We derive an analytical form for resonance lineshapes in two-dimensional (2D) Fourier transform spectroscopy. Our starting point is the solution of the optical Bloch equations for a two-level system in the 2D time domain. Application of the projection-slice theorem of 2D Fourier transforms reveals the form of diagonal and cross-diagonal slices in the 2D frequency data for arbitrary inhomogeneity. The results are applied in quantitative measurements of homogeneous and inhomogeneous broadening of multiple resonances in experimental data.

We have experimentally studied the propagation of two optical fields in a dense rubidium ͑Rb͒ gas in the case when an additional microwave field is coupled to the hyperfine levels of Rb atoms. The Rb energy levels form a close-⌳ three-level system coupled to the optical fields and the microwave field. It has been found that the maximum transmission of the probe field depends on the relative phase between the optical and the microwave fields. We have observed both constructive and destructive interferences in electromagnetically induced transparency. A simple theoretical model and a numerical simulation have been developed to explain the observed experimental results.

We report the observation of double-quantum coherence signals in a gas of potassium atoms at twice the frequency of the one-quantum coherences. Since a single atom does not have a state at the corresponding energy, this observation must be attributed to a collective resonance involving multiple atoms. These resonances are induced by weak interatomic dipole-dipole interactions, which means that the atoms cannot be treated in isolation, even at a low density of 1012 cm−3.

Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system’s nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system’s Hamiltonian.

Interacting many-body systems are characterized by stable configurations of objects--ranging from elementary particles to cosmological formations--that also act as building blocks for more complicated structures. It is often possible to incorporate interactions in theoretical treatments of crystalline solids by introducing suitable quasiparticles that have an effective mass, spin or charge which in turn affects the material's conductivity, optical response or phase transitions. Additional quasiparticle interactions may also create strongly correlated configurations yielding new macroscopic phenomena, such as the emergence of a Mott insulator, superconductivity or the pseudogap phase of high-temperature superconductors. In semiconductors, a conduction-band electron attracts a valence-band hole (electronic vacancy) to create a bound pair, known as an exciton, which is yet another quasiparticle. Two excitons may also bind together to give molecules, often referred to as biexcitons, and even polyexcitons may exist. In indirect-gap semiconductors such as germanium or silicon, a thermodynamic phase transition may produce electron-hole droplets whose diameter can approach the micrometre range. In direct-gap semiconductors such as gallium arsenide, the exciton lifetime is too short for such a thermodynamic process. Instead, different quasiparticle configurations are stabilized dominantly by many-body interactions, not by thermalization. The resulting non-equilibrium quantum kinetics is so complicated that stable aggregates containing three or more Coulomb-correlated electron-hole pairs remain mostly unexplored. Here we study such complex aggregates and identify a new stable configuration of charged particles that we call a quantum droplet. This configuration exists in a plasma and exhibits quantization owing to its small size. It is charge neutral and contains a small number of particles with a pair-correlation function that is characteristic of a liquid. We present experimental and theoretical evidence for the existence of quantum droplets in an electron-hole plasma created in a gallium arsenide quantum well by ultrashort optical pulses.

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We study dynamics of a two-level system driven by a strong off-resonant electromagnetic field. We derive an analytical solution for arbitrary pulse shape. We discuss possible applications and presented experimental demonstration of the results obtained.

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