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arXiv:0811.2784 · Science

Complete Characterization of Quantum-Optical Processes

Mirko Lobino, Dmitry Korystov, Connor Kupchak, Eden V. Figueroa, Barry C. Sanders, Alexander I. Lvovsky

Published Sep 26, 2008• 153 citations
arXivHTMLPDF

Abstract

The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.

DOI
10.1126/science.1162086

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The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, i.e. classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
We review the method for characterizing, with arbitrarily high accuracy, any quantum optical process, which our group has developed over the past few years. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We present a simple scheme for calculating the process matrix from this information. We demonstrate the capability of our protocol by demonstrating complete characterization of an optical memory based on electromagnetically induced transparency.
This thesis introduces and implements a characterization procedure called coherent state quantum process tomography and applies it to a selection of quantum operations. The procedure holds advantages over previous quantum process tomography methods, a pri- mary one is that a process can be characterized by measuring its effect on a set of coherent states which are readily available from a laser source. After introduction of the characterization procedure, the method is tested on a simple process of an electro-optical modulator and polarizing beam splitter. The accuracy of the characterization is verified by comparison of the predicted action of the reconstructed process tensor versus the actual experiment involving a squeezed vacuum state. The algorithm is then implemented and verified on a quantum memory system based on electromagnetically induced transparency, a system that was previously shown capable of storing a squeezed vacuum state. Lastly, a new optical storage system based on a gradient echo memory scheme is con- structed and optimized to achieve memory retrieval efficiencies of >80%. To characterize this system, a modified coherent state quantum process tomography algorithm based on the method of maximum likelihood estimation is employed. Despite the high efficiency values, the presence of excess noise resulted in the degradation of the storage device per- formance to be below the benchmarks of a quantum memory system. This estimation algorithm is also successfully implemented on the non-deterministic processes of photon creation and annihilation.
The goal of this work is to examine the coherence of classical light fields in order to assess their usefulness for quantum-informational tasks and to draw conclusions about the properties of the light source. To this end, we use and extend several optical homodyne tomography techniques employing four-port, eight-port, and sixteen-port detection schemes. To understand the role of coherence of a light field in solving a quantum informational task such as coherent qubit control, we begin by analyzing the qubit excitation process from a resource-theoretical perspective. By simulating the light-matter interactions, we demonstrate how the quantum coherence of the driving light field emerges as a key ingredient for coherent qubit control. At the same time, we show how the presence of thermal noise or dephasing significantly degrades the achievable quantum coherence of the light field. After studying the coherence properties of conventional lasers, we turn to non-conventional coherent light sources and investigate the emission of a non-resonantly excited exciton-polariton condensate. By employing long-lived polaritons and minimizing interactions with the reservoir, we optimize the condensation process and achieve a pronounced buildup of quantum superpositions in the condensate immediately above the condensation threshold. Finally, we shift our focus entirely to the matter system itself and use the coherence of the emitted light field to investigate its dynamics. For this purpose, we introduce a sixteen-port detection scheme that enables non-stationary and conditional analyses tailored to the requirements of semiconductor spectroscopy. Benchmarking the setup with a thermal light field, then demonstrate how we can resolve the stochastic fluctuations of the thermal state on the femtosecond level. Overall, our results establish connections between quantum optics, quantum information science, and semiconductor physics, providing insights relevant for quantum technologies and future hybrid quantum devices.
We report a technique for experimental characterization of an M -mode quantum optical process, generalizing the single-mode coherent-state quantum-process tomography method [ 1 , 2 ]. By measuring the effect of the process on multi-mode coherent states via balanced homodyne tomography, we obtain the process tensor in the Fock basis. This rank- tensor, which predicts the effect of the process on an arbitrary density matrix, is iteratively reconstructed directly from the experimental data via the maximum-likelihood method. We demonstrate the capabilities of our method using the example of a beam splitter, reconstructing its process tensor within the subspace spanned by the first three Fock states. In spite of using purely classical probe states, we recover quantum properties of this optical element, in particular the Hong–Ou–Mandel effect.
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data compared to state-of-the-art methods. We link this advantage to reduced overfitting. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of large-scale physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.