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arXiv:1003.3194 · Physical Review Letters

Planck Spectroscopy and Quantum Noise of Microwave Beam Splitters

M. Mariantoni, E. P. Menzel, Frank Deppe, Miguel Ángel Araque Caballero, A. Baust, T. Niemczyk, Eric A. Hoffmann, E. Solano, Achim Marx, R. Gross

Published Sep 20, 2010• 75 citations
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Abstract

We use a correlation function analysis of the field quadratures to characterize both the blackbody radiation emitted by a 50 Ω load resistor and the quantum properties of two types of beam splitters in the microwave regime. To this end, we first study vacuum fluctuations as a function of frequency in a Planck spectroscopy experiment and then measure the covariance matrix of weak thermal states. Our results provide direct experimental evidence that vacuum fluctuations represent the fundamental minimum quantum noise added by a beam splitter to any given input signal.

DOI
10.1103/physrevlett.105.133601

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We use a correlation function analysis of the field quadratures to characterize both the blackbody radiation emitted by a 50 Ω load resistor and the quantum properties of two types of beam splitters in the microwave regime. To this end, we first study vacuum fluctuations as a function of frequency in a Planck spectroscopy experiment and then measure the covariance matrix of weak thermal states. Our results provide direct experimental evidence that vacuum fluctuations represent the fundamental minimum quantum noise added by a beam splitter to any given input signal.
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.
When a coherent electromagnetic wave passes through a beam splitter (BS), it is divided equally into two parts. However, the quantum noise associated with the resulting coherent states, despite being reduced in amplitude by half, remains fundamentally constrained by the quantum noise limit, independent of the intensity. By placing a mirror at the unused input port of the BS, a standing wave is formed in the vicinity of the mirror, which influences the vacuum fluctuations of the coherent state at the BS output. Using semi-classical and quantum mechanical approaches, we calculate the vacuum fluctuations induced by the mirror and demonstrate that the vacuum noise originating from the mirror side periodically reaches zero at the BS output. Leveraging this effect, we show that the vacuum fluctuations of the light split by the BS can be readily reduced below the quantum noise limit. Furthermore, through feedback mechanisms, the vacuum fluctuations of the electromagnetic field at the other output port can also be suppressed below the quantum noise limit. These findings provide a pivotal insight into the manipulation of electromagnetic noise, with broad implications for all experiments involving quantum noise control.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.
The statistics of electron transport in a quantum conductor is affected by fluctuations of its voltage bias. Here, we show experimentally how a third order correlation in the electromagnetic field arises from the noise of a tunnel junction in the microwave domain being modulated by the vacuum fluctuations generated by a resistor at ultralow temperature. This provides a way to measure the vacuum fluctuations experienced by the junction, not offset by the unavoidable noise added by the detection setup.
A new quantum measurement scheme of intensity difference fluctuation between two light beams of equal mean intensity is presented. In this system a beam splitter is used as the coupling device and the twin beams with high quantum correlation are injected into its dark port as the input meter wave instead of the usual vacuum field. A measurement satisfying all the quantum nondemolition criteria is experimentally achieved. The measured sum of the transfer coefficients and the conditional variance are, respectively, Ts+Tm=1.31{T}_{s}{+T}_{m}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.31Ts​+Tm​=1.31 and ${V}_{s/m}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2.1\mathrm{dB}$.