Coherent optical control of the wave function of zero-dimensional exciton polaritons

Abstract

Control of the wave function of confined microcavity polaritons is demonstrated experimentally and theoretically by means of tailored resonant optical excitation. Three dimensional confinement is achieved by etching mesas on top of the microcavity spacer layer. Resonant excitation with a continuous-wave laser locks the phase of the discrete polariton states to the phase of the laser. By tuning the energy and momentum of the laser, we achieve precise control of the momentum pattern of the polariton wave function. This is an efficient and direct way for quantum control of electronic excitations in a solid.Polaritons in semiconductor microcavities are hybrid quasiparticles consisting of a superposition of photons and excitons. Due to their photon component, polaritons are characterized by a quantum coherence length in the several micron range. Owing to their exciton content, they display sizeable interactions, both mutual and with other electronic degrees of freedom. These unique features have produced striking matter wave phenomena, such as Bose-Einstein condensation, 1,2 or parametric processes 3,4 able to generate entangled polariton states. 5,6 The key feature of polaritons with respect to confinement is their very small effective mass, which is about 10 5 times smaller than the free-electron mass. Hence, confinement within micrometer sized traps is sufficient to produce an atomlike spectrum with discrete energy levels. Recently, several paradigms for spatial confinement of polaritons in semiconductor devices have been established. 7-10 This opens the way to quantum devices in which polaritons can be used as a vector of quantum information. 11 Their electronic component can be accessed and controlled optically, through their photonic component. This holds promise for preparation of quantum states, which might then be transferred to longer lived elements of quantum storage ͑e.g., localized spins͒, or as a mechanism for mediating interactions between such elements over long distances, as proposed in Ref. 12. Precise control of the polariton wave function is then an essential requirement.In this Rapid Communication we demonstrate the manipulation of the wave function of confined zero-dimensional ͑0D͒ exciton polaritons under resonant optical excitation. The excited wave functions are monitored by collecting the coherent emission from the polariton traps. Control of the spatial and momentum probability distribution of the confined polaritons is achieved by tuning either the incidence angle or the energy of the excitation beam. Our results are supported by numerical simulations based on the coupled Gross-Pitaevskii equations for excitons and photons.The sample we used to carry out our studies consists of a single quantum well embedded in a planar microcavity with a pattern of differently sized round mesas on the spacer layer. 13 Patterning the cavity thickness results in a modulation of the photon resonance energy, which corresponds to a potential trap, with finite-energy barriers, able to confine polaritons. The con...

Probability density tomography of microcavity polaritons confined in cylindrical traps of various sizes

“…Microcavity polaritons can therefore be confined in the in-plane directions by traps with sizes in the micrometer range. While the imaging of carriers confined in semiconductor heterostructures is generally forbidden due to the small confinement size, probability density (PD) patterns of polaritons confined in micrometer size traps can be accessed by standard optical means [3,4].…”

“…Microcavity polaritons can therefore be confined in the in-plane directions by traps with sizes in the micrometer range. While the imaging of carriers confined in semiconductor heterostructures is generally forbidden due to the small confinement size, probability density (PD) patterns of polaritons confined in micrometer size traps can be accessed by standard optical means [3,4].We previously engineered a GaAs/AlAs microcavity with a single embedded InGaAs QW, featuring traps for the exciton-polaritons. These traps consist in quasi-circular mesas which were etched on the cavity spacer to locally enlarge the cavity length, thus providing a cylindrical confining potential for the photonic modes.…”

Hydrodynamic nucleation of quantized vortex pairs in a polariton quantum fluid

“…Their dual light-matter nature gives them many advantages. Thanks to a one-to-one coupling to the extra-cavity field, with conservation of in-plane momentum and energy, exciton polaritons can be easily optically injected, manipulated 20,21 , and detected. Thanks to their excitonic part, polaritons can interact with each other, leading to spectacular nonlinear behaviours 22 .…”

Symmetry-Breaking Effects for Polariton Condensates in Double-Well Potentials

“…In that case, the anti-symmetric branch is stable for x m 2 ½2:0; 4:8 ; the symmetric branch is now stable for x m 2 ½1:0; 1:9 ; starting the Hopf cascade at x m ¼ 4:5: The asymmetric branch is stable for x m 2 ½1:0; 2:0 ; while being oscillatorily unstable for other values of x m : In the present work, we studied the existence of solutions, their spectral stability and nonlinear dynamics for the case of a polariton condensate confined in a quasi-1D double well potential. Motivated by recent developments for the study of polaritons in such settings [26][27][28][29][30][31][32][52][53][54][55], and by the work of Ref. [15] which proposed a two-well model, we presented a systematic Galerkin analysis for the model with the gain over a localized spot and nonlinear saturation loss formulated in Refs.…”

“…Yet, highly anisotropic traps (similar to what has been done in atomic BECs [23][24][25]) can be envisioned which reduce the effective dynamics to a quasi one-dimensional (1D) setting [26][27][28][29][30][31]. Moreover, recent experimental advances have enabled the use of thin microwires in order to guide the condensates along the direction of the wire [32].…”