The Rayleigh limit has so far applied to all microscopy techniques that rely on linear optical interaction and detection in the far field. Here we demonstrate that detecting the light emitted by an object in higher-order transverse electromagnetic modes (TEMs) can help achieving sub-Rayleigh precision for a variety of microscopy-related tasks. Using optical heterodyne detection in TEM01, we measure the position of coherently and incoherently emitting objects to within 0.0015 and 0.012 of the Rayleigh limit, respectively, and determine the distance between two incoherently emitting objects positioned within 0.28 of the Rayleigh limit with a precision of 0.019 of the Rayleigh limit. Heterodyne detection in multiple higher-order TEMs enables full imaging with resolution significantly below the Rayleigh limit in a way that is reminiscent of quantum tomography of optical states.

Abstract. We demonstrate that a photon echo can be implemented by alloptical means using an array of on-chip high-finesse ring cavities whose parameters are chirped in such a way as to support equidistant spectra of cavity modes. When launched into such a system, a classical or quantum optical signal -even a single-photon field -becomes distributed between individual cavities, giving rise to prominent coherence echo revivals at well-defined delay times, controlled by the chirp of cavity parameters. This effect enables long storage times for highthroughput broadband optical delay and quantum memory. All-optical photon echo and memory on a chip 2 Abstract. We demonstrate that a photon echo can be implemented by all-optical means using an array of on-chip highfinesse ring cavities whose parameters are chirped in such a way as to support equidistant spectra of cavity modes. When launched into such a system, a classical or quantum optical signal -even a single-photon field -becomes distributed between individual cavities, giving rise to prominent coherence echo revivals at well-defined delay times, controlled by the chirp of cavity parameters. This effect enables long storage times for high-throughput broadband optical delay and quantum memory.A photon echo [1, 2] is a broad class of optical phenomena where a coherence induced in a quantum system by an optical field is emitted in a form of a well-resolved intense optical signal, similar to the spin echo in nuclear magnetic resonance. Over decades, photon echo has been in use as a powerful method of coherent spectroscopy, providing unique information on transient processes in gases, liquid, and solids [3]. Photon-echo revivals in molecular rotational coherences have been shown to enable efficient quantum control of molecular alignment [4], photochemical reactions [5], as well as synthesis of ultrashort field waveforms [6]. In the era of quantum information, photon echo is viewed as a promising strategy for quantum data storage and quantum memories [7,8,9, 10] (recent reviews see also in [11,12,13,14]).Here, we show that a photon echo can be implemented by purely optical means using an array of on-chip high-finesse ring cavities whose parameters are chirped in such a way as to support equidistant spectra of cavity modes. A classical or quantum optical signal launched into such a system becomes distributed between individual cavities, giving rise to prominent coherence echo revivals at well-defined delay times, controlled by the chirp of cavity parameters. This effect enables long storage times for high-throughput broadband optical delay and quantum memory.We consider an array of N single-mode highfinesse chirped cavities with an equidistant spectrum of modes with a mode spacing ∆ (Fig. 1). An optical field coupled into such an array remains distributed between the cavities until all the cavity modes can re-emit in phase, giving rise to an intense photon-echo signals at the output. With appropriate coupling between the nanofiber and the cavities, which is possible, e.g....

We have found a new hidden symmetry of time reversal light-atom interaction in the photon echo quantum memory with Raman atomic transition. The time-reversed quantum memory creates generalized conditions for the ideal compression/decompression of time duration of the input light pulses and its wavelength. Based on a general analytical approach to this scheme, we have studied the optimal conditions for the light field compression/decompression in resonant atomic systems characterized by realistic spectral properties. The demonstrated necessary conditions for the effective quantum conversion of the light waveform and wavelength are also discussed for various possible realizations of the quantum memory scheme. The performed study promises new capabilities for fundamental study of the light-atom interaction and deterministic quantum manipulation of the light field, significant for quantum communication and quantum computing.

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