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Physical Review X

Optical Preparation and Coherent Control of Ultrafast Nonlinear Quantum Superpositions in Exciton Gases: A Case Study for Atomically Thin Semiconductors

Florian Katsch, Andreas Knorr

Published Nov 24, 2020• 17 citations
Publisher

Abstract

We report on the optical preparation of coherent superpositions of exciton and biexciton states manifested in temporal nonlinear oscillations in interacting exciton gases.The effect is illustrated for atomically thin semiconductors, where the reflected light reveals these interactions in a unique way.The occurring nonlinear coherent oscillations are counteracted by incoherent excitation-induced dephasing, a phenomenon which originates from a new type of quantum interference between excitons and the twoexciton scattering continuum.To improve the experimental accessibility, we discuss different methods to control the oscillation modulation depth by modifying the mutual interplay of the exciton-biexciton superposition and excitation-induced dephasing.We find that the coherent optical response can be manipulated by the polarization degree of the exciting light field, the laser detuning, external magnetic fields, and quantum coherent feedback.The extraordinary temporal behavior and its control distinguishes the nonlinear coherent oscillations from atomic Rabi oscillations and enables their engineering based on our proposed control schemes.

DOI
10.1103/physrevx.10.041039

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We report on the optical preparation of coherent superpositions of exciton and biexciton states manifested in temporal nonlinear oscillations in interacting exciton gases.The effect is illustrated for atomically thin semiconductors, where the reflected light reveals these interactions in a unique way.The occurring nonlinear coherent oscillations are counteracted by incoherent excitation-induced dephasing, a phenomenon which originates from a new type of quantum interference between excitons and the twoexciton scattering continuum.To improve the experimental accessibility, we discuss different methods to control the oscillation modulation depth by modifying the mutual interplay of the exciton-biexciton superposition and excitation-induced dephasing.We find that the coherent optical response can be manipulated by the polarization degree of the exciting light field, the laser detuning, external magnetic fields, and quantum coherent feedback.The extraordinary temporal behavior and its control distinguishes the nonlinear coherent oscillations from atomic Rabi oscillations and enables their engineering based on our proposed control schemes.
Turbulence and chaos in a semiconductor crystal? These are just some of the intriguing predictions of nonlinear optics with coherent excitons. In this chapter we discuss some aspects of nonlinear coherent optics with the participation of the excitons, photons, and biexcitons. As in many nonlinear systems, these effects arise because of feedback mechanisms, i.e., the light impinging on the system affects the electronic states, which in turn affect the dielectric constant of the medium through which the light passes. These effects are closely related to the phenomena of self-organization [1-8] and optical bistability [7-10] and self-pulsations and the appearance of chaos [2-6]. The cooperative nonlinear coherent processes in optical systems have recently attracted much attention [7-20]. These investigations have stimulated the development of new mathematical methods [21-31] and have opened up possibilities for many new applications. The theoretical and the experimental investigations in these directions give rise to the theory of solitons [32∧2] and lead to the new developments in the optics of ultrashort pulses [43-58]. Ultrafast phenomena such as self-induced transparency and nutation are related to the propagation of solitons and pulse trains, whereas the transient stages of the ultrashort lightpulse penetration in the media are described by area theorems. These coherent ultrafast phenomena typically take place during intervals of time less than the relaxation time, i.e., femtoseconds to picoseconds in typical solids. Collisions and incoherent scattering processes destroy the coherent evolution of the excited particles. But if coherent macroscopic states of the excitons, photons, and biexcitons have been formed because of spontaneous or induced BEC, in this case one can consider their time evolution over intervals of time much greater than the relaxation time.
Two-pair correlations are shown to induce dependences of the nonlinear optical response of semiconductors that can be used for a coherent manipulation of the resulting emission. Influences of biexcitonic transitions as well as transitions to two-pair scattering states are discussed within a microscopic density matrix approach. It is shown that the coherent control of biexciton beats is selective with respect to the propagation direction of the emitted signal, in contrast to the control of beats where all beat partners are generated by single photon processes. Furthermore, it is demonstrated that memory structures induced by exciton?exciton scattering states enable coherent manipulations of the excitonic line shape that allow us to estimate lower bounds for the corresponding memory time from experimentally accessible data.
Optically induced coherences reveal key features of nonlinearities in the optical response of semiconductors and can be employed to obtain information about dynamical processes via such techniques as transient four-wave mixing and differential transmission. This thesis presents experimental observations of three previously unrecognized aspects of coherent nonlinear optical phenomena occurring in gallium arsenide and multiple quantum wells: excitation-induced dephasing, two-photon biexcitonic coherence, and electronic Raman coherence. Results are analyzed using optical Bloch equations, which emphasize the potential generalization to other semiconductor systems. Excitation-induced dephasing is similar to classical line broadening. The work in this thesis shows for the first time that this incoherent effect is directly responsible for the dominant coherent optical nonlinearity in bulk gallium arsenide. Exact analytic models show that excitation-induced dephasing accounts for the previously unexplained polarization and density dependence of four-wave mixing signals obtained at the 1s exciton resonances in gallium arsenide. This thesis also presents the first observation of the two-photon biexcitonic coherence in a gallium arsenide multiple quantum well using a modified Michelson phase-conjugate interferometer to directly observe the 770-Terahertz oscillation of the nonradiative superposition of the electronic ground state and the biexciton state. The contribution of the two-photon coherence to the nonlinear optical response is thereby confirmed, in addition to the well-known stepwise biexcitonic response. Finally, the short-lived electronic Raman coherence between the light- and heavy-hole 1s excitons in gallium arsenide is conclusively demonstrated for the first time. The Raman coherence provides direct access to dephasing processes not detectable in conventional linear spectroscopy. Similar non-radiative coherences are related to population trapping, electromagnetically induced transparency, and lasing without inversion in atomic systems, and the new observations in gallium arsenide suggest that analogous phenomena may occur in semiconductors.
We present an overview of our results concerning the influence of two-pair continuum coherences on the transient nonlinear optical response of semiconductor microcavities. We show that the interplay between these 4-particle coherences and the nonperturbative light-matter interaction produces highly desirable almost decoherence-free exciton-exciton collisions on the lower polariton branch. This effect gives rise to the very different nonlinear absorption rates on the two polariton branches observed in many experiments and make possible to reach a very high degree of amplification in samples with large Rabi splitting. Moreover, we show that the availability of almost decoherence free exciton-exciton collisions can be used for the realization of coherent trapping of polariton emission and amplification. This coherent manipulation and trapping of many-particle polariton states can be performed employing both ultrafast and continuous wave operation.
The focus of the thesis is nonlinear transient optical properties and coherent control of single interface fluctuation quantum dots (QD's). When single exciton and biexciton resonances were driven by strong resonant laser pulses, Rabi oscillations of these transitions were observed in the differential transmission (DT) geometry. These results extend the concept of coherent control to the limit of single quantum confined systems in solids and have important implications for the feasibility of building quantum information processing devices using semiconductor QD's. Exciton Rabi oscillations are equivalent to arbitrary single-bit operations. The pulsed control of the exciton-biexciton transition is utilized as the optical operation for building a two-bit controlled rotational gates (CROT) in a single QD. A fidelity of 0.79 was obtained from numerical evaluation of the gate operation itself assuming typical decay parameters measured from these dots. Next, the nonradiative quantum coherence between two orthogonally polarized excitons confined in a single QD was studied. By using pulses with large enough bandwidth and the proper polarization, two exciton states are simultaneously excited. The quantum beats between the two exciton states were temporally resolved as the relative phase between the two dipole oscillations changed. It was found that the nonradiative coherence time is limited by the lifetimes of the excitons involved even in the strong field regime. In the basis of the pseudo-spin Bloch vectors of exciton transitions, the total wavefunction following the pulsed excitation is an entangled state, i.e. the wavefunction is non-factorizable. Finally, the quantum coherence between the biexciton, exciton, and the crystal ground states was studied in a novel quantum beat experiment, where the oscillations only existed when the pump and probe pulses overlapped in time. Laser pulses generated after a passive pulse shaper with just enough bandwidth to cover both the exciton and biexciton transitions were used in this experiment. The appearance of the beats is indicative of a reasonably long coherence time between the biexciton and other states even in the presence of strong pulsed excitations.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.