Direct Frequency-Comb-Driven Raman Transitions in the Terahertz Range

Frequency comb measurements for 6G terahertz nano/microphotonics and metamaterials

Next-generation 6G communication holds the potential to revolutionize data transfer, enabling the realization of eXtended Reality (XR) with enhanced sensory experiences. To achieve this, advanced components such as high-performance intensity/phase modulators, waveguides, multiplexers, splitters, combiners, and filters operating in terahertz (THz) regime, specifically within the frequency range of 0.1-1 THz, are essential. However, existing microwave equipment and vector network analyzers designed for this frequency range suffer from limitations in resolution, stability, and accuracy when evaluating the intensity and phase responses of critical 6G THz devices. In this comprehensive review, we delve into the critical device requirements and emerging trends in next-generation 6G communication, essential performance evaluation parameters, comparisons between microwave and nano/microphotonic devices for testing, and the application of high-resolution THz sensors in 6G Internet-of-Things (IoT) scenarios. Notably, a frequency comb in the photonic regime emerges as the prime candidate for achieving precision evaluations of 6G networks and devices. Consequently, this review highlights the latest research in frequency comb measurements in the 6G THz frequency regime, with a particular emphasis on nano/microphotonic devices and metamaterials. The integration of frequency comb measurements into 6G and THz photonic devices and networks promises to accelerate the realization of high-density next-generation 6G communication.

Photonic comb-rooted synthesis of ultra-stable terahertz frequencies

Stable terahertz sources are required to advance high-precision terahertz applications such as molecular spectroscopy, terahertz radars, and wireless communications. Here, we demonstrate a photonic scheme of terahertz synthesis devised to bring the well-established feat of optical frequency comb stabilization down to the terahertz region. The source comb is stabilized to an ultra-low expansion optical cavity offering a frequency instability of 10-15 at 1-s integration. By photomixing a pair of comb lines extracted coherently from the source comb, terahertz frequencies of 0.10-1.10 THz are generated with an extremely low level of phase noise of -70 dBc/Hz at 1-Hz offset. The frequency instability measured for 0.66 THz is 4.4 × 10-15 at 1-s integration, which reduces to 5.1×10-17 at 65-s integration. Such unprecedented performance is expected to drastically improve the signal-to-noise ratio of terahertz radars, the resolving power of terahertz molecular spectroscopy, and the transmission capacity of wireless communications.

Atom Interferometer Driven by a Picosecond Frequency Comb

We demonstrate a light-pulse atom interferometer based on the diffraction of free-falling atoms by a picosecond frequency-comb laser. More specifically, we coherently split and recombine wave packets of cold ^{87}Rb atoms by driving stimulated Raman transitions between the |5s ^{2}S_{1/2},F=1⟩ and |5s ^{2}S_{1/2},F=2⟩ hyperfine states, using two trains of picosecond pulses in a counterpropagating geometry. We study the impact of the pulses' length as well as the interrogation time onto the contrast of the atom interferometer. Our experimental data are well reproduced by a numerical simulation based on an effective coupling that depends on the overlap between the pulses and the atomic cloud. These results pave the way for extending light-pulse interferometry to transitions in other spectral regions and therefore to other species, for new possibilities in metrology, sensing of gravito-inertial effects, and tests of fundamental physics.

Improved Isotope-Shift-Based Bounds on Bosons beyond the Standard Model through Measurements of the ^{2}D_{3/2}-^{2}D_{5/2} Interval in Ca^{+}

We perform high-resolution spectroscopy of the 3d ^{2}D_{3/2}-3d ^{2}D_{5/2} interval in all stable even isotopes of ^{A}Ca^{+} (A=40, 42, 44, 46, and 48) with an accuracy of ∼20  Hz using direct frequency-comb Raman spectroscopy. Combining these data with isotope shift measurements of the 4s ^{2}S_{1/2}↔3d ^{2}D_{5/2} transition, we carry out a King plot analysis with unprecedented sensitivity to coupling between electrons and neutrons by bosons beyond the standard model. Furthermore, we estimate the sensitivity to such bosons from equivalent spectroscopy in Ba^{+} and Yb^{+}. Finally, the data yield isotope shifts of the 4s ^{2}S_{1/2}↔3d ^{2}D_{3/2} transition at 10 parts per billion through combination with recent data of Knollmann, Patel, and Doret [Phys. Rev. A 100, 022514 (2019)PLRAAN2469-992610.1103/PhysRevA.100.022514].

A new Collinear Apparatus for Laser Spectroscopy and Applied Science (COALA)

We present a new collinear laser spectroscopy setup that has been designed to overcome systematic uncertainty limits arising from high-voltage and frequency measurements, beam superposition, and collisions with residual gas that are present in other installations utilizing this technique. The applied methods and experimental realizations are described, including an active stabilization of the ion-source potential, new types of ion sources that have not been used for collinear laser spectroscopy so far, dedicated installations for pump-and-probe measurements, and a versatile laser system referenced to a frequency comb. The advanced setup enables us to routinely determine transition frequencies, which was so far demonstrated only for a few cases and with lower accuracy at other facilities. It has also been designed to perform accurate high-voltage measurements for metrological applications. Demonstration and performance measurements were carried out with Ca⁺ and In⁺ ions.

Radio frequency polarization modulation based on an optical frequency comb

We propose a method to generate stabilized radio-frequency polarization modulation based on optical frequency combs. Two pulse trains with the same repetition rate and different offset frequencies generate arbitrary polarization states that are modulated at the offset frequency difference. Long-term stability of the polarization modulation is demonstrated with the modulation frequency at f_rep/2. Modulation at f_rep/4 is also demonstrated to show the flexibility of the technique. We employ an electrical delay line to fine-tune the polarization states that constitute the time-dependent modulation.

Optical frequency analysis on dark state of a single trapped ion

We demonstrate an optical frequency analysis method using the Fourier transform of detection times of fluorescence photons emitted from a single trapped ⁴⁰Ca⁺ ion. The response of the detected photon rate to the relative laser frequency deviations is recorded within the slope of a dark resonance formed in the lambda-type energy level scheme corresponding to two optical dipole transitions. This approach enhances the sensitivity to the small frequency deviations and does so with reciprocal dependence on the fluorescence rate. The employed lasers are phase locked to an optical frequency comb, which allows for precise calibration of optical frequency analysis by deterministic modulation of the analyzed laser beam with respect to the reference beam. The attainable high signal-to-noise ratios of up to a MHz range of modulation deviations and up to a hundred kHz modulation frequencies promise the applicability of the presented results in a broad range of optical spectroscopic applications.

Frequency-comb spectroscopy on pure quantum states of a single molecular ion

Spectroscopy is a powerful tool for studying molecules and is commonly performed on large thermal molecular ensembles that are perturbed by motional shifts and interactions with the environment and one another, resulting in convoluted spectra and limited resolution. Here, we use quantum-logic techniques to prepare a trapped molecular ion in a single quantum state, drive terahertz rotational transitions with an optical frequency comb, and read out the final state nondestructively, leaving the molecule ready for further manipulation. We can resolve rotational transitions to 11 significant digits and derive the rotational constant of 40CaH+ to be B R = 142 501 777.9(1.7) kilohertz. Our approach is suited for a wide range of molecular ions, including polyatomics and species relevant for tests of fundamental physics, chemistry, and astrophysics.

Initialization of quantum simulators by sympathetic cooling

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

Direct Kerr frequency comb atomic spectroscopy and stabilization

Microresonator-based soliton frequency combs, microcombs, have recently emerged to offer low-noise, photonic-chip sources for applications, spanning from timekeeping to optical-frequency synthesis and ranging. Broad optical bandwidth, brightness, coherence, and frequency stability have made frequency combs important to directly probe atoms and molecules, especially in trace gas detection, multiphoton light-atom interactions, and spectroscopy in the extreme ultraviolet. Here, we explore direct microcomb atomic spectroscopy, using a cascaded, two-photon 1529-nm atomic transition in a rubidium micromachined cell. Fine and simultaneous repetition rate and carrier-envelope offset frequency control of the soliton enables direct sub-Doppler and hyperfine spectroscopy. Moreover, the entire set of microcomb modes are stabilized to this atomic transition, yielding absolute optical-frequency fluctuations at the kilohertz level over a few seconds and <1-MHz day-to-day accuracy. Our work demonstrates direct atomic spectroscopy with Kerr microcombs and provides an atomic-stabilized microcomb laser source, operating across the telecom band for sensing, dimensional metrology, and communication.

Vanishing and Revival of Resonance Raman Scattering

The possibility to manipulate quantum coherence and interference, apart from its fundamental interest in quantum mechanics, is essential for controlling nonlinear optical processes such as high harmonic generation, multiphoton absorption, and stimulated Raman scattering. We show, analytically and numerically, how a nonlinear optical process via resonance Raman scattering (RRS) can be manipulated in a four-level double-Λ system by using pulsed laser fields. We find that two simultaneously excited RRS paths involved in the system can generate an ultimately destructive interference in the broad-bandwidth-limit regime. This, in turn, reduces the four-level system to an equivalent three-level system in a V configuration capable of naturally vanishing RRS effects. We further show that this counterintuitive phenomenon, i.e., the RRS vanishing, can be prevented by transferring a modulated phase of the laser pulse to the system at resonance frequencies. This work demonstrates a clear signature of both quantum destructive and constructive interference by actively controlling resonant multiphoton processes in multilevel quantum systems, and it therefore has potential applications in nonlinear optics, quantum control, and quantum information science.

Versatile Control of ^{9}Be^{+} Ions Using a Spectrally Tailored UV Frequency Comb

We demonstrate quantum control of ^{9}Be^{+} ions directly implemented by an optical frequency comb. Based on numerical simulations of the relevant processes in ^{9}Be^{+} for different magnetic field regimes, we demonstrate a wide applicability when controlling the comb's spectral properties. We introduce a novel technique for the selective and efficient generation of a spectrally tailored narrow-bandwidth optical frequency comb near 313 nm. We experimentally demonstrate internal state control and internal-motional state coupling of ^{9}Be^{+} ions implemented by stimulated-Raman manipulation using a spectrally optimized optical frequency comb. Our pulsed laser approach is a key enabling step for the implementation of quantum logic and quantum information experiments in Penning traps.

Phase transfer between three visible lasers for coherent population trapping

Stringent conditions on the phase relation of multiple photons are a prerequisite for novel protocols of high-resolution coherent spectroscopy. In a recent experiment, we have implemented an interrogation process of a Ca⁺-ion cloud based on three-photon coherent population trapping, with the potential to serve as a frequency reference in the THz range. This high-resolution interrogation has been made possible by phase-locking both laser sources for cooling and repumping of the trapped ions to a clock laser at 729 nm by means of an optical frequency comb. The clock laser, a titanium-sapphire laser built in our lab locked onto two high-finesse cavities reaches a linewidth of a few Hertz and a frequency stability below 10^-14 at 1 s, performances which can be copied onto the two other sources. In this paper, we discuss the performances of the phase transfer between the three involved lasers via the optical frequency comb.