Propagation of nonclassical optical radiation through a semiconductor slab

Abstract

Based on a microscopic derivation of the emission spectra of a bulk semiconductor we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.PACS numbers: 42.50. Nn, 42.50.Ct The progress of experimental techniques has rendered it possible to almost completely measure the quantum statistics of radiation-matter systems, so that correlation functions up to, in principle, arbitrarily high orders can be detected (for a review of the various methods, see, e. g., Ref.[1]). Within the framework of quantum optics, the theoretical study of the interaction of light with complex material systems is typically based on simplifying model systems, effective-Hamiltonian schemes or related semi-phenomenological concepts rather than rigorous microscopic calculations [2].On the other hand, in many-particle quantum theory, including semiconductor theory, much effort has been spent on the development of methods for microscopically describing complex material systems. This includes the description of coherent optical interactions by semiconductor Bloch equations and semiconductor luminescence equations as well as the development of nonequilibrium Green's function methods [3,4]. In principle, these methods lead to infinite hierarchies of correlations, which are usually treated by properly developed methods of truncations and/or decorrelations.It is well known that semiconductors can be used to generate nonclassical radiation [5]. In particular, the development of nano-structured systems has opened new possibilities of the generation and application of nonclassical radiation in integrated systems. For example, the correlated emission of single photons can be demonstrated by using quantum dots [6] and bound excitons in semiconductors [7]. Experiments with quantum wells [8] and quantum dots [9,10,11] also show the potential of semiconductors for the generation of entangled photons, which are of interest in quantum information processing.In order to properly describe the generation and/or propagation of nonclassical radiation through complex material systems such as semiconductor slabs, one has simultaneously to deal with both higher-order radiationfield correlation functions and many-particle quantum statistics of the material system. Within the frame of macroscopic quantum electrodynamics (QED), methods of describing the quantized electromagnetic field in linearly responding (dispersing and absorbing/amplifying) media have been developed, with special emphasis on quantum-noise effects [12,13,14,15,16,17]. Based on given constitutive relations of the material system, field correlation functions of arbitrary order can be calculated in this way. On the other hand, methods of many-particle theory can be used to treat the radiation-matter interaction within the frame of mic...

Enhanced squeezing by absorption

“…Hence, the quantum-well emission spectrum depends both on the emission spectrum of the excitons and the absorption spectrum. This result [9] is consistent with both the input-output formalism of quantum optics [22] and Kirchhoffs law of radiation in non-equilibrium many-body systems [23]. Thus, in our system absorption dominates the transmission properties.…”

“…The absorption spectrum a(ω) follows from the input-output formalism [22], which relates it to the susceptibility χ(ω). We apply a simple oscillator model,…”

“…We want to apply the input-output formalism developed in [25,22]. The source fields in time and frequency domain are related aŝ…”

“…The exciton-emission spectrum S x ( ) w can be calculated using the Wiener-Khintchine theorem [24] with the source field given by the collective exciton operators, and the QRT [12]. The absorption spectrum a ( ) w follows from the inputoutput formalism [22], which relates it to the susceptibility ( ) c w . We apply a simple oscillator model,…”

“…In the following section, we deduce general quantum-well correlations from the excitonic fluorescence correlations and the absorption. We want to apply the input-output formalism developed in [22,25]. The source fields in time and frequency domain are related as…”