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, as schematically depicted in the right panel of Fig.1.

Fig1: In the upper panel, the 2-dimensional momentum space image of the transmission under high excitation

power shows the polariton states created by two laser beams impinging at different angles (KC and KA) and same energy. The lower panel shows the polariton dispersion (Energy versus Wavevector, along the direction -1 -1 corresponding to KY=0 of the upper panel). The vertical lines indicate the value of KA=0.5μm and KC=-1µm and the horizontal line indicates the pumping energy E=1.481eV. On the right, the operational roles of each component of a polariton transistor are sketched in analogy to what happens in an electronic-based transistor.

The principle is to use only a small polariton population in the control state to switch on and off the polariton density in the address state. To achieve this goal, experimentally, we use the k-dependent polariton resonance to set the detuning of the address at a value in which the bistable behavior reduces to a single-threshold jump , while the control remains in resonance with the polariton dispersion at ( ). The polariton densities N of address and control state excited independently, i.e. without interaction between them, are shown in Fig. 2a and Fig. 2b, respectively.

Fig.2: Polariton densities in the address state (panel a) and control state (panel b), under increasing power of the address and control beam, respectively.

The threshold power for the non-linear address transmission (Fig. 2a) is found at , which corresponds to for the diameter spot of used in this experiment. As shown in Fig. 2a, the address population increases abruptly at , then only linearly for higher powers and, increasing further the address power, a saturation will eventually occur due to the blueshift of the polariton branch with respect to the address energy. Conversely, since the control is in resonance with the polariton branch, the efficient injection of polaritons occurs at any power, with a linear increase of the population at low intensities and a saturation at higher intensities (Fig. 2b). Therefore, no threshold is observed for the control state, as expected for detuning .

The effect of the interaction between polaritons in the control and address states can be observed in Fig. 3a, where the characteristic curves of the address population are shown for different fixed values of the control power, . The presence of polaritons in the control state shifts the characteristic curves of the address, lowering the threshold from ( ) to ( ). Therefore, polaritons in the control state can be used to switch on and off the polariton fluid fed by the address beam, while the address power is set to a fixed value: when (red, vertical line, in Fig.3a), the address is in the on state (green circle in Fig. 3a) or in the off state (black circle in Fig. 3a) depending on the control power . This operational principle is verified in Fig.3b, where the address density (blue triangles) is plotted as a function of the control power for a fixed power of the address ( ), corresponding to the red line in Fig. 3a. The address state switches on for , which corresponds to .

Fig. 3: (a) The polariton density in the address state versus the address power is plotted for different powers of the control: PC=0.6mW (green line), PC=0.3mW (black line), PC=0.2mW (blue line) and without control (light blue line). The red line indicates the power of the address for which a small change in the control power brings the state from off (black circle) to on (green circle). (b) Address densities (blue triangles) and relative gain (red dots) against control power, taken for an address power of PA=3.7mW, corresponding to the position of the red line in panel a. This plot shows the amplification of a weak control power into the address densities, in analogy to an electronic transistor, where the Source-Drain current is powered by the address, while the Gate is replaced by the control. (c) The amplification (Output/Control) CA at threshold P th is plotted as a function of the energy detuning ΔEA between the exciting laser and the polariton branch. The gain increases for higher address detuning showing also the possibility to modulate the amount of amplification. (d) Theoretical simulations of the address densities (dashed lines) and gain A (dots) as a function of the control power (measured in units of the address threshold P th), for different A A A address intensities: 0.70P th, 0.76P th, 0.83P th (corresponding to the green, red and black color respectively).

Due to the lack of hysteresis, the address state can be switched off simply decreasing below the same threshold. The extinction ratio of the address transmission below and above threshold is, in this case, . It is important to stress that the polariton density in the address is controlled by a smaller polariton density in the control, thus giving an amplification for . The gain G, defined as the ratio between the polariton population in the address state and the polaritons required for the control operation (the analog to the definition of gain in electronic transistor, ), is plotted by red circles in Fig. 3b, as a function of the control power . At threshold, , a maximum gain is obtained, showing that the density of the address is more than one order of magnitude larger than the control density.

In our case, the threshold power corresponds to a density of about 8 polaritons/µm2 in the control state, which means an activation energy of few attojoules/µm2 (see Supplementary Information for more details). Even considering the relatively wide laser spot used in these experiments to avoid any diffraction effect due to finite cavity width, the polariton population in the whole area is anyhow reaching an energy of few femtojoule, figure which could be strongly reduced by, for instance, designing ad hoc waveguides and mesa structures with lateral size down to a few micrometers.

Another interesting point is that the value of the amplification at threshold can be modulated by tuning the energy of the exciting laser, obtaining a higher gain when the detuning of the address is increased, as shown in Fig.3c. In this case, we are considering polaritons with wavevector , and the range of energy detuning for which the system is still in the optical discriminator regime, allowing to vary the value of the gain from 4 to 19 (note that, in order to obtain a higher gain for larger detuning, the address power has to be increased accordingly). The polariton densities of control and address have been theoretically simulated, as described in the Supplementary Information, and confirm the experimental observation of a strong gain at threshold, which is triggered by a polariton density lower than 10 polariton/µm2 in the control state. These numbers can be improved even further with microcavities of higher finesse and by reducing the address detuning (though, in this case, with a tradeoff of a smaller gain). In Fig.3d, the simulations are run for three different powers of the address beam (0.70 , 0.76 and 0.83 , corresponding to the green, red and black color respectively), showing that the control threshold can be lowered by, for instance, tuning the address power.

The possibility of fabricating transistor structures with different detuning, by changing locally the photonic potential of the cavity, and combining two or more control beams, enables the use of a polariton transistor as a logic gate with variable gain. For example, an “AND” gate can be imagined as two input controls and one address output, which is switched on only if both the controls are present (note that at least 4 transistors are required to perform the same logic operation with current CMOS technology). Moreover, changing the incoming wavevector of the inputs may lead each control state to have different weights in contributing to the activation of the address, furnishing the basis for new logics, neuronal-like, with polariton networks [32]. In this scheme the output of one transistor is a polariton fluid, which can be used as the control input for the next transistor, without the need for laser light as the optical mediator, a first step towards an in-plane integrated polariton logic technology. Note that the address input does not need to be localized in each element gate, because it could be either a single laser beam spread all over the chip area or guided into each gate from in plane semiconductor waveguides.

Our results demonstrate that the output polariton flow of a transistor, fed by an address laser beam, can be switched on/off by a second, much weaker, polariton state of control, providing an all-optical, semiconductor integrated system for logic operation with very low activation energy. Moreover, given that the output signal and the control input can be interchanged, the amplified address could in principle be used to control several of these devices. In order to achieve such a complex configuration, further efforts must be devoted to the growth of high quality sample with patterned structures, where the polariton flow can be guided through small diameter area, allowing the output flow to be diverted, via ballistic propagation in polariton guides [35], into several inputs for controlling the next in series transistors. The operation of such a polariton device would happen all inside of the microcavity allowing for multiple interconnections to occur in the plane of the semiconductor chip without the need for free space laser beams or optical waveguides, which use up an extremely wide operational area. Finally, we must note that the most basic requirements, needed for every logic device, like cascadability, fan-out, logic level restoration and isolation of the address and control states, are naturally satisfied in this work due to the peculiar properties of microcavity polaritons.

Aknowledgements

We would like to thank A. Bramanti and V. Scarpa for useful discussion and P. Cazzato for the technical assistance with the experiments. This work has been partially funded by the FIRB Italnanonet and the POLATOM ESF Research Networking Program.

References:

1. Kao, K.C. and G.A. Hockham, Dielectric-fibre surface waveguide for optical frequencies. Proceedings of the IEE, 1966. 2. Miller, D.A.B., Physical reasons for optical interconnection. Int. J. Optoelectron., 1997. 11: p. 155. 3. Nazarathy, M., et al., All-optical linear reconfigurable logic with nonlinear phase erasure. J. Opt. Soc. Am. A, 2009. 26(8): p. A21-A39. 4. Hwang, J., et al., A single-molecule optical transistor. Nature, 2009. 460(7251): p. 76-80. 5. Paul, B.C., A. Agarwal, and K. Roy, Low-power design techniques for scaled technologies. Integr. VLSI J., 2006. 39(2): p. 64-89. 6. Bohr, M.T., Nanotechnology goals and challenges for electronic applications. Nanotechnology, IEEE Transactions on, 2002. 1: p. 56. 7. Wada, O., Femtosecond all-optical devices for ultrafast communication and signal processing. New Journal of Physics, 2004. 6: p. 183. 8. Glesk, I., et al., All-optical switching using nonlinear subwavelength Mach-Zehnder on silicon. Opt. Express, 2011. 19(15): p. 14031-14039. 9. Johnston, W.J., J.P. Prineas, and A.L. Smirl, Ultrafast all-optical polarization switching in Bragg-spaced quantum wells at 80 K. Journal of Applied Physics, 2007. 101(4): p. 046101-3. 10. Almeida, V.R., et al., All-optical control of light on a silicon chip. Nature, 2004. 431(7012): p. 1081-1084. 11. Mori, T., Y. Yamayoshi, and H. Kawaguchi, Low-switching-energy and high-repetition- frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface- emitting laser. Applied Physics Letters, 2006. 88: p. 101102. 12. Miller, D.A.B., Are optical transistors the logical next step? Nat Photon, 2010. 4(1): p. 3-5. 13. Savasta, S., O. Di Stefano, and R. Girlanda, Many-Body and Correlation Effects on Parametric Polariton Amplification in Semiconductor Microcavities. Physical Review Letters, 2003. 90(9): p. 096403. 14. Savvidis, P.G., et al., Angle-Resonant Stimulated Polariton Amplifier. Physical Review Letters, 2000. 84(7): p. 1547. 15. Huang, R., F. Tassone, and Y. Yamamoto, Experimental evidence of stimulated scattering of excitons into microcavity polaritons. Physical Review B, 2000. 61(12): p. R7854. 16. Ciuti, C., et al., Theory of the angle-resonant polariton amplifier. Physical Review B, 2000. 62(8): p. R4825. 17. Stevenson, R.M., et al., Continuous Wave Observation of Massive Polariton Redistribution by Stimulated Scattering in Semiconductor Microcavities. Physical Review Letters, 2000. 85(17): p. 3680. 18. Saba, M., et al., High-temperature ultrafast polariton parametric amplification in semiconductor microcavities. Nature, 2001. 414(6865): p. 731-735. 19. Baas, A., et al., Optical bistability in semiconductor microcavities. Physical Review A, 2004. 69(2): p. 023809. 20. Tredicucci, A., et al., Optical bistability of semiconductor microcavities in the strong-coupling regime. Physical Review A, 1996. 54(4): p. 3493. 21. Gippius, N.A. and et al., Nonlinear dynamics of polariton scattering in semiconductor microcavity: Bistability vs. stimulated scattering. EPL (Europhysics Letters), 2004. 67(6): p. 997. 22. Whittaker, D.M., Numerical modelling of the microcavity OPO. physica status solidi (c), 2005. 2(2): p. 733-737. 23. Gippius, N.A., et al., Polarization Multistability of Cavity Polaritons. Physical Review Letters, 2007. 98(23): p. 236401. 24. Kasprzak, J., et al., Bose-Einstein condensation of exciton polaritons. Nature, 2006. 443(7110): p. 409-414. 25. Balili, R., et al., Bose-Einstein Condensation of Microcavity Polaritons in a Trap. Science, 2007. 316(5827): p. 1007-1010. 26. Amo, A., Collective fluid dynamics of a polariton condensate in a semiconductor microcavity. Nature, 2009. 457: p. 291-295. 27. Amo, A., Superfluidity of polaritons in semiconductor microcavities. Nature Phys., 2009. 5: p. 805-810. 28. Sanvitto, D., et al., Persistent currents and quantized vortices in a polariton superfluid. Nat Phys, 2010. 6(7): p. 527-533. 29. Amo, A., et al., Polariton superfluids reveal quantum hydrodynamic solitons. Science, 2011. 332(6034): p. 1167-1170. 30. Sanvitto, D., et al., All-optical control of the quantum flow of a polariton condensate. Nat Photon, 2011. 5(10): p. 610-614. 31. Christopoulos, S., et al., Room-Temperature Polariton Lasing in Semiconductor Microcavities. Physical Review Letters, 2007. 98(12): p. 126405. 32. Liew, T.C.H., A.V. Kavokin, and I.A. Shelykh, Optical circuits based on polariton neurons in semiconductor microcavities. Phys. Rev. Lett., 2008. 101: p. 016402. 33. Shelykh, I.A., et al., Proposal for a Mesoscopic Optical Berry-Phase Interferometer. Physical Review Letters, 2009. 102(4): p. 046407. 34. Liew, T.C.H., et al., Exciton-polariton integrated circuits. Physical Review B, 2010. 82(3): p. 033302. 35. Wertz, E., et al., Spontaneous formation and optical manipulation of extended polariton condensates. Nat Phys, 2010. 6(11): p. 860-864. 36. Amo, A., et al., Exciton-polariton spin switches. Nat Photon, 2010. 4(6): p. 361-366. 37. Bajoni, D., Optical bistability in a GaAs-based polariton diode. Phys. Rev. Lett., 2008. 101: p. 266402. 38. Paraïso, T.K., et al., Multistability of a coherent spin ensemble in a semiconductor microcavity. Nat Mater, 2010. 9(8): p. 655-660. 39. Cancellieri, E., et al., Multistability of a two-component exciton-polariton fluid. Physical Review B, 2011. 83(21): p. 214507. 40. Cancellieri, E., et al., Frictionless flow in a binary polariton superfluid. 2011. 41. Adrados, C., et al., Motion of Spin Polariton Bullets in Semiconductor Microcavities. Physical Review Letters, 2011. 107(14): p. 146402. 42. Johne, R., et al., Polaritonic analogue of Datta and Das spin transistor. Physical Review B, 2010. 81(12): p. 125327.

All-optical polariton transistor

Supplementary Information

Two-component Gross-Pitaevskii equation. A standard way to model the dynamics of the system of resonantly-driven polaritons in a planar microcavity is to use a Gross-Pitaevskii equation for coupled cavity and exciton field ( and ) generalized to include the effects of the resonant pumping and decay :

(1)

where the single particle polariton Hamiltonian H_0 reads:

Where is the cavity dispersion as a function of the in-plane wave vector and where the photon mass is and is the bare electron mass. For these simulations a flat exciton dispersion relation will be assumed and the case of zero detuning at normal incidence considered. The parameters , and are the Rabi frequency and the excitonic and photonic decay rates respectively and are taken close to experimental values: , , and . In this model polaritons are injected into the cavity in two states (address and control) by two coherent and monochromatic laser fields. The two laser fields share the same smoothen top- hat spatial profile with intensities and for the address and the control respectively, and with full width at half maximum equal to 160 m. The two laser fields share also the same frequency but have different in-plane momentum and . The exciton-exciton interaction strength is set to one by rescaling both the cavity and excitonic fields and the pump intensities. Our theoretical results come from the numerical solution of equation (1) over a two-dimensional grid (256x256) in a 280x280 box using a fifth-order adaptive-step Runge-Kutta algorithm. All the analyzed quantities are taken when the system has reached the steady state condition after 1000 ps. The number of polaritons in the control state at thresholds results to be 3, 5 and 7 polaritons/ for the black, red and green curve in Fig4.d, respectively. Evaluation of the polariton densities. Considering control excitation intensities of , the transmission from the cryostat window (96%) and the reflection on the sample surface (30%), the injected powers is , which, for a spot diameter of , yields a maximum density of , which corresponds to . In the calculation, we have used as the intensity of the photons entering the cavity, as the polariton lifetime, while is the polariton energy and is the spot area.