Phone numbersPolariton Phenomena in Semiconductor Microcavities
Fig. 1: Schematic diagrams of planar microcavity structure with quantum wells embedded in the antinodes of confined photonic mode.
Researchers
| Academic Staff: |
Maurice Skolnick David Whittaker |
|---|---|
| Research Fellows: | Dmitry Krizhanovskii |
| Post-Docs: | Dipankar Sarkar |
| PhD Students: |
Robert Bradley Kurumurthy Guda Maksym Sich |
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Fig. 2 (a, b): Dispersion curves of a planar microcavity. LP, UP: lower and upper polariton branches, on logarithmic scale in a) and linear in b) for non-resonant and resonant excitation respectively. a) corresponds to the formation of a quasiequilibrium BEC and b) to the OPO high density signal and idler polariton phases.
Semiconductor quantum microcavities (QMC) are one-dimensional planar structures grown by layer-by-layer epitaxial techniques. The cavity plays the role of a "defect" in a periodic stack of layers providing strong localisation of light along the growth direction, the so-called Fabry-Perot localised mode. Strongly magnified optical fields of the Fabry-Perot mode can interact with excitonic states of quantum wells (QWs) grown in the cavity. In the strong coupling regime this interaction leads to the creation of a new type of quasiparticle, the "microcavity polariton". Their optical properties are of great fundamental interest because these quasi-particles possess properties of light (photons) and matter (excitons) at the same time. The polaritons can undergo Bose-Einstein condensation to macroscopically occupied states in well defined regions of k-space. Reviews by the group can be found in Semiconductor Science and Technology 13, 645 (1998) [link], IEEE Sel Topics in Quantum Electronics 8, 1060 (2002) [link].
There are a few ways to excite polariton condensates using external laser sources. Firstly, MC structures can be excited at high energy well above exciton level (Fig 2 a)), the free carriers which are created relax first into the lower energy polariton and, eventually, a polariton Bose-Einstein condensate at k around zero is formed at sufficiently high pump densities.
The second way to create a polariton condensate at k=0 is to use laser pumping resonant with the lower polariton branch shown in Fig.2 b). Direct polariton-polariton scattering from the pump results in condensed signal and idler states, which form an optical parametric oscillator (OPO). The OPO signal has properties similar to BECs formed under nonresonant pumping, since its phase is independent of that of the pump.
Recent results:
- Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate
A.P. Love, D.N. Krizhanovskii, D.M. Whittaker, R. Bouchekioua, D. Sanvitto, S. Al Rizeiqi, R.A. Bradley, M.S. Skolnick, P.R. Eastham, R. André, Le Si Dang
Physical Review Letters 101 067404 (2008) http://link.aps.org/doi/10.1103/PhysRevLett.101.067404
Fig. 3: Image of multiple polariton condensates formed in energy-momentum space well above condensation threshold.
In this work we demonstrated that polariton BECs exhibit long phase memory times, two order of magnitude longer than the particle lifetime. Such long times permit the fundamental mechanisms determining the phase memory times to be revealed. We showed that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first order correlation function. This lineshape, and the long decay times (~150ps) of both first and second order coherence functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system.
Fig. 4: Long decay times of the first (a) and the second (b) order correlation functions of an individual condensate modes
We also show that polariton BEC consists of a number multiple condensates separated by a small energy distance. This effect arise from nonequilibrium character of polaritons and polariton interactions with transverse photonic disorder.
- Self-organization of multiple polariton-polariton scattering in semiconductor microcavities
D.N. Krizhanovskii, S.S. Gavrilov, A.P.D. Love, D. Sanvitto, N.A. Gippius, S.G. Tikhodeev, V.D. Kulakovskii, D.M. Whittaker, M.S. Skolnick, J.S. Roberts
Physical Review B 77 115336 (2008) http://link.aps.org/doi/10.1103/PhysRevB.77.115336
In this paper we show that the highly occupied microcavity (MCs) polariton system exhibits a new type of phase transition, not previously observed in the physics of non-linear systems. This new behaviour is a result of the unique, continuous transverse mode dispersion in microcavities with a point of inflection and finite energy at k = 0.
We employ cw resonant excitation, with the excitation significantly detuned with respect to the LP dispersion. At powers below threshold (Pth) the scattered polaritons form a figure-of-eight in k-space (Fig 5.a), as determined by energy and momentum conservation. At P~0.95 Pth significant spectral narrowing of the emission from the states on the figure–of eight is observed indicating the onset of macroscopic occupation (Fig.5b). However, with further increase of P to ~1.05 Pth we observe an abrupt transition of the stimulated emission from these states away from k = 0 to one that is strongly localized at k=0 (Fig.5c). Such emission is stable at higher excitation powers (Fig 5d).
The observed transition differs from a non-equilibrium first order phase transition, where the order parameter has a discontinuity at threshold and the system undergoes a transition directly into a stable phase due to the bistable response to the driving parameter. To our knowledge, there are no other non-linear systems which exhibit similar behavior: well-known non-linear optical systems, such as lasers and parametric generators have only one or a few amplified longitudinal harmonics and thus do not exhibit the self-organisation.
Fig. 5: 2D images of lower polariton emission in k space (upper) and E-k space (lower) for increasing excitation powers. At P>30 mW an abrupt transition of the scattered MC polaritons from states on the figure-of-eight to a directional one at k~0 is observed.
Spontaneous vortices/antivortices in the polariton condensate formed under resonant pumping
Topological defects occur in many areas of science, including particle physics, cosmology, condensed matter physics and optics. Vortices are typical examples, which occur in bosonic condensates, such as dilute gases, liquid helium, superconductors and polariton BECs. We observed spontaneous vortex formation in the microcavity optical parametric oscillator (OPO) carrying finite Orbital Angular Momentum (OAM). We also demonstrate that a weak probe beam carrying OAM enables imprinting of a vortex state on to macroscopically occupied polariton states.
The OPO was excited using a laser beam without OAM. Figure 6a shows an image of the "signal" emission at k=0 in real space above threshold. At the edge of the emission a defect is formed with a dip in the emission intensity (region A). Figure 6b shows the interference pattern between the "signal" image in Fig.6a and the same image inverted in so that region A is mixed with region B. The fork-like dislocation indicates the spontaneous formation of a quantised vortex with finite OAM (L=1) in the signal. The phase relationship between pump, signal and idler results also in an anti-vortex in the idler state of OAM L=-1.
Fig. 6: a) Real space image of signal emission at k=0. b) Interference pattern demonstrating vortex state.
The Lab
Our microcavity lab contains a helium bath cryostat with a wide angular aperture. Excitation of the samples is by either of our 2 Ti:Sapphire lasers or via our diode laser for work requiring single mode excitation. The setup allows for a wide range of excitation angles and detection angles. Our setup contains both a Mach-Zehnder interferometer for measuring coherence times of the samples as well as a Hanbury-Brown & Twiss interferometer for g2 function measurements via two fast APDs. Our setup allows for automated images to be made, either in real space or k-space, via our spectrometer and PIXIS CCD. Our spatial light modulator allows modulation of both phase and amplitude of the laser beams driving polariton condensates, with the ability to study various topological defects, such as vortices and vortex lattices.
