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Observing the Conditional Decoherence of a Mixed State of Light

Marc Aßmann, M. Kira, Steven T. Cundiff

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We demonstrate a method to capture the temporal evolution of a light field using continuous-variable conditional two-time Wigner functions. Reference beams with fixed phase relationship to the signal are not required.
DOI
10.1364/cleo_si.2014.stu3e.6

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•Jan 1, 2010•1 citation
Continuous variable quantum state tomography is one of the most powerful techniques to study the properties of light fields in quantum optics. However, the need for a fixed phase reference has so far prevented widespread usage in other fields such as semiconductor spectroscopy. Here, we introduce nonstationary quantum state tomography, which adapts the technique to the special requirements of ultrafast spectroscopy. In detail, we gain access to the amplitude and phase of light fields with a temporal resolution of about 100 fs without the need for a fixed phase reference. Furthermore, we show how our technique allows us to perform conditional studies of stochastic dynamics that are inaccessible experimentally by conventional means and demonstrate the capabilities experimentally by monitoring the stochastic dynamics of a thermal light field on the sub-ps scale. Finally, we discuss differences and similarities to more standard Hanbury Brown--Twiss photon correlation experiments, which may be considered as the discrete variable analogs of our technique.
Beam splitters allow us to superpose two continuous single-mode quantum systems. To study the behavior of their strong mode mixing dynamics, we consider variable beam splitters and their dynamics using Wigner’s phase space distribution, W , the evolution of which is governed by the continuity equation ∂∂ τ W =− ∇ ⋅ J . We derive the form of the corresponding Wigner current, J , of each outgoing mode after tracing out the other. The influence of the modes on each other is analyzed and visualized using their respective Wigner distributions and Wigner currents. This allows us to perform geometrical analyses of the mode interactions, casting new light on beam splitter behavior. Several of the presented results should be immediately testable in experiments.
Quantum systems entanglement in continuous variables has been receiving increasing attention from the scientific community. The transverse spatial shape of photons (i.e. transverse position and momentum degree of freedom) is such a continuous variable systems, which due to its ease of control is prone to be used for testing some of the new physical predictions that continuous variables quantum systems can offer, as the improvement of the security of quantum key distribution cryptography and the efficiency enhancement of quantum communication protocols. Following this line, the mean goal of this Thesis has been the characterization and measurement of the spatial shape of photons. Another outstanding problem in Quantum Optics Information Technology (QOIT) is the coherent and reversible storage of photons states in matter, i.e. the necessity of a quantum memory. Theoretical and experimental results about this topic have been showed. Below we summarize the more important contributions of this Thesis: Demonstration about the non-validity of the OAM transformation rule FORr highly focused light beams: We have shown from a theoretical and experimental point of view that the OAM transformation rule is not valid for highly focused light beams, since Dove prisms inherently introduce astigmatism, and therefore further OAM changes. We have analyzed how light beams with a well defined value of the OAM per photon, after traversing the Dove prism, are transformed into a superposition of states with well defined OAM. The violation of the rule, turns out to be more important for highly focused light beams. We have provided a quantitative study of the properties of the Dove prism, and we have verified experimentally the validity of the theoretical results in a series of experiments with a commercially available Dove prism. Presentation of a new method to measure the amplitude and phase of Laguerre-Gaussian like beams: A method to measure the amplitude an phase of Laguerre-Gaussian like beams have been presented, from a theoretical and experimental point of view. This method is based on a small variation of the spiral phase interferometry technique, which allows to avoid some technical problems that can be found in the reconstruction of finite sized beams and beams with phase singularities. A few examples of the use of our technique for the characterization of complex beams have been presented. Description of the transverse spatial shape of bipartite entangled photons generated in Spontaneous Parametric Down Conversion (SPDC) using the Wigner function formulism: We have show some theoretical and experimental results regarding the spatial Wigner function of entangled paired photons generated in SPDC. Concretely, we have studied the remote preparation of one of the photons of the pair, for the photon being in a Gaussian beam and in a superposition of two modes. Also, we have analyzed and measured the case of the Wigner function of only one of the two photons of the pair, which shows that one photon of the pair is in a statistical mixture of modes. Finally, an experiment to completely measure the spatial state of the two photons was proposed, and also analytical expressions for the results one would expect in this case were given. Investigation about the storage of spatial light polarization grating into the Zeeman ground states of cold cesium atoms: We have investigated theoretically and experimentally the dynamics of light grating stored in electromagnetically induced transparent (EIT) medium associated with a degenerate two-level system. The dependence of the stored light grating with the intensities of the incident and reading beams has been investigated. Bragg diffraction into the stored grating has been employed to probe the dynamics under different conditions showing reasonable results in agreement with the theoretical model developed. Moreover, we also have observed the coherent evolution of the stored grating in the presence of an applied magnetic field, which allows collapses and revivals of the stored grating, which is associated with the Larmor precession of the induced grating around the applied magnetic field. We think that the results of this Thesis are an important step in order to explore the quantum capabilities of the transverse spatial shape of photons and can encourage going further in this line of research. Moreover, the investigation on the dynamics of light grating stored in an EIT medium is of considerable importance for a better understanding of the coherent memory for multidimensional state spaces. Thus, a further and more detailed investigation of the topics presented here should be of special interest for the scientific community.