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave ͑DSW͒. Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical onedimensional ͑1D͒ dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three-and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

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We have developed an evaporative cooling technique that accelerates the circulation of an ultra-cold 87 Rb gas, confined in a static harmonic potential. As a normal gas is evaporatively spun up and cooled below quantum degeneracy, it is found to nucleate vorticity in a Bose-Einstein condensate. Measurements of the condensate's aspect ratio and surface-wave excitations are consistent with effective rigid-body rotation. Rotation rates of up to 94% of the centrifugal limit are inferred. A threshold in the normal cloud's rotation is observed for the intrinsic nucleation of the first vortex. The threshold value lies below the prediction for a nucleation mechanism involving the excitation of surface-waves of the ground-state condensate. 03.75.Fi,67.90.+z,67.57.Fg,32.80.Pj To paraphrase an ancient riddle, what happens when an irresistible torque meets an irrotational fluid? The answer has been known for more than 50 years: a quantized vortex is nucleated. Vortices alone contribute to a superfluid's rotation, so that the bulk of the fluid may remain curl-free. The nucleation of vortices in bulk superfluid Helium has been the topic of extensive study (for a review see [1]). In the archetypical experiment, a rotatable pot filled with a mixture of superfluid and normal liquid Helium undergoes gradual angular acceleration. The normal fluid and the walls of the pot rotate together as a rigid body, defining a rotating environment. At some threshold angular velocity, a vortex line is nucleated at the circumference of the pot, and then quickly migrates inward until it is collinear with the axis of rotation. Further angular acceleration results in the nucleation of more vortices; eventually the fluid is filled with an array of vortex lines [2]. A central theme [3] of this research is the question: to what extent is the nucleation process "extrinsic," i.e. dependent on such details as the roughness of the surface of the walls, and to what extent is it "intrinsic" [4,5], i.e. driven (in the limit of microscopically smooth walls) by the flow of normal fluid along the boundary of the superfluid? In the analogous rotating-potential experiments with a dilutegas Bose-Einstein condensate (BEC), the confining potential and the normal fluid typically rotate at different rates [6]. In this context, the extrinsic-intrinsic question can be restated as: is it the confining potential or the normal fluid that defines the rotating environment?Vortices in a BEC have been created with wavefunction engineering [7], through the decay of solitons [8,9], and in the wake of moving objects [10,11]. The first rotatingpotential experiment to detect vortices in a BEC was performed by the Paris group [12]; results have also been obtained by the MIT [13] and Oxford [14] groups. In these experiments the role of the normal fluid was secondary to that of the rotating potential; it is conceivable the normal fluid was not rotating at all. This paper presents vortex nucleation experiments performed in the opposite limit, namely in the environment of a rotating...

The broadband, coherent nature of narrow-linewidth fiber frequency combs is exploited to measure the full complex spectrum of a molecular gas through multiheterodyne spectroscopy. We measure the absorption and phase shift experienced by each of 155 000 individual frequency-comb lines, spaced by 100 MHz and spanning from 1495 to 1620 nm, after passing through hydrogen cyanide gas. The measured phase spectrum agrees with the Kramers-Kronig transformation of the absorption spectrum. This technique can provide a full complex spectrum rapidly, over wide bandwidths, and with hertz-level accuracy.

We directly image Tkachenko waves in a vortex lattice in a dilute-gas Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a consequence of the small but nonvanishing elastic shear modulus of the vortex-filled superfluid. The frequencies are measured for rotation rates as high as 98% of the centrifugal limit for the harmonically confined gas. Agreement with a hydrodynamic theory worsens with increasing rotation rate, perhaps due to the increasing fraction of the volume displaced by the vortex cores. We also observe two low-lying m=0 longitudinal modes at about 20 times higher frequency.

The transfer of high-quality time-frequency signals between remote locations underpins a broad range of applications including precision navigation and timing, the new field of clock-based geodesy, long-baseline interferometry, coherent radar arrays, tests of general relativity and fundamental constants, and the future redefinition of the second [1-7]. However, present microwave-based time-frequency transfer [8-10] is inadequate for state-of-the-art optical clocks and oscillators [1,11-15] that have femtosecond-level timing jitter and accuracies below 1E-17; as such, commensurate optically-based transfer methods are needed. While fiber-based optical links have proven suitable [16,17], they are limited to comparisons between fixed sites connected by a specialized bidirectional fiber link. With the exception of tests of the fundamental constants, most applications instead require more flexible connections between remote and possibly portable optical clocks and oscillators. Here we demonstrate optical time-frequency transfer over free-space via a two-way exchange between coherent frequency combs, each phase-locked to the local optical clock or oscillator. We achieve femtosecond-scale timing deviation, a residual instability below 1E-18 at 1000 s and systematic offsets below 4E-19, despite frequent signal fading due to atmospheric turbulence or obstructions across the 2-km link. This free-space transfer would already enable terrestrial links to support clock-based geodesy. If combined with satellite-based free-space optical communications, it provides a path toward global-scale geodesy, high-accuracy time-frequency distribution, satellite-based relativity experiments, and "optical GPS" for precision navigation