Invited Article: A compact optically coherent fiber frequency comb.

We describe the design, fabrication, and performance of a self-referenced, optically coherent frequency comb. The system robustness is derived from a combination of an optics package based on polarization-maintaining fiber, saturable absorbers for mode-locking, high signal-to-noise ratio (SNR) detection of the control signals, and digital feedback control for frequency stabilization. The output is phase-coherent over a 1-2 µm octave-spanning spectrum with a pulse repetition rate of ∼200 MHz and a residual pulse-to-pulse timing jitter <3 fs well within the requirements of most frequency-comb applications. Digital control enables phase coherent operation for over 90 h, critical for phase-sensitive applications such as timekeeping. We show that this phase-slip free operation follows the fundamental limit set by the SNR of the control signals. Performance metrics from three nearly identical combs are presented. This laptop-sized comb should enable a wide-range of applications beyond the laboratory.

Comb-calibrated laser ranging for three-dimensional surface profiling with micrometer-level precision at a distance.

Non-contact surface mapping at a distance is interesting in diverse applications including industrial metrology, manufacturing, forensics, and artifact documentation and preservation. Frequency modulated continuous wave (FMCW) laser detection and ranging (LADAR) is a promising approach since it offers shot-noise limited precision/accuracy, high resolution and high sensitivity. We demonstrate a scanning imaging system based on a frequency-comb calibrated FMCW LADAR and real-time digital signal processing. This system can obtain three-dimensional images of a diffusely scattering surface at stand-off distances up to 10.5 m with sub-micrometer accuracy and with a precision below 10 µm, limited by fundamental speckle noise. Because of its shot-noise limited sensitivity, this comb-calibrated FMCW LADAR has a large dynamic range, which enables precise mapping of scenes with vastly differing reflectivities such as metal, dirt or vegetation. The current system is implemented with fiber-optic components, but the basic system architecture is compatible with future optically integrated, on-chip systems.

Operation of an optically coherent frequency comb outside the metrology lab.

We demonstrate a self-referenced fiber frequency comb that can operate outside the well-controlled optical laboratory. The frequency comb has residual optical linewidths of < 1 Hz, sub-radian residual optical phase noise, and residual pulse-to-pulse timing jitter of 2.4 - 5 fs, when locked to an optical reference. This fully phase-locked frequency comb has been successfully operated in a moving vehicle with 0.5 g peak accelerations and on a shaker table with a sustained 0.5 g rms integrated acceleration, while retaining its optical coherence and 5-fs-level timing jitter. This frequency comb should enable metrological measurements outside the laboratory with the precision and accuracy that are the hallmarks of comb-based systems.

Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz.

We demonstrate a dual-comb spectrometer using stabilized frequency combs spanning 177 to 220 THz (1360 to 1690 nm) in the near infrared. Comb-tooth-resolved measurements of amplitude and phase generate over 4×10(5) individually resolved spectral elements at 100 MHz point spacing and kilohertz-level resolution and accuracy. The signal-to-noise ratio is 100 to 3000 per comb tooth. Doppler-broadened phase and amplitude spectra of CO(2), CH(4), C(2)H(2), and H(2)O in a 30 m multipass cell agree with established spectral parameters, achieving high-resolution measurements with optical bandwidth generally associated with blackbody sources.

Coherent linear optical sampling at 15 bits of resolution.

Linear optical sampling characterizes a sample by measuring the distortions on a transmitted optical field, thereby quantifying the sample's optical response. By exploiting the high mutual coherence between two phase-locked femtosecond fiber lasers, we achieve very high signal-to-noise ratio measurements of transmitted optical electric fields through coherent averaging. We measure the optical electric fields with 15.16 bits of dynamic range (91 dB in intensity) and with 525 fs timing resolution over a 10 ns time window, in a 5.1 s averaging period.

Fiber-laser frequency combs with subhertz relative linewidths.

We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the heterodyne beat signal between two independent frequency combs that are phase locked to a common cw optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz relative linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter of approximately 1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is approximately 1 fs. This performance approaches that of Ti:sapphire frequency combs.

Observations on sound propagation in rapidly rotating Bose-Einstein condensates.

Repulsive laser potential pulses applied to vortex lattices of rapidly rotating Bose-Einstein condensates create propagating density waves which we have observed experimentally and modeled computationally to high accuracy. We have observed a rich variety of dynamical phenomena ranging from interference effects and shock-wave formation to anisotropic sound propagation.

Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates.

We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.

Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level.

We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates Omega > 99% of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy 2 variant Planck's over 2pi Omega. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.

Observation of Tkachenko oscillations in rapidly rotating Bose-Einstein condensates.

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.

Observation of long-lived vortex aggregates in rapidly rotating Bose-Einstein condensates.

We study the formation of large vortex aggregates in a rapidly rotating dilute-gas Bose-Einstein condensate. When we remove atoms from the rotating condensate with a tightly focused, resonant laser, the density can be locally suppressed, while fast circulation of a ring-shaped superflow around the area of suppressed density is maintained. Thus a giant vortex core comprising 7 to 60 phase singularities is formed. The giant core is only metastable, and it will refill with distinguishable single vortices after many rotation cycles. The surprisingly long lifetime of the core can be attributed to the influence of strong Coriolis forces in the condensate. In addition we have been able to follow the precession of off-center giant vortices for more than 20 cycles.

Nonequilibrium effects of anisotropic compression applied to vortex lattices in bose-einstein condensates.

We have studied the dynamics of large vortex lattices in a dilute-gas Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal structure, large-amplitude quadrupolar shape oscillations of the condensate are shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an m=-2 mode, we observe shifting of lattice planes, changes of lattice structure, and sheetlike structures in which individual vortices appear to have merged. Excitation of an m=+2 mode dissolves the regular lattice, leading to randomly arranged but still strictly parallel vortex lines.

Driving Bose-Einstein-condensate vorticity with a rotating normal cloud.

We have developed an evaporative cooling technique that accelerates the rotation of an ultracold 87Rb 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 condensate.

Use of surface-wave spectroscopy to characterize tilt modes of a vortex in a Bose-Einstein condensate.

A vortex in a condensate in a nonspherical trapping potential will in general experience a torque. The torque will induce tilting of the direction of the vortex axis. We observe this behavior experimentally and show that by applying small distortions to the trapping potential, we can control the tilting behavior. By suppressing vortex tilt, we have been able to hold the vortex axis along the line of sight for up to 15 sec. Alternatively, we can induce a 180 degrees tilt, effectively reversing the charge on the vortex as observed in the lab frame. We characterize the vortex nondestructively with a surface-wave spectroscopic technique.