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arXiv:1206.3405 · Physical Review A

Characterizing quantum microwave radiation and its entanglement with superconducting qubits using linear detectors

Christopher Eichler, Deniz Bozyigit, Andreas J. Wallraff

Published Sep 10, 2012• 134 citations
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Abstract

Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasiprobability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.

DOI
10.1103/physreva.86.032106

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A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.
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Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
We study quantum state tomography, entanglement detection and channel noise reconstruction of propagating quantum microwaves via dual-path methods. The presented schemes make use of the following key elements: propagation channels, beam splitters, linear amplifiers and field quadrature detectors. Remarkably, our methods are tolerant to the ubiquitous noise added to the signals by phase-insensitive microwave amplifiers. Furthermore, we analyse our techniques with numerical examples and experimental data, and compare them with the scheme developed in Eichler et al (2011 Phys. Rev. Lett. 106 220503; 2011 Phys. Rev. Lett. 107 113601), based on a single path. Our methods provide key toolbox components that may pave the way towards quantum microwave teleportation and communication protocols.
We study quantum state tomography, entanglement detection and channel noise reconstruction of propagating quantum microwaves via dual-path methods. The presented schemes make use of the following key elements: propagation channels, beam splitters, linear amplifiers and field quadrature detectors. Remarkably, our methods are tolerant to the ubiquitous noise added to the signals by phase-insensitive microwave amplifiers. Furthermore, we analyse our techniques with numerical examples and experimental data, and compare them with the scheme developed in Eichler et al (2011 Phys. Rev. Lett. 106 220503; 2011 Phys. Rev. Lett. 107 113601), based on a single path. Our methods provide key toolbox components that may pave the way towards quantum microwave teleportation and communication protocols.
We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.