Yuri G. Rubo

Observation of half-quantum vortices in an exciton-polariton condensate

Quantum Division The notion of quantum mechanics is that variables are expressed as integer values. In quantum fluids, for instance, vortices are quantized in terms of the polarization and phase shifts observed as multiples of 2π, that is, full rotations of each variable around the vortex core. Theoretical work has predicted that in some instances there should be half-quantum vortices, where circumventing the vortex core is characterized by just π rotations of the phase and polarization. By observing exciton-polariton condensates Lagoudakis et al. (p. 974) present evidence for the existence of these long-predicted half-quantum vortices. Evidence is presented for the existence of half-quantum vortices in exciton-polariton condensates. Singly quantized vortices have already been observed in many systems, including the superfluid helium, Bose-Einstein condensates of dilute atomic gases, and condensates of exciton-polaritons in the solid state. Two-dimensional superfluids carrying spin are expected to demonstrate a different type of elementary excitations referred to as half-quantum vortices, characterized by a π rotation of the phase and a π rotation of the polarization vector when circumventing the vortex core. We detect half-quantum vortices in an exciton-polariton condensate by means of polarization-resolved interferometry, real-space spectroscopy, and phase imaging. Half-quantum vortices coexist with single-quantum vortices in our sample.

Polariton polarization-sensitive phenomena in planar semiconductor microcavities

From a theoretical point of view, we discuss a variety of phenomena linked to the spin and polarization degree of freedom of exciton-polaritons in semiconductor microcavities. We start with linear optical effects including the optical spin Hall effect, formation of polarization vortices and ballistic propagation of polarized exciton-polaritons. Next, the interplay between spin-dependent dynamics and Bose condensation in the 2D system of microcavity polaritons is addressed. Theoretically, this many-body system of interacting particles is described by the spinor Gross-Pitaevskii equations. These equations provide a description of the time evolution of polarized polariton fields under different conditions of optical excitation as well as an understanding of the phenomena of superfluidity, multistability and hysteresis via renormalization of the dispersion of elementary excitations. The comprehension of polarization-sensitive dynamics can be made through the introduction of several effective fields of different nature acting on the polariton pseudospin. The theory of parametric scattering of exciton-polaritons is presented, using the second quantization formalism. It is found that the combination of nonlinearity and various mechanisms of spin reorientation leads to self-organization and the formation of polarized patterns such as polarization crosses, vortices and rings. The manipulation of polariton spins can lead to various applications in signal processing, including the construction of optical logic gates and spin memory elements; the creation of spin currents; and the control of polarized signal propagation in the microcavity plane. The concept of polariton neurons is discussed in this connection.

Polarization multistability of cavity polaritons.

New effects of polarization multistability and polarization hysteresis in a coherently driven polariton system in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.

Half Vortices in Exciton Polariton Condensates

It is shown that vortices in linearly polarized polariton condensates in planar semiconductor microcavities carry two winding numbers (k, m). These numbers can be either integer or half-integer simultaneously. Four half-integer vortices (1/2, 1/2), (-1/2, -1/2), (1/2, -1/2), and (-1/2, 1/2) are anisotropic, possess the smallest energy, and define the Kosterlitz-Thouless transition temperature. The condensate concentration remains finite within the core of the half vortex and the condensate polarization becomes fully circular in the core center.

Magnetic properties of graphene quantum dots

Using the tight-binding approximation we calculated the magnetic susceptibility of graphene quantum dots (GQD) of different geometrical shapes and sizes, smaller than the magnetic length, when the magnetic properties are governed by the electron edge states. Two types of edge states can be discerned: the zero-energy states (ZES) located exactly at the zero-energy Dirac point, and the dispersed edge states (DES) with the energy close, but not exactly equal to zero. DES are responsible for the temperature independent diamagnetic response, while ZES provide the temperature dependent spin Curie paramagnetism. The hexagonal, circular and randomly shaped GQDs contain mainly DES and, as a result, they are diamagnetic. The edge states of the triangular GQDs are ZES and these dots reveal the interplay between the spin paramagnetism, dominating for small dots and at low temperatures, and bulk orbital diamagnetism, dominating for large dots and at high temperatures.

Spontaneous Spin Bifurcations and Ferromagnetic Phase Transitions in a Spinor Exciton-Polariton Condensate

This work was supported by Grants EPSRC No. EP/G060649/1, EU No. CLERMONT4 235114, EU No. INDEX 289968, Spanish MEC (MAT2008-01555), Greek GSRT ARISTEIA Apollo program and Fundacion La Caixa, and Mexican CONACYT No. 251808. FP acknowledges financial support through an EPSRC doctoral prize fellowship at the University of Cambridge and a Schrodinger fellowship at the University of Oxford.

Radiative coupling and weak lasing of exciton-polariton condensates

In spite of having finite life-time exciton-polaritons in microcavities are known to condense at strong enough pumping of the reservoir. We present an analytical theory of such Bose-condensates on a set of localized one-particle states: condensation centers. To understand physics of these arrays one has to supplement the Josephson coupling by the radiative coupling caused by the interference of the light emitted by different centers. Combination of these couplings with the one-site interaction between the bosons leads to a rich nonlinear dynamics. In particular, a new regime of radiation appears. We call it weak lasing: the centers have macroscopic occupations and radiate coherently, but the coupling alone is sufficient for stabilization. The system can have several stable states and switch between them. Moreover, the time reversal symmetry in this regime is, as a rule, broken. A number of existing experimental puzzles find natural interpretation in the framework of this theory.

Weak lasing in one-dimensional polariton superlattices

Significance Bose–Einstein condensation of polaritons in periodically modulated cavities is a very interesting fundamental effect of the physics of many-body systems. It is also promising for application in solid-state lighting and information communication technologies. By a simple microassembling method, we created periodically modulated polariton condensates at room temperature, and observed the stabilization of the coherent condensate due to the spontaneous symmetry-breaking transition. This manifests a previously unidentified type of phase transition, leading to a novel state of matter: the weak lasing state. The optical imaging in both direct and reciprocal space provides clear evidence for the weak lasing in the specific range of the pumping intensities. Bosons with finite lifetime exhibit condensation and lasing when their influx exceeds the lasing threshold determined by the dissipative losses. In general, different one-particle states decay differently, and the bosons are usually assumed to condense in the state with the longest lifetime. Interaction between the bosons partially neglected by such an assumption can smear the lasing threshold into a threshold domain—a stable lasing many-body state exists within certain intervals of the bosonic influxes. This recently described weak lasing regime is formed by the spontaneously symmetry breaking and phase-locking self-organization of bosonic modes, which results in an essentially many-body state with a stable balance between gains and losses. Here we report, to our knowledge, the first observation of the weak lasing phase in a one-dimensional condensate of exciton–polaritons subject to a periodic potential. Real and reciprocal space photoluminescence images demonstrate that the spatial period of the condensate is twice as large as the period of the underlying periodic potential. These experiments are realized at room temperature in a ZnO microwire deposited on a silicon grating. The period doubling takes place at a critical pumping power, whereas at a lower power polariton emission images have the same periodicity as the grating.

Spin Order and Phase Transitions in Chains of Polariton Condensates

We demonstrate that multiply coupled spinor polariton condensates can be optically tuned through a sequence of spin-ordered phases by changing the coupling strength between nearest neighbors. For closed four-condensate chains these phases span from ferromagnetic (FM) to antiferromagnetic (AFM), separated by an unexpected crossover phase. This crossover phase is composed of alternating FM-AFM bonds. For larger eight-condensate chains, we show the critical role of spatial inhomogeneities and demonstrate a scheme to overcome them and prepare any desired spin state. Our observations thus demonstrate a fully controllable nonequilibrium spin lattice.

A sub-femtojoule electrical spin-switch based on optically trapped polariton condensates

Practical challenges to extrapolating Moores law favour alternatives to electrons as information carriers. Two promising candidates are spin-based and all-optical architectures, the former offering lower energy consumption, the latter superior signal transfer down to the level of chip-interconnects. Polaritons-spinor quasi-particles composed of semiconductor excitons and microcavity photons-directly couple exciton spins and photon polarizations, combining the advantages of both approaches. However, their implementation for spintronics has been hindered because polariton spins can be manipulated only optically or by strong magnetic fields. Here we use an external electric field to directly control the spin of a polariton condensate, bias-tuning the emission polarization. The nonlinear spin dynamics offers an alternative route to switching, allowing us to realize an electrical spin-switch exhibiting ultralow switching energies below 0.5 fJ. Our results lay the foundation for development of devices based on the electro-optical control of coherent spin ensembles on a chip.