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Register a new userHeterodyne Sensing of Microwaves with a Quantum Sensor
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Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However the spectral resolution in such protocols is limited ultimately by sensor lifetime. Here we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW-signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally we achieve a spectral resolution below $1 rm{Hz}$ for a $4 rm{GHz}$ signal far below the sensor lifetime limit of kilohertz. Furthermore we show control over the interaction of the MW-field with the two level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to highest sensitivity, the Floquet dynamics allows robust control independent from the systems resonance frequency. Our work is important for future studies in sensing weak microwave signals in wide frequency range with high spectral resolution.
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The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators cite{Teufel2011,Chan2011}. While heterodyne detection of the cavity field preserves asymmetries which provide a key signature that mechanical oscillators has attained the quantum regime, detection of a rotating quadrature of the light averages out important quantum correlations, yielding a weaker signal and lower sensitivity than homodyne detection. In turn, homodyning, detects a single optical quadrature, but loses the important quantum sideband asymmetries. In the present work we present and experimentally demonstrate a technique, involving judicious construction of the autocorrelators of the output current using filter functions, which can restore the lost correlations (whether classical or quantum), drastically augmenting the useful information extracted: the filtering adjusts for moderate errors in the locking phase of the local oscillator, allowing efficient single-shot measurement of hundreds of different field quadratures and rapid mapping of detailed features from a simple heterodyne trace. One may also control whether the correlations are recovered in isolation or interfere with the usual stationary heterodyne sidebands. In the latter case we obtain a spectrum of hybrid homodyne-heterodyne character, with motional sidebands of combined amplitudes comparable to homodyne. We term such recovery of lost heterodyne correlations with filter functions r-heterodyning: although investigated here in a thermal regime, its robustness and generality represents a promising new approach to sensing of quantum-scale displacements.
Homodyne and heterodyne detection represent twin-pillars of quantum displacement sensing using optical cavities, having permitted major breakthroughs including detection of gravitational waves and of the motion of quantum ground-state cooled mechanical oscillators. Both can suffer disadvantages as diagnostics in quantum optomechanics, either through symmetrisation (homodyne), or loss of correlations (heterodyne). We show that, for modest heterodyne beat frequencies ($Omega sim omega_M/10 gg Gamma$), judicious construction of the autocorrelation of the measured current can either recover (i) a spectrum with strong sidebands but without an imprecision noise floor (ii) a spectrum which is a hybrid, combining both homodyne and heterodyne sideband features. We simulate an experimental realisation with stochastic numerics and find excellent agreement with analytical quantum noise spectra. We term such retrospective recovery of lost heterodyne correlations r-heterodyning: as the method simply involves post-processing of a normal heterodyne time signal, there is no additional experimental constraint other than on the magnitude of $Omega$.
Propagating quantum microwaves have been proposed and successfully implemented to generate entanglement, thereby establishing a promising platform for the realisation of a quantum communication channel. However, the implementation of quantum teleportation with photons in the microwave regime is still absent. At the same time, recent developments in the field show that this key protocol could be feasible with current technology, which would pave the way to boost the field of microwave quantum communication. Here, we discuss the feasibility of a possible implementation of microwave quantum teleportation in a realistic scenario with losses. Furthermore, we propose how to implement quantum repeaters in the microwave regime without using photodetection, a key prerequisite to achieve long distance entanglement distribution.
Continuous-variable quantum key distribution exploits coherent measurements of the electromagnetic field, i.e., homodyne or heterodyne detection. The most advanced security analyses developed so far relied on idealised mathematical models for such measurements, which assume that the measurement outcomes are continuous and unbounded variables. As any physical measurement device has finite range and precision, these mathematical models only serve as an approximation. It is expected that, under suitable conditions, the predictions obtained using these simplified models are in good agreement with the actual experimental implementations. However, a quantitative analysis of the error introduced by this approximation, and of its impact on composable security, have been lacking so far. Here we present a theory to rigorously account for the experimental limitations of realistic heterodyne detection. We focus on asymptotic security against collective attacks, and indicate a route to include finite-size effects.
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 analyze 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.
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