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Physical Review Applied

Frequency Superresolution with Spectrotemporal Shaping of Photons

Manav Shah, Linran Fan

Published Mar 24, 2021• 11 citations
Publisher

Abstract

Quantum sensing and metrology promise useful insights and alternative techniques to surpass the measurement limits of a classical framework. Significant improvement has been made in the areas of imaging, positioning, timing, interferometry, communication, and information processing through quantum detection and estimation techniques. In this Letter, we focus on the application of quantum information for spectral measurements. Specifically, we study the quantum limit to resolve two spectral modes with small frequency separation. We show that frequency superresolution can be achieved with spectrotemporal shaping of input fields before detection. Through a numerical optimization algorithm, we design the apparatus for spectrotemporal shaping based on phase modulation and dispersion engineering. This scheme can achieve performance close to the quantum limit with minimum resources, showing the robustness for experimental implementation and real-world applications.

DOI
10.1103/physrevapplied.15.034071

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Quantum sensing and metrology promise useful insights and alternative techniques to surpass the measurement limits of a classical framework. Significant improvement has been made in the areas of imaging, positioning, timing, interferometry, communication, and information processing through quantum detection and estimation techniques. In this Letter, we focus on the application of quantum information for spectral measurements. Specifically, we study the quantum limit to resolve two spectral modes with small frequency separation. We show that frequency superresolution can be achieved with spectrotemporal shaping of input fields before detection. Through a numerical optimization algorithm, we design the apparatus for spectrotemporal shaping based on phase modulation and dispersion engineering. This scheme can achieve performance close to the quantum limit with minimum resources, showing the robustness for experimental implementation and real-world applications.
Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.
Continuously monitored quantum systems are emerging as promising platforms for quantum metrology, where a central challenge is to identify measurement strategies that optimally extract information about unknown parameters encoded in the complex quantum state of emitted radiation. Different measurement strategies effectively access distinct temporal modes of the emitted field, and the resulting choice of mode can strongly impact the information available for parameter estimation. While a ubiquitous approach in quantum optics is to select frequency modes through spectral filtering, the metrological potential of this technique has not yet been systematically quantified. We develop a theoretical framework to assess this potential by modeling spectral detection as a cascaded quantum system, allowing us to reconstruct the full density matrix of frequency-filtered photonic modes and to compute their associated Fisher information. This framework provides a minimal yet general method to benchmark the performance of spectral measurements in quantum optics, allowing to identify optimal filtering strategies in terms of frequency selection, detector linewidth, and metrological gain accessible through higher-order frequency-resolved correlations and mean-field engineering. These results lay the groundwork for identifying and designing optimal sensing strategies in practical quantum-optical platforms.
Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.
Quantum physics holds promise to revolutionise a number of technologies by enabling performance beyond what is feasible with classical resources, such as secure communications, precision measurement and high-speed simulation and computation. To realise this, quantum information must be encoded into one of the physical degrees of freedom of light. The time-frequency (TF) domain provides a infinite-dimensional space which is naturally compatible with integrated optical platforms. Additionally, future quantum networks will require coherent coupling of quantum systems that do not necessarily exhibit TF mode overlap. The ability to generate, coherently control and measure a variety of TF states of quantum light is therefore a necessary step towards implementing optical quantum technologies. Developing the building blocks for future optical quantum applications calls for an assortment of methods for measuring the properties of TF states of quantum light. Whilst much progress has been made towards this goal recently, deficiencies with existing methods remain. Efficient spectrally-resolved detection away from the telecoms wavelength range and a robust approach to single-photon state characterisation that is sensitive to the spectral phase have so far proven challenging. Additionally, accessing quantum advantages requires measurements that are sensitive to the nonclassical correlations that can exist between separate subsystems. However, until now a flexible approach to determining the full quantum state of systems of multiple time/frequency entangled photons has been lacking. Here we develop a toolbox of techniques for the measurement of TF quantum states of light for few-photon systems, and apply these to the task of precision measurement. Firstly, we propose, construct and demonstrate efficient single-photon spectrometers based on dispersive time-to-frequency mapping, using chirped fibre Bragg gratings to apply the necessary group delay dispersion. We use two such devices operating in coincidence to realise a full phase-sensitive reconstruction of the TF state of a single photon, by spectrally resolving the output of a nonclassical interference process with an external reference. We also demonstrate a complementary, optical reference-free method. This characterisation tool, an implementation of electro-optic spectral shearing interferometry with coincident spectrally-resolved single-photon detection, melds techniques from ultrafast metrology and quantum optics. We proceed to demonstrate the flexibility of this device by reconstructing a wide range of test pulses generated with a pulse shaper. By implementing this technique in conjunction with spectrally-resolved detection of a second photon, we realise complete characterisation of the TF wave function of a spectrally-entangled broadband photon pair. This method is robust to a wide range of inputs and is generalisable to spectrally mixed states and across a wide range of wavelengths, including to spectrally non-degenerate photon pairs. To demonstrate, we generate an entangled photon pair with controllable TF entanglement and perform a full reconstruction. Lastly, we present a new technique for using TF entangled photon pairs to realise quantum-enhanced measurement of a time delay in a quantum channel in the presence of environmental noise. This scheme is based on entanglement-enhanced rejection of background light. A simple experiment demonstrating the feasibility of such a measurement is presented.
The resolution limits of classical spectroscopy can be surpassed by quantum-inspired methods leveraging the information contained in the phase of the complex electromagnetic field. Their counterpart in spatial imaging has been widely discussed and demonstrated; however, the spectral-domain implementations are few and scarce. We experimentally demonstrate a spectroscopic super-resolution method aimed at broadband light (tens to hundreds of GHz), and based on the spectral-domain analog of image inversion interferometry. In a proof-of-principle experiment, we study the paradigmatic problem of estimating a small separation between two incoherent spectral features of equal brightness, with a small number of photons per coherence time. On the grounds of asymptotic estimation theory, more than a two-fold improvement over the spectral direct imaging is demonstrated in terms of required resources (photons) for a given estimator variance. The setup is based on an actively stabilized Mach–Zehnder-type interferometer with electro-optic time lenses and passive spectral dispersers implementing the inversion. As such, the method promises on-chip integration, good scalability, and further applications, e.g., for mode sorting.
Quantum metrology has been shown to surpass classical limits of correlation, resolution, and sensitivity. It has been introduced to interferometric radar schemes, with intriguing preliminary results. Even quantum-inspired detection of classical signals may be advantageous in specific use cases. Following ideas demonstrated so far only in the optical domain, where practically no thermal background photons exist, we realize room-temperature microwave frequency super-resolved phase measurements with trillions of photons, while saturating the Cramer-Rao bound of sensitivity. We experimentally estimate the interferometric phase using the expectation value of the parity operator by two methods. We achieve superresolution up to 1200 times better than the wavelength with 25-ns integration time and 56-dB SNR.