Studying the coherent interaction of light with matter can give insight into both the properties of the matter and the interaction itself. Matter properties include information about the energy levels, electromagnetic susceptibilities, elementary excitations and their many-body dynamics. Typically these studies involve the use of a coherent spectroscopy such as transient four-wave-mixing or multidimensional coherent spectroscopy.

### Coherent interaction of light with semiconductors

Coherent spectroscopy of semiconductors tends to focus on excitons because they have a large oscillator strength and relatively long coherence times. Excitons were studied extensively since the 1980s using TFWM. Recently, we have been using the new technique of multidimensional coherent spectroscopy to improve our understanding of excitons in quantum wells and quantum dots.

In quantum wells, two-dimensional coherent spectroscopy clearly shows the essential role of many-body correlations in the coherent response of excitons (Li, 2006). Further studies show excellent agreement with a microscopic theory of the coherent response, but only when many-body correlations beyond a mean field treatment were included (Zhang, 2007). Recently, we have been using two-dimensional spectroscopy to study 110-oriented quantum wells, n-doped CdTe quantum wells and InAs double wells.

More recently, we have used two-dimensional coherent spectroscopy to study epitaxially grown semiconductor quantum dots, both “natural” quantum dots and InAs dots. A big advantage of two-dimensional coherent spectroscopy is the ability to make measurements as a function of energy within the inhomogeneous distribution, which is equivalent to making measurements as function of quantum dot size. The studies of natural quantum dots have looked at the interaction of excitons with phonons and other excitons (Moody, 2011a) and the relaxation from the quantum wells states into the quantum dots (Moody, 2011b). In InAs dots, we observe that the biexciton binding energy does not vary with dot size (Moody, 2013a) and that an upper cross peak can appear due to χ(5) contributions (Moody, 2013b). It is also possible to observe the fine structure splitting (Moody, 2013c).

### Semiconductor quantum optics

Traditional spectroscopy only exploits the classical properties of light, such as it intensity of wavelength. However, more information can be by varying the quantum statistics of light. However, this is challenging because the most interesting effects occur at high excitation level, and it is difficult to generate high intensity states with any statistics other than a coherent state. One approach to overcoming this difficulty is to use the Glauber-Sudershan formula, which allows a measurement for arbitrary quantum-optical statistics to be expressed in terms of measurements for coherent states (Kira, 2011). We are currently using this approach to search for exotic quasi-particles in an optically excited semiconductor.

We are also pursuing methods of generating intense light with statistics other a coherent state. As a first step, we need the ability to measure the quantum statistics. We implemented an optical homodyne tomography setup. A strong local oscillator (LO) is mixed with a weak source and light is split equally between two detectors. The difference of the two photocurrents is proportional to the product of the electric fields of the local oscillator and source. With this technique, we can reconstruct the full quantum state of the source pulse with a time resolution equal to the duration of the LO pulse. We employ two LO pulses to sample the source pulse at different times t_{1}and t_{2}, and extract the second order correlation function g^{(2)}(t_{1},t_{2}) using the technique developed by Mike Raymer’s group at the University of Oregon.

We have demonstrated this technique by characterizing pulses from the same laser that produces the LO, which gives a coherent state. We have also used it to characterize the emission of a laser diode below and above threshold. Below threshold the output corresponds to a thermal state, whereas above threshold it transitions to a coherent state. Our results show that just above threshold, the output is noisier than expected from semiclassical laser theory (Roumpos, 2013a).

This work is mostly done in collaboration with Mackillo Kira at the University of Marburg, Germany.

### Coherent optical phenomena in atomic gases

We have been using multidimensional coherent spectroscopy to study atomic vapors, mainly potassium and rubidium. Our initial experiments used a potassium vapor as a “test” system for which the two-dimensional spectrum could be calculated exactly using the optical Bloch equations (Dai, 2010). More recent work showed that the double quantum spectrum of a potassium vapor showed clear resonances, although no resonances were expected based on the single-atom level structure (Dai, 2012). These double quantum resonances are due to interactions amongst the atoms. Currently we are working on improving our understanding of these effects by studying rubidium, where a double-quantum signal does arise from the single atom level structure, and thus provides a “reference” too which the interaction induced signal can be compared.

We have also used a potassium vapor as a test system to demonstrate three-dimensional coherent spectroscopy and show that it can be used to extract the parameters of the Hamiltonian governing the atoms and their interaction with light. These measurements could provide necessary information for implementations of coherent control (Li, 2013).

Currently, we are beginning to apply multidimensional spectroscopy to electronic transition in diatomic molecules.

### Previous areas of research

Our group is currently active in the research areas listed above. We have worked on a number of additional areas in the past including surface second harmonic generation, spin dynamics, quantum interference of injected photocurrents and the Franz-Keldysh effect.