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Analytical analysis of single-photon correlations emitted by disordered semiconductor heterostructures.

P. Bozsoki, Hoyer, Walter, M. Kira, Imre Varga, P. Thomas, S. W. Koch, Henning Schomerus

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In a recent publication [Phys. Rev. Lett. 97, 227402 (2006), cond-mat/0611411], it has been demonstrated numerically that a long-range disorder potential in semiconductor quantum wells can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.

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In a recent publication [Phys. Rev. Lett. 97, 227402 (2006), cond-mat/0611411], it has been demonstrated numerically that a long-range disorder potential in semiconductor quantum wells can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.
We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found evidence for a non-universal behavior in this model and found no indications of a universal infinite randomness fixed point (IRFP) scenario. We show that these data are not in the asymptotic regime since the system sizes that have been considered are of the same order of magnitude or much smaller than the crossover length x_W. We give a scaling form for the xx-spin-correlation function that takes this crossover length into account and that is compatible with the IRFP scenario and a random singlet phase.
In a recent letter [Phys. Rev. Lett. 78, 515 (1997); cond-mat/9612034] Roemer and Schreiber report on numerical calculations that led them to conclude that the previously observed enhancement of the localization length L2L_2L2​ of two interacting particles (TIP) vanishes in the thermodynamic limit. We point out that such a claim (i) is in conflict with the scaling theory of localization, (ii) ignores a consistent picture from a wealth of published numerical data and analytical investigations, and (iii) directly contradicts new numerical results obtained with a Green function method that is well adapted to the problem under study. The claim of Roemer and Schreiber is based on extrapolating from L<360 to infinity. Our data clearly shows the two particle localization length L2L_2L2​ to be significantly enhanced and independent of system size between L=100 and L=1000, as expected on physical grounds.
Even though the quantized interaction between light and matter in the photoelectric effect is considered one of the cornerstones in the development of quantum mechanics, it was long thought impossible to directly observe the quantized nature of light itself. The advent of light-intensity autocorrelation techniques in the 1950s, first developed to study the size of stars, changed little in this perception, until true single-photon correlation spectroscopy from trapped ions was proven to be possible in the late 1970s: Photons from a single quantum emitter tend to arrive in bunches, but each light quantum is spaced apart in time—it is antibunched. Initially considered only as the workhorse of atomic quantum optics, over the past two decades, photon correlation techniques have become a standard in fields as diverse as quantum-information processing, biological imaging, polymer physics, and materials science, in general. The technique is particularly useful for probing materials that are specifically designed to emit or absorb light in optoelectronic devices, such as light-emitting diodes, solar cells, or lasers. The central question in such studies is how large a mesoscopic piece of material can become and still behave as an atom-like source of single photons. What interactions may arise between multiple excitations within a material, and what sort of dark states may give rise to intermittency in the stream of photons? We review the many different classes of optoelectronic materials for which photon-correlation spectroscopy has proven to offer useful insight into excited-state dynamics, ranging from molecular, over semiconductor to metallic nanostructures. The technique is particularly suited to probing mesoscopic aggregates of organic semiconductors since each single molecule acts as a quantum emitter itself.
We study subwavelength position measurement via spontaneous emission spectroscopy with two photons. Our model systems are a single $\ensuremath{\Lambda}$-type three-level atom, in which a dual interaction generates two independent photons, and an MMM-type five-level atom, which emits two photons in a double-Raman process. The difference is that the MMM-type system emits correlated pairs of photons, while the photon pairs from the $\ensuremath{\Lambda}$ system are uncorrelated. In order to evaluate the performance of the position measurement, we introduce an analysis scheme motivated by a possible experimental measurement procedure. We find characteristic differences in the spontaneous emission spectra of the two systems arising from the photon correlation in the MMM-type system. But interestingly, the effect of this photon pair correlation on the conditional position probability distribution does not lead to an increase in the position information of the single atom. Nevertheless, both schemes allow for an efficient measurement of the particle position with unambiguous position determination over a wide range of parameters.