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Characterizing frequency correlations via polarization measurements : Using the decoherence of a two-photon polarization state as a tool to measure frequency correlations in spontaneous parametric down conversion

Jaime Moreno

Published Jan 1, 2023• 0 citations
OpenAlex

Abstract

Developing techniques for characterizing quantum mechanical systems has been a major topic of research, especially in recent years, as quantum technologies, such as quantum communication and quantum cryptography, have grown to become an important asset in modern society. Although techniques such as quantum state tomography is an effective method to characterize a system consisting of two-level systems, the characterization of continuous degree of freedom such as space or frequency stills represents a time-consuming task as the state space scales exponentially with the dimension of the system. In this work, we show an indirect approach for measuring properties of high-dimensional degrees of freedom by coupling them to two-dimensional subsystems that can be measured efficiently via quantum state tomography. In our case, the property of interest is the correlation factor of the joint spectral amplitude describing the two-photon frequency states, which are coupled to the polarization degree of freedom using a completely positive trace-preserving map, called a dephasing channel. The action of the map on the polarization state induces a decoherence effect that depends on the initial frequency state, thus allowing to retrieve information about the frequency correlation factor by only measuring the decoherence in the polarization state. In the experimental part, we produced a pair of photons using spontaneous parametric down-conversion and characterized the joint spectral intensity with stimulated emission tomography. The decoherence was controlled with a birefringent material that acts as a dephasing channel. The polarization state was measured after the dephasing channel for two different initial frequency configurations using quantum state tomography. The bounds for the frequency correlation factor were calculated from the fidelity of the two polarization states and the generalized data processing inequality. The results of this work show that the polarization decoherence can be used as a tool to measure the frequency correlation factor of the joint spectral amplitude.

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Developing techniques for characterizing quantum mechanical systems has been a major topic of research, especially in recent years, as quantum technologies, such as quantum communication and quantum cryptography, have grown to become an important asset in modern society. Although techniques such as quantum state tomography is an effective method to characterize a system consisting of two-level systems, the characterization of continuous degree of freedom such as space or frequency stills represents a time-consuming task as the state space scales exponentially with the dimension of the system. In this work, we show an indirect approach for measuring properties of high-dimensional degrees of freedom by coupling them to two-dimensional subsystems that can be measured efficiently via quantum state tomography. In our case, the property of interest is the correlation factor of the joint spectral amplitude describing the two-photon frequency states, which are coupled to the polarization degree of freedom using a completely positive trace-preserving map, called a dephasing channel. The action of the map on the polarization state induces a decoherence effect that depends on the initial frequency state, thus allowing to retrieve information about the frequency correlation factor by only measuring the decoherence in the polarization state. In the experimental part, we produced a pair of photons using spontaneous parametric down-conversion and characterized the joint spectral intensity with stimulated emission tomography. The decoherence was controlled with a birefringent material that acts as a dephasing channel. The polarization state was measured after the dephasing channel for two different initial frequency configurations using quantum state tomography. The bounds for the frequency correlation factor were calculated from the fidelity of the two polarization states and the generalized data processing inequality. The results of this work show that the polarization decoherence can be used as a tool to measure the frequency correlation factor of the joint spectral amplitude.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.
The spectral distribution of photon pairs produced by spontaneous parametric downconversion (SPDC) is one of the most exploited degrees of freedom in multiphoton experiments. Consequently, the characterization of such correlations is, without a doubt, a task of utmost importance. Common methods for measuring the joint spectral intensity (JSI) of correlated photon pairs often exhibit several drawbacks, such as the requirement for a bright source to offset high losses or the need for two-dimensional measurements, which can lead to prolonged acquisition times. In this work, we experimentally demonstrate a technique that allows for the reconstruction of the JSI from a single interferometric measurement, thus reducing the dimensionality of the problem. The reconstructed JSIs show good agreement with those obtained directly through a fiber spectrometer, confirming the effectiveness of our approach. This technique significantly enhances the efficiency of JSI characterization, offering a resource-efficient method for quantum state characterization in SPDC-based experiments.
This work is focused on the engineering and characterization of the frequency-time properties of photon pairs generated with a semiconductor source. This device emits photons propagating in opposite directions at telecom wavelengths using spontaneous parametric down-conversion at room temperature. A microcavity integrated in the source allows the resonance of the transverse pump beam, enhancing the efficiency of the nonlinear interaction. We give a theoretical description of the down-conversion process in the source and we show how the spatial and spectral properties of the pump beam impact the properties of the photons, in particular their degree of entanglement in frequency allowing a versatile engineering. The variety of states that can be produced is illustrated using the Joint Spectral Amplitude. Two techniques allowing the characterization of the Joint Spectral Intensity have been implemented. The first one is a single photon spectrograph. The second one, based on the stimulation of the down-conversion process showed a dramatic improvement in terms of resolution and integration time. Both techniques allowed the demonstration of the frequency correlation engineering by varying the waist and curvature radius of the pump beam. Examples of more exotic states and a technique to characterize their chronocyclic Wigner function are theoretically investigated. The relationship between time-frequency properties and degree of entanglement in polarization of the biphoton is also explored.
The measurement of correlations between different degrees of freedom is an important, but in general extremely difficult task in many applications of quantum mechanics. Here, we report an all-optical experimental detection and quantification of quantum correlations between the polarization and the frequency degrees of freedom of single photons by means of local operations acting only on the polarization degree of freedom. These operations only require experimental control over an easily accessible two-dimensional subsystem, despite handling strongly mixed quantum states comprised of a continuum of orthogonal frequency states. Our experiment thus represents a photonic realization of a scheme for the local detection of quantum correlations in a truly infinite-dimensional continuous-variable system, which excludes an efficient finite-dimensional truncation.
Spontaneous parametric down-conversion (SPDC) is the most often used source of entangled photon states in quantum optics. Recently, it has been suggested in theory that the reduction of polarization entanglement between the photon pair generated via the type-II SPDC process pumped by a ultrafast laser is due to the asymmetry in the joint spectrum function, which is the indicative of the frequency entanglement between the two photons. In this paper, we report the measurement of the joint spectrum function (i.e., direct observation of the degree of frequency entanglement) of the two-photon state of type-II SPDC in both cw- and ultrafast-laser pumping conditions. We observed that, in agreement with the theory, the degree of frequency entanglement (the shape of the joint spectrum function) is indeed different for cw- and ultrafast-pumped type-II SPDC. Our results are of importance in "engineering" the two-photon state for specific quantum applications, such as quantum cryptography.
Photons are useful quantum systems for investigating the fundamental and practical aspects of dephasing, decoherence, and other types of open quantum dynamics. However, descriptions of open dynamics of photonic systems are usually in terms of decoherence functions and in many cases an explicit master-equation-based description is not available. This is particularly true when considering multipartite photonic open systems having possibly correlated environments. We obtain generic master equations for the reduced dephasing dynamics of a two-photon polarization state coupled to respective frequency degrees of freedom when the frequency degrees of freedom that form the environment are initially correlated. Our results show the explicit dependence of the operator form of the master equation and the decay rates on these correlations as well as on various types of frequency distributions. Furthermore, we use the recently developed bath-positive decomposition method to treat an initially correlated polarization-frequency state of a photon and demonstrate how this allows us to gain new insight and detailed information on how the contributions of different origins influence the photonic dephasing.