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We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

Fast optical pulses create a plasma of electrons and holes in a semiconductor in which excitons (pairs of holes and electrons) and combinations of two excitons emerge; now a stable liquid-like droplet of electrons and holes has been detected and called a ‘dropleton’. Excitons, plasmons and phonons are some of the better known quasiparticles — exotic entities that act in some respects like ordinary particles. New types do not come along all that often but here is one — a fundamentally new many-body particle named the 'dropleton'. Mackillo Kira and colleagues have identified this new quantum entity, a quantum droplet created when four or more electrons and holes (electronic vacancies) form a tiny correlation bubble via the Coulomb attraction, in direct-gap semiconductors such as gallium arsenide. The cover illustrates the pair-correlation function g(r) of quantum droplets — the central peak of the correlation function shows that electrons and holes are likely to be co-located and the ripples show that otherwise they form regularly spaced shells. Interacting many-body systems are characterized by stable configurations of objects—ranging from elementary particles to cosmological formations1,2,3—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 charge4,5 which in turn affects the material’s conductivity, optical response or phase transitions2,6,7. Additional quasiparticle interactions may also create strongly correlated configurations yielding new macroscopic phenomena, such as the emergence of a Mott insulator8, superconductivity or the pseudogap phase of high-temperature superconductors9,10,11. In semiconductors, a conduction-band electron attracts a valence-band hole (electronic vacancy) to create a bound pair, known as an exciton12,13, which is yet another quasiparticle. Two excitons may also bind together to give molecules, often referred to as biexcitons14, and even polyexcitons may exist15,16. In indirect-gap semiconductors such as germanium or silicon, a thermodynamic phase transition may produce electron–hole droplets whose diameter can approach the micrometre range17,18. 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.

We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum, and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the double well coherent optical response. Coherent and incoherent contributions to the coupling between the two quantum well excitons are clearly separated. An excellent agreement with density matrix calculations reveals that coherent interwell coupling originates from many-body interactions.

The homogeneous and inhomogeneous linewidths of the heavy-hole exciton resonance in a (110)-oriented GaAs multiple-quantum-well sample are measured using optical two-dimensional Fourier transform spectroscopy. By probing the optical nonlinear response for polarization along the in-plane crystal axes [1$\overline{1}$0] and [001], we measure different homogeneous linewidths for the two orthogonal directions. This difference is found to be due to anisotropic excitation-induced dephasing, caused by a crystal-axis-dependent absorption coefficient. The extrapolated zero-excitation density homogeneous linewidth exhibits an activation-like temperature dependence. We find that the homogeneous linewidth extrapolated to zero excitation density and temperature is $\ensuremath{\sim}$34 $\ensuremath{\mu}$eV, while the inhomogeneous linewidth is $\ensuremath{\sim}$1.9 meV for both polarizations.

In optical two-dimensional Fourier-transform (2DFT) spectroscopy, understanding how the spectral line shape is affected by pulse propagation in the sample is crucial for an accurate interpretation of spectra. We report an experimental study of pulse propagation effects in 2DFT spectroscopy performed in a dense atomic vapor. The spectral line shape can be dramatically distorted due to high optical density as well as the physical thickness of a sample. The spectral distortion can be partially corrected by using a reference pulse copropagating with the signal combined with appropriate data processing.

Optical single- and double-quantum three-dimensional Fourier-transform spectra are obtained for atomic vapors. We show that three-dimensional spectra can be used to identify the Hamiltonian of complex systems and to reveal the nature of many-body interactions.

Exciton, trion, and biexciton dephasing rates are measured for an ensemble of InAs quantum dots using two-dimensional Fourier-transform spectroscopy. The two-dimensional spectra reveal that the dephasing rate of each excitonic state is similar for all dots in the ensemble and the rates are independent of excitation density. An additional spectral feature (too weak to be observed in the time-integrated four-wave mixing signal) appears at high excitation density and is attributed to the ${\ensuremath{\chi}}^{(5)}$ biexcitonic nonlinear response.

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., Knowledge of the Hamiltonian of a quantum system is essential for predicting and controlling its behaviour. Li et al. use optical three-dimensional Fourier-transform spectroscopy to separate and study each pathway, gaining quantitative insight into the quantum pathways of an atomic vapour Hamiltonian.

The emission energy dependence of the biexciton binding energy is investigated in three semiconductor quantum dot (QD) systems that exhibit different quantum well $\ensuremath{\rightarrow}$ QD confinement. Using two-dimensional Fourier-transform spectroscopy, we demonstrate that in strongly confining InAs QDs, the binding energy is independent of exciton emission energy and fluctuations in the ground state $\ensuremath{\rightarrow}$ exciton transition energy are strongly correlated with those of the exciton $\ensuremath{\rightarrow}$ biexciton. In contrast, the biexciton binding energy increases with emission energy in weakly confining interfacial GaAs QDs, and the level of correlation of exciton-biexciton broadening is reduced. A comparison with simulations reveals the significance of the strength and nature of confinement on Coulomb interactions responsible for biexciton renormalization.

We study asymmetric double InGaAs quantum well samples, featuring three different barrier widths, using optical two-dimensional Fourier transform spectroscopy. Depending on the barrier width, we observe different coupling mechanisms between the two wells.

We present the use of three-dimensional coherent spectroscopy to isolate quantum pathways. Isolation of individual quantum pathways allows the parameters of the Hamiltonian to be determined. We demonstrate this possibility using an atomic vapor.

Coherent excitonic interactions in an InGaAs asymmetric double quantum well are studied using two-dimensional coherent spectroscopy. Density matrix calculations reveal that an excitation-induced shift is the dominant many-body interaction responsible for the coupling.

We report a 2DFT spectroscopic study of many-body interactions in a GaAs quantum well sample optically excited by a pre-pulse. The 2D spectra reveal quantitative information about the many-body states prepared with various pre-pulse intensities.

The frequency-frequency correlation function for excitons in a GaAs quantum well is measured using optical two-dimensional Fourier transform spectroscopy and a numerical fitting procedure. We also report frequency-frequency correlation functions for biexciton and two-exciton states.

We report crystal-axis dependent homogeneous linewidths of the heavy hole exciton resonance in a (110)-oriented GaAs quantum well measured using two-dimensional Fourier transform spectroscopy. The increase in homogeneous linewidth with temperature shows an activation-like behavior.

The phenomenon of spectral diffusion is common to a variety of inhomogeneously broadened systems. Spectral diffusion can be quantified through the frequency–frequency correlation function (FFCF), which is often approximated using observables from a variety of experimental techniques. We present a direct measurement of the temperature-dependent FFCF for excitons in semiconductor quantum wells using two-dimensional coherent spectroscopy. This technique enables the FFCF to be quantified without making any assumptions of the FFCF dynamics. Our results show that the Gauss–Markov approximation, which assumes exponential decay dynamics of the FFCF, is only valid for sample temperatures above 50 K. We compare our results with those obtained by the ellipticity and center-line slope measurements.

Studies have shown that many-body interactions among semiconductor excitons can produce distinct features in two-dimensional optical spectra. However, to the best of our knowledge, the dynamics of many-body interactions have not been measured in two-dimensional (2D) spectroscopy studies. Here we measure 2D spectra of GaAs quantum wells at many different ``waiting'' times and study the time dependence of the spectral features. Characteristic signatures of exciton polarization correlations manifest in the diagonal peaks decay at the exciton dephasing rate, consistent with theoretical predictions. Other many-body interactions manifest in off-diagonal features decay much more slowly. These persistent off-diagonal features must be due to many-body interactions involving exciton populations, and their persistence cannot be predicted by theoretical descriptions restricted to the coherent limit.

Exchange-mediated fine-structure splitting of bright excitons in an ensemble of InAs quantum dots is studied using optical two-dimensional Fourier-transform spectroscopy. By monitoring the non-radiative coherence between the bright states, we find that the fine-structure splitting decreases with increasing exciton emission energy at a rate of 0.1 μ eV / meV . Dephasing rates are compared to population decay rates to reveal that pure dephasing causes the exciton optical coherences to decay faster than the radiative limit at low temperature, independent of excitation density. Fluctuations of the bright state transition energies are nearly perfectly correlated, protecting the non-radiative coherence from interband dephasing mechanisms.

Many-body interactions in a doped CdTe/CdMgTe quantum well are investigated using optical 2D Fourier-transform spectroscopy. The nature of coherent exciton-trion correlations is examined by analyzing lineshapes in the 2D spectra.

We present an experimental and theoretical study of phase-dependent interference effects in multi-photon excitation under bichromatic radio-frequency (rf) field. Using an intense rf pulse, we study the interference between the three-photon and one-photon transition between the Zeeman sub-levels of the ground state of $^{87}$Rb that allows us to determine the carrier-envelope phase of the fields even for long pulses., 10 pages, 5 figures

We present an experimental and theoretical study of Carrier-Envelope Phase effects on bound state atomic excitation. We investigated the influence of CEP on multiphoton transitions between the Zeeman sublevels of the ground state of 87Rb.

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 ${10}^{12}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$.

Optical multidimensional Fourier transform spectroscopy excites a sample with a sequence of ultrafast pulses. A spectrum is constructed by taking Fourier transforms with respect to pulse delays, which are interferometrically controlled.

We study the superfluorescence (SF) from a gas of rubidium atoms. The atoms of a dense vapor are excited to the 5D state from the 5S state by a two-photon process driven by 100-fs laser pulses. The atoms decay to the 6P state and then to the 5S state. The SF emission at 420 nm on the 6P-5S transition is recorded by a streak camera with picosecond time resolution. The time duration of the generated SF is tens of picoseconds, which is much shorter than the time scale of the usual relaxation processes, including spontaneous emission and atomic coherence dephasing. The dependence of the time delay between the reference input pulse and SF is measured as a function of laser power. The experimental data are described quantitatively by a simulation based on the semiclassical atom-field interaction theory. The observed change in scaling laws for the peak intensity and delay time can be elucidated by an SF theory in which the sample length is larger than the cooperation length.

We present an experimental and theoretical study of carrier-envelope phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigated the influence of CEP on the control of phase dependent multi-photon transitions between the Zeeman sub-levels of the ground state of $^{87}$Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better then the period of optical oscillations., 8 Pages, 6 Figures

We have experimentally demonstrated an ultra-dispersive optical prism made from a coherently driven Rb atomic vapor. The prism possesses spectral angular dispersion that is 6 orders of magnitude higher than that of a prism made of optical glass; such angular dispersion allows one to spatially resolve light beams with different frequencies separated by a few kilohertz. The prism operates near the resonant frequency of atomic vapor and its dispersion is optically controlled by a coherent driving field.

We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. We discuss the implications and possible applications of our results.

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.

We have experimentally studied propagation of two optical fields in a dense rubidium (Rb) vapor in the case when an additional microwave field is coupled to the hyperfine levels of Rb atoms. The Rb energy levels form a close-lambda three-level system coupled to the optical fields and the microwave field. It has been found that the maximum transmission of a probe field depends on the relative phase between the optical and the microwave fields. We have observed both constructive and destructive interference in electromagnetically induced transparency (EIT). A simple theoretical model and a numerical simulation have been developed to explain the observed experimental results., 7 pages, 6 figures

We study the dipole-dipole spectral broadening of a resonance line at high atomic densities when the self-broadening dominates. The selective reflection spectrum of a weak probe beam from the interface of the cell window and rubidium vapor are recorded in the presence of a far-detuned pump beam. The excitation due to the pump reduces the self-broadening. We found that the self-broadening reduction dependence on the pump power is atomic density independent. These results provide experimental evidence for the disordered exciton based theory of self-broadening, and can be useful for the description of the interaction of a strong optical field with a dense resonance medium., 4 pages, 6 figures

We have studied phase dynamics in EIT. We observed how the transmission decreases and recovers when the phase of the optical field changes abruptly. The result can be used for the fast control of EIT.

We study the possibility of creating spatial patterns having subwavelength size by using the so-called dark states formed by the interaction between atoms and optical fields. These optical fields have a specified spatial distribution. Our experiments in Rb vapor display spatial patterns that are smaller than the length determined by the diffraction limit of the optical system used in the experiment. This approach may have applications to interference lithography and might be used in coherent Raman spectroscopy to create patterns with subwavelength spatial resolution., Comment: 5 pages, 5 figures

Performing experiments with Rb-atoms and RF fields, we have demonstrated several nonlinear effects, such as multi-photon transitions and excitation of coherence using far-detuned field with different time-shape pulses. Our results agree with our theoretical predictions.

We have experimentally demonstrated an ultra-dispersive atomic prism with the highest spectral angular dispersion ever shown (six orders of magnitude higher than glass prism). Its dispersion is optically controlled by a coherent driving field.

We have theoretically predicted and experimentally demonstrated an ultra-dispersive atomic prism made of coherently driven Rb atomic vapor. The prism posses spectral angular dispersion that six orders of magnetude higher than the prism made from optical glass; it is the highest spectral angular dispersion that has been ever shown (such angular dispersion allows one to resolve spatially light separated by a few kHz). The prism is working near the resonant frequency of atomic vapor, and its dispersion is optically controlled by coherent driving field.

We study the EIT of Rb vapor under the condition when a microwave field resonant to the hyperfine transition has been applied. Developed theory and applications will be discussed.

We review our recent work on multi-dimensional coherent optical spectroscopy (MDCS) of semiconductor nanostructures. Two approaches, appropriate for the study of semiconductor materials, are presented and compared. A first method is based on a non-collinear geometry, where the Four-Wave-Mixing (FWM) signal is detected in the form of a radiated optical field. This approach works for samples with translational symmetry, such as Quantum Wells (QWs) or large and dense ensembles of Quantum Dots (QDs). A second method detects the FWM in the form of a photocurrent in a collinear geometry. This second approach extends the horizon of MDCS to sub-diffraction nanostructures, such as single QDs, nanowires, or nanotubes, and small ensembles thereof. Examples of experimental results obtained on semiconductor QW structures are given for each method. In particular, it is shown how MDCS can assess coupling between excitons confined in separated QWs.

We report the experimental observation of EIT in Cs2 in Lambda configuration. The width of EIT is smaller than widths of molecular transitions and has different dependence on temperature. Application to quantum storage is discussed.

A novel lipase-producing thermophilic strain TW1, assigned to Geobacillus sp. TW1 based on 16S rRNA sequence, was isolated from a hot spring in China. Based on this strain, a lipase gene encoding 417 amino acids was cloned. Subsequently, the lipase gene was expressed in Escherichia coli and purified as a fusion protein with glutathione S-transferase. The results showed that the recombinant lipase had an activity optimum at 40 degrees C and pH at 7.0-8.0. It was active up to 90 degrees C at pH 7.5, and stable over a wide pH ranging from 6.0 to 9.0. The recombinant lipase was stable in 1 mM enzyme inhibitors (EDTA, 2-ME, SDS, PMSF or DTT), as well as in 0.1% detergents (Tween 20, Chaps or Triton X-100). Its catalytic function was enhanced in the presence of Ca(2+), Mg(2+), Zn(2+), Fe(2+) or Fe(3+), but inhibited by Cu(2+), Mn(2+), and Li(+). By comparison with the crude lipase, the recombinant lipase had similar properties and was characteristic of thermostable enzymes. Our study presented a rapid overexpression and purification of the lipase gene from thermophile, aimed at improving the enzyme yield for industrial applications.

Quantitative knowledge of a system’s Hamiltonian enables researchers to predict and control quantum systems.

We have developed a technique to perform optical two-dimensional Fourier-transform (2DFT) spectroscopy in a reflection geometry. Various reflection 2DFT spectra are obtained for an atomic vapor. The technique is useful for the cases where optical 2DFT spectroscopy cannot be performed in the transmission geometry.

We report the observation of coherent UV light pulses by the coherent scattering of IR pulses from atomic rubidium vapor. Rubidium atoms were first excited by a 100 fs pulse from the 5S ground state to the 5D state via a two-photon transition. The atoms were then pumped by an IR pulse resonant to the 5D–12P transition. The presence of the IR pulse triggered the instantaneous emission of a UV light pulse on the 12P–5S transition. The pulse had a time duration of tens of picoseconds, which was measured by a picosecond-resolution streak camera. The temporal shape of the generated light is explained by a simplified atom–field interaction theory.

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 studied the noise spectra in a nonlinear magneto-optical rotation experiment in a rubidium vapor. We observed the reduction of noise in the intensity difference of two orthogonally polarized components of the laser beam. The dependence of the noise level on both the frequency and the longitudinal magnetic field has been studied. We found that the optimal condition for the noise reduction is to work around zero longitudinal magnetic field, where the intensity correlation between the two orthogonally polarized components is maximum. Our results can be used to reduce or eliminate the atomic excess noise, therefore improving the sensitivity of nonlinear magneto-optical rotation magnetometers and other atom-optical based applications., Comment: 5 pages, 5 figures

We study sub-Doppler saturation resonances at cesium molecular transitions in the absorption band B1Πu ← X1∑g+ near 780 nm by using a commercial diode laser. The saturation power is measured as low as 5.7 mW with the laser beam diameter of 0.1 cm. Optical saturation is associated with the optical pumping of molecular ground-state levels. The long relaxation time of ground-state levels could attract interest to electromagnetically induced transparency and quantum state memory in the molecular gas. We propose to use the molecular transitions as references for doubled-frequency sources in the communication band around 1550 nm.