Conventional semiconductor laser emission relies on stimulated emission of photons, which sets stringent requirements on the minimum amount of energy necessary for its operation. In comparison, exciton-polaritons in strongly coupled quantum well microcavities can undergo stimulated scattering that promises more energy-efficient generation of coherent light by 'polariton lasers'. Polariton laser operation has been demonstrated in optically pumped semiconductor microcavities at temperatures up to room temperature, and such lasers can outperform their weak-coupling counterparts in that they have a lower threshold density. Even though polariton diodes have been realized, electrically pumped polariton laser operation, which is essential for practical applications, has not been achieved until now. Here we present an electrically pumped polariton laser based on a microcavity containing multiple quantum wells. To prove polariton laser emission unambiguously, we apply a magnetic field and probe the hybrid light-matter nature of the polaritons. Our results represent an important step towards the practical implementation of polaritonic light sources and electrically injected condensates, and can be extended to room-temperature operation using wide-bandgap materials.

We study the loading of a nonequilibrium, dissipative system of composite bosons -exciton polaritons -into a one dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and confirm that polariton-phonon scattering is a key energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.Introduction.-Since the initial demonstration of Bose-Einstein condensation of microcavity exciton polaritons [1], one particular direction of research has been focused on engineering the potential landscape of polaritons. These potentials have been created by deposition of metal on the microcavity surface [2], interference of surface acoustic waves [3], deep etching of micropillars [4], fabrication of shallow mesas [5], and deposition of semiconductor micro-rods on a silicon grating [6]. Periodic arrangements of these potentials have been used to study the formation of gap solitons [7,8] and graphene-like band spectra (including Dirac cones) [4,9], are predicted to be prime candidates for the generation of topological polariton states [10][11][12], and hold high promise for implementation of quantum simulators in solid state systems [13].

We consider the nonlinear terahertz emission by the system of cavity polaritons in the regime of polariton lasing. To account for the quantum nature of terahertz-polariton coupling, we use the Lindblad master equation approach and demonstrate that quantum microcavities reveal a rich variety of nonlinear phenomena in the terahertz range, including bistability, short terahertz pulse generation, and terahertz switching.

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We propose an all-optical nonlinear router based on a double barrier gate connected to periodically modulated guides. A semiconductor microcavity is driven nonresonantly in-between the barriers to form an exciton-polariton condensate on a discrete state that is subject to the exciton blueshift. The subsequent coherent optical signal is allowed to propagate through a guide provided that the condensate energy is resonant with a miniband or is blocked if it faces a gap. While a symmetric sample operates as an optical switch, its asymmetric counterpart embodies a router turned to be polarization selective under applied magnetic field.

We have investigated theoretically the interaction between individual quantum dot with broken inversion symmetry and electromagnetic field of a single-mode quantum microcavity. It is shown that in the strong coupling regime the system demonstrates nonlinear optical properties and can serve as emitter of the terahertz radiation at Rabi frequency of the system. Analytical results for simplest physical situations are obtained and numerical quantum approach for calculating emission spectrum is developed.

We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

In this work, we combine a systematic experimental investigation of the power-and temperaturedependent evolution of the spatial coherence function, g ð1Þ ðrÞ, in a one dimensional exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g ð1Þ ðrÞ is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g ð1Þ ðrÞ reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in one dimensional condensate systems.