Semiconductor quantum dots (QDs) which are the solid-state analog of atomic systems serve routinely as a viable platform for basic quantum mechanical experiments and detailed understanding of light-matter interactions. The use of QDs for quantum applications such as generation of single photons and entangled photon pairs, photon echo based quantum memories and quantum gates have been demonstrated often and are well documented.

The basic quantum mechanical phenomena of Ramsey interference in QD systems have also been reported. Early measurements of Ramsey fringes in a single GaAs QD, which was formed by width fluctuations of a quantum well, were observed using photoluminescence (PL) measurements by Bonadeo. Similarly, Ramsey-type oscillations in a single InGaAs QD selected from a low density self-assembled system were reported by Toda and Htoon. Photocurrent measurements in electric-fieldtunable single QD systems was used to demonstrate Ramsey interference by Stufler and by Michaelis. Two and three pulse photon echo experiments also enabled
observation of Ramsey fringes in a single InAs/GaAs QD, as reported by H. Jayakumar. A different aspect of Ramsey interference addressed the spin-state of QDs which was interrogated using ultrafast optical techniques by Press by Kim and by Lagoudakis. Common to all these reports is the fact that only isolated single quantum dots, held at cryogenic temperatures, were used.

A different class of quantum coherent experiments in semiconductor media were reported by Choi who showed Rabi oscillations in a quantum cascade semiconductor laser. Coherent light matter interactions in QD ensembles were studied by Marcinkevvicius who demonstrated electromagnetic induced transparency in a stack of InGaAs/GaS QDs and by Suzuki who used two-dimensional coherent spectroscopy to study an ensemble of InAs/GaAs QDs. Those experiments were also performed at cryogenic temperatures. A different approach to induce and observe quantum coherent phenomena in QD systems is to use short optical excitations and electrically driven QD ensembles operating at room temperature. The platform we employ is a QD based semiconductor optical amplifier (QD SOA) which is a long waveguide that provides optical gain. Such experiments have to overcome several hurdles. The first is the short room temperature coherence time which was previously determined from temperature dependent PL linewidth of a single QD by Bayer and through transient four wave mixing, measured in a GaAs QD SOA by Borri. Both techniques yield a coherence time of approximately 350 fs. Other difficulties stem from the QD ensemble inhomogeneity and the fact that incoherent interactions such as two photon absorption and a Kerr-like effect associated with it take place simultaneously and can mask coherent interactions. Nevertheless, using 100-150 fs excitation pulses, Rabi oscillations were demonstrated by Karni in an InAs/InP QD and by Capua in InAs/InP quantum dash (wire-like nano structures) SOAs employing the cross frequency resolved optical gating (X-FROG) technique and later by Kolarczik in an InAs/GaAs QD SOA using a technique called FROSCH. The role of the gain inhomogeneity and the incoherent interactions was considered by Karni as was a demonstration of coherent control to enhance the Rabi oscillations by using shaped excitation pulses. A different type of coherent control with a two-pulse pump-probeX-FROG was used by Capua to demonstrate cyclical instantaneous frequency variation of the probe pulse in a QD SOA that was biased to the absorption regime. No trace of a periodic intensity oscillation was observed in that experiment probably because of a severe dot inhomogeneity and a significantly reduced interaction of the electromagnetic field with the QDs due to off resonant excitations.

This paper describes direct observation of Ramsey fringes in a room temperature InAs/InP QD SOA operating in the high gain regime. A series of experiments using a pump-probeX-FROG system that includes shaping of the pump pulse, demonstrated a clear oscillatory behavior, with a period equal to an optical cycle, of both the intensity and the instantaneous frequency profiles of a 150 fs wide probe pulse. The oscillation modulation depth decreases with the nominal input pulse delay thereby enabling direct mapping of the process of de-coherence and the extraction of the coherence time which was found to be 410 fs.

An additional major finding described in this paper is an oscillation of the output temporal pulse separation which is caused by the coupling between the real and imaginary parts of the material susceptibility. The pulse separation oscillates with the same periodicity as the intensity and instantaneous frequency but lags behind them by a quarter of a cycle due to the complex nature of the susceptibility. The variation of the output temporal separation is
a direct result of the distributed nature of the pulse propagation along the SOA and cannot be observed in any experiment using a single QD.

The clear observation of the Ramsey fringes was made possible by the superb properties of the present QD SOA  and of the pulse shaper which ensures no input pulse overlap and an optimized induction of a specific coherent state by the pump pulse so as to maximize the Ramsey resonance effect. The experimental results were confirmed by a comprehensive numerical model.