All-Optical Polariton Transistor

All-optical polariton transistor D. Ballarini1, M. De Giorgi1,2, E. Cancellieri3, R. Houdré4, E. Giacobino5, R. Cingolani1, A. Bramati5, G. Gigli1,2,6, D. Sanvitto1,2 1Istituto Italiano di Tecnologia, IIT-Lecce, Via Barsanti, 73010 Lecce, Italy. 2NNL, Istituto Nanoscienze - CNR, Via Arnesano, 73100 Lecce, Italy. 3Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, Spain. 4Institut de Physique de la Matière Condensée, Faculté des Sciences de Base, bâtiment de Physique, Station 3, EPFL, CH-1015 Lausanne, Switzerland 5Laboratoire Kastler Brossel, Université Pierre et Marie Curie-Paris 6, École Normale Supérieure et CNRS, UPMC Case 74, 4 place Jussieu, 75005 Paris, France. 6Innovation Engineering Department, University of Salento, Via Arnesano, 73100 Lecce, Italy. While optical technology provides the best solution for the transmission of information, optical logics is still in its infancy. In particular, energy considerations impose to reduce the power required for nonlinear interactions in future optical devices, which, in addition, should be compatible with present semiconductor technology. Exciton-polaritons are composite particles, resulting from the strong coupling between excitons and photons, which have recently demonstrated exceptional properties like huge non-linearities, condensation and superfluidity. Here we experimentally demonstrate a switching scheme for polaritons moving in the plane of a microcavity which satisfy all the requirements for an all-optical transistor. Two laser beams are converted into polariton quasi- particles, which are used as input states for generating and controlling the output, obtaining up to 19 times amplification. Moreover this polariton transistor shows to work with an interchangeable input- output signal, and needing an energy activation as low as few attojoules/µm2. Light beams can carry information over long distances, and have proved to be better than electronic wires for low-loss transmissions at high data rate [1-4]. Optical connections could, in principle, operate faster and with lower energy consumption than electronic ones even at very short distances, down to chip interconnects [5, 6]. Therefore, the capability to implement high-speed, low-energy, optical logics in all-optical integrated circuits is highly desirable and represents a challenge for future information processing [7]. Several systems have been studied to develop all-optical switches, including Mach- Zehnder interferometers in semiconductor materials [8], spin polarization in multiple quantum wells [9], waveguide-coupled ring resonator in silicon [10] and polarization bistability in vertical cavity emitting structures [11]. However, if a switch has to be used as a logic element, it must satisfy some critical conditions such as cascadability (the output and input should be compatible to allow for connections in series of several devices), logic level restoration, isolation of the input/output, and, most importantly, the possibility to feed with one output several inputs and viceversa (fan-out/fan-in), which are not simultaneously accomplished so far by all schemes suggested for optical logic [4, 12]. In this context, microcavity polaritons constitute a very interesting kind of semiconductor quasi- particles, which are a mixture of electron-holes (exciton) and light. What makes them very attractive is the combination of photonic features (their mass is 10-4 times that of an electron) with the strong particle-particle interactions typical of electronic states, which results in the possibility to perform fast and efficient switching. Under resonant excitation, the main nonlinear processes in a polariton system are parametric scattering and optical bistability, both induced by the polariton-polariton interactions, which are observed at power thresholds orders of magnitude lower than in standard dielectrical optical crystals [13-23]. Recently, the observation of a non-equilibrium Bose-Einstein condensed phase [24, 25] of polaritons paved the way to the study of new quantum phenomena typical of superfluids which could lead to virtually loss-free operations and communication [26-30] up to room temperature [31]. Given their low operational powers and their high propagation velocities (1% of light speed), polaritons have attracted in the last years more investigation on their potential use as optical switches in integrated circuits [32, 33]. In these proposals, the information is carried by polariton quasi-particles propagating inside the plane of the microcavity (perpendicular to the growing direction of the sample), demonstrating the feasibility of optical integrated circuits based on “polariton neurons”. In such devices, lateral confinement of the propagating polariton fluid is expected to be realized by metallic deposition on the top of the microcavity, or by modeling the photonic potential of the cavity through precise etching of the structure [34, 35]. In particular, the possibility to switch on and propagate a coherently- driven condensed-phase of polaritons has been demonstrated [36], as well as the low-power optical bistability in polariton diodes [37] and the polariton polarization multistability [38]. In all these works, however, the lack of amplification and the non-interchangeability of the inputs prevent their use as truly optical transistor for the realization of logic gates for polariton fluids. Here we experimentally demonstrate the working principle of a polariton transistor in a semiconductor planar microcavity based on the nonlinear interactions between two polariton fluids. The resonance of a polariton state (address) is shifted in energy by injecting a small polariton population into a second state (control). Polaritons in the control state are used as a gate signal to switch on and off the transmission of the address state, with a density increase of more than one order of magnitude. When the address density is switched on, the address polaritons propagate in the microcavity plane with the correct energy to be used as control state for the following transistors and with densities high enough to feed the control of several subsequent stages, one of the missing features that would make the implementation of integrated polariton logics extremely appealing. In our experiments, which have been performed in transmission configuration and at a temperature of 10 K, we use a single mode, continuous wave, laser beam, divided in two paths, to impinge with different in-plane wavevectors on a GaAs/AlAs microcavity (front/back reflectors with 21/24 pairs with three In0.04Ga0.96As quantum wells). The two beams are used to resonantly excite two states of the lower polariton branch, control and address, which share the same energy, , but have different finite momenta in the microcavity plane, and respectively. The polariton density N in each state is proportional to the polariton transmission , which has been measured both in real and momentum space, and can be calculated according to the formula N , where is the intensity of the photons exiting the cavity, is the polariton lifetime, is the polariton energy and is the spot area. The energy blueshift of a single polariton state as a function of the polariton density results in optical bistability, which depends on the detuning between the excitation energy and the polariton resonance , and on the polariton linewidth [19, 23]. However, in the case of two pumping lasers, the interactions between polaritons in different states induce a richer phenomenology [39, 40]. In particular, when the intensity of one of the lasers remains constant, while the other varies, the blueshift of the polariton dispersion can be sustained by any of the two lasers, and the bistability thresholds are strongly affected by the intensity of the second beam, as proposed in Ref. [39]. Moreover, the dynamics of moving polariton quantum fluids are even more intriguing, given that, at wavevectors different from , non local effects hamper the bistable behaviour of a polariton bullet propagating in the microcavity plane [41, 42]. On the other hand, the bistability behavior is not suited for implementing a polariton optical transistor, given the irreversibility of the process: once the address population is turned on by the control, the polariton signal remains unaffected by any change of the control state. For this reason, in this work we set the laser detuning in a way so that the hysteresis loop is reduced to a single jump. In this case the system is in the “optical discriminator” regime and the upper and lower thresholds of the hysteresis loop degenerate to only one single power [19]. In the upper panel of Fig.1 the image of the transmission in the 2-dimensional momentum space shows the control and address states, which are saturated in order to appreciate the weak emission from the microcavity ring due to laser elastic scattering. In the lower panel of Fig.1, the polariton dispersion along , under non-resonant, low power, excitation is shown. The control and address momenta, and , are indicated by solid vertical lines, while the pumping energy is indicated by a dashed horizontal line. Given the condition , to a smaller momentum corresponds a larger detuning of the exciting laser with respect to the polariton resonance (for , the detunings and between the exciting laser and the polariton resonance for the address and control state, respectively, satisfy the condition ). The transmission of the address state can be controlled by the polariton population in the control state,

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