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AIP conference proceedings

Hanbury Brown and Twiss Noise Correlations to Probe the Statistics of GHz Photons Emitted by Quantum Conductors

D. C. Glattli

Published Jan 1, 2005• 1 citation
Publisher

Abstract

In microwave current noise power measurements, a detector is used which measures the power emitted by the device in the external circuit. This power can be viewed as a flux of (microwave) photons. An interesting question is the nature of the photon statistics associated with the noise power. While for thermal noise one expects classical photon statistics (Bose‐Einstein), recently it has been shown theoretically that shot noise may lead to non‐classical photon statistics. We propose an original cryogenic experimental scheme to characterize the statistics of photons emitted by conductors at GHz frequency. The experiments, a microwave analog of optical Hanbury Brown Twiss photon correlations, is able to distinguish the statistics of the black‐body radiation associated with thermal electronic noise from the statistics of a coherent monochromatic microwave source. The experiments displays the sensitivity required for future investigations of non classical photons emitted by quantum conductors.

DOI
10.1063/1.2036794

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In microwave current noise power measurements, a detector is used which measures the power emitted by the device in the external circuit. This power can be viewed as a flux of (microwave) photons. An interesting question is the nature of the photon statistics associated with the noise power. While for thermal noise one expects classical photon statistics (Bose‐Einstein), recently it has been shown theoretically that shot noise may lead to non‐classical photon statistics. We propose an original cryogenic experimental scheme to characterize the statistics of photons emitted by conductors at GHz frequency. The experiments, a microwave analog of optical Hanbury Brown Twiss photon correlations, is able to distinguish the statistics of the black‐body radiation associated with thermal electronic noise from the statistics of a coherent monochromatic microwave source. The experiments displays the sensitivity required for future investigations of non classical photons emitted by quantum conductors.
We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.
We report on an Hanbury Brown-Twiss experiment probing the statistics of microwave photons emitted by a tunnel junction in the shot-noise regime at low temperature. By measuring the cross correlation of the fluctuations of the occupation numbers of the photon modes of both detection branches, we show that while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to hν/e.
We present an investigation of orbital entanglement in mesoscopic conductors. Several schemes for generation of orbital entanglement are discussed, such as normal‐superconducting, electron‐hole and dynamic orbital entanglers. The generated, orbitally entangled state is investigated with the focus on the state emitted in an electronic analog of the optical Hanbury Brown Twiss experiment. The one and two particle properties of the emitted state are described in terms of reduced density matrices. Approaches to detect and characterize the entanglement based on zero frequency shot noise are discussed, with the focus on a complete reconstruction of the emitted state via quantum state tomography.
In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n^{2}+n photon number variance of thermal microwave photons emitted from a blackbody radiator for mean photon numbers, 0.05≲n≲1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.
We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown-Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.
The standard expressions for the noise that is due to photon fluctuations in thermal background radiation typically apply only for a single detector and are often strictly valid only for single-mode illumination. I describe a technique for rigorously calculating thermal photon noise, which allows for arbitrary numbers of optical inputs and detectors, multiple-mode illumination, and both internal and external noise sources. Several simple examples are given, and a general result is obtained for multimode detectors. The formalism uses scattering matrices, noise correlation matrices, and some fundamentals of quantum optics. The covariance matrix of the photon noise at the detector outputs is calculated and includes the Hanbury Brown and Twiss photon-bunching correlations. These correlations can be of crucial importance, and they explain why instruments such as autocorrelation spectrometers and pairwise-combined interferometers are competitive (and indeed common) at radio wavelengths but have a sensitivity disadvantage at optical wavelengths. The case of autocorrelation spectrometers is studied in detail.