Optical two-dimensional coherent spectroscopy (2DCS) has become a powerful tool for studying energy-level structure, dynamics, and coupling in many systems including atomic ensembles. Various types of two-dimensional (2D) spectra, including the so-called single-quantum, zero-quantum, and double-quantum 2D spectra, of both
D lines (
D1 and
D2 transitions) of potassium (K) atoms have been reported previously. For rubidium (Rb), a major difference is that the
D lines are about 15 nm apart as opposed to only about 3 nm for K. Simultaneously exciting both
D lines of Rb atoms requires a broader laser bandwidth for the experiment. Here, we report a broadband optical 2DCS experiment in a Rb atomic vapor. A complete set of single-quantum, zero-quantum, and double-quantum 2D spectra including both
D lines of Rb atoms were obtained. The experimental spectra were reproduced by simulated 2D spectra based on the perturbation solutions to the optical Bloch equations. This work in Rb atoms complements previous 2DCS studies of K and Rb with a narrower bandwidth that covers two
D lines of K or only a single
D line of Rb. The broadband excitation enables the capability to perform double-quantum and multiquantum 2DCS of both
D lines of Rb to study many-body interactions and correlations in comparison with K atoms.
Interactions between particles in quantum many-body systems play a crucial role in determining the electric, magnetic, optical, and thermal properties of the system. The recent progress in the laser-pulse technique has enabled the manipulations and measurements of physical properties on ultrafast timescales. Here we propose a method for the direct and ultrafast probing of quantum many-body interaction through coherent two-dimensional (2D) spectroscopy. Using a two-band fermionic Hubbard model for the minimum two-site lattice system, we find that the 2D spectrum of a noninteracting system contains only diagonal peaks; the interparticle interaction manifests itself in the emergence of off-diagonal peaks in the 2D spectrum before all the peaks coalesce into a single diagonal peak as the system approaches the strongly interacting limit. The evolution of the 2D spectrum as a function of the time delay between the second and third laser pulses can provide important information on the ultrafast time variation of the interaction.
Optical two-dimensional coherent spectroscopy (2DCS) is a powerful ultrafast spectroscopic technique that can greatly benefit from the unique features of a femtosecond laser operating at a kHz repetition rate. However, isolating specific nonlinear signal in the collinear geometry, especially with a kHz laser, presents challenges. We present an experimental implementation of optical 2DCS in a collinear geometry using a femtosecond laser operating at a 5 KHz repetition rate. The desired nonlinear signal is selectively extracted in the frequency domain by lock-in detection. Both pump-probe and optical 2DCS experiments were conducted on a rubidium vapor. The signal-to-noise ratio of pump-probe and 2DCS spectra was characterised under various experimental parameters. The study highlights the importance of the lock-in reference frequency in overcoming the limitations imposed by low repetition rates, thereby paving the way for the application of collinear optical 2DCS in material systems requiring kHz femtosecond lasers.
We propose and demonstrate pump-probe spectroscopy of rubidium absorption that reveals the sub-Doppler hyperfine structure of the ${}^{5}{\mathrm{S}}_{1/2}\ensuremath{\leftrightarrow}{}^{5}{\mathrm{P}}_{3/2}$ (
D2) transitions. The counterpropagating pump and probe lasers are independently tunable in frequency, with the probe operating at the single-photon level. The two-dimensional spectrum measured as the laser frequencies are scanned shows fluorescence, Doppler-broadened absorption dips, and sub-Doppler features. The detuning between the pump and probe lasers allows compensation of the Doppler shift for all atomic velocities in the room-temperature vapor, meaning we observe sub-Doppler features for all atoms in the beam. We detail a theoretical model of the system that incorporates fluorescence, saturation effects, and optical pumping and compare this with the measured spectrum, finding a mean absolute percentage error of 3.11%. This high level of agreement allows us to extract the number density and temperature of the
Rb vapor from the two-dimensional spectrum. In the future this technique could be used as an atomic frequency standard for calibrating and characterising a single-photon or low-light-level source.
Femtosecond phase-coherent two-dimensional (2D) spectroscopy has been experimentally demonstrated as the direct optical analog of 2D nuclear magnetic resonance. An acousto-optic pulse shaper created a collinear three-pulse sequence with well-controlled and variable interpulse delays and phases,which interacted with a model atomic system of rubidium vapor. The desired nonlinear polarization was selected by phase cycling (coadding experimental results obtained with different interpulse phases). This method may enhance our ability to probe the femtosecond structural dynamics of macromolecules.