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The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g., the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical signal processing (e.g., time-correlated noise optimal filtering) to emerging quantum technologies (e.g., super-resolution TF sensing) which rely on or benefit from coherent low-noise TF operations. Here a versatile low-noise single-photon-compatible implementation of the FRT is presented. Optical TF FRT can be synthesized as a series of a spectral disperser, a time-lens, and another spectral disperser. Relying on the state-of-the-art electro-optic modulators (EOM) for the time-lens, our method avoids added noise inherent to the alternatives based on non-linear optical interactions (such as wave-mixing, cross-phase modulation, or parametric processes). Precise control of the EOM-driving radio-frequency signal enables fast all-electronic control of the FRT angle. In the experiment, we demonstrate FRT angles of up to 1.63 rad for pairs of coherent temporally separated 11.5 ps-wide pulses in the near-infrared (800 nm). We observe a good agreement between the simulated and measured output spectra in the bright-light and single-photon-level regimes, and for a range of pulse separations (20 ps to 26.7 ps). Furthermore, a tradeoff is established between the maximal FRT angle and optical bandwidth, with the current setup accommodating up to 248 GHz of bandwidth. With the ongoing progress in EOM on-chip integration, we envisage excellent scalability and vast applications in all-optical TF processing both in the classical and quantum regimes.
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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.
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A scheme for the measurement of a microwave (MW) electric field is proposed via multi-photon coherence in Rydberg atoms. It is based on the three-photon electromagnetically induced absorption (TPEIA) spectrum. In this process, the multi-photon produces a narrow absorption peak, which has a larger magnitude than the electromagnetically induced transparency (EIT) peak under the same conditions. The TPEIA peak is sensitive to MW fields, and can be used to measure MW electric field strength. We found that the magnitude of TPEIA peaks shows a linear relationship with the MW field strength. The simulation results show that the minimum detectable strength of the MW fields is about 1/10 of that based on an common EIT effect, and the probe sensitivity could be improved by about four times. Furthermore, the MW sensing based on three-photon coherence seems to be robust against the changes in the control field and shows a broad tunability, and the scheme may be useful for designing novel MW sensing devices.
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The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing, and computing. In this Letter, we present the experimental realization of the fractional Fourier transform in the time-frequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing, and superresolved parameter estimation.
Asunto(s)
Comunicación , Física , Análisis de Fourier , Movimiento CelularRESUMEN
Despite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements. Our method is based on introducing a series of controlled time and frequency shifts, where the latter is performed via an electro-optic modulator allowing a fully-electronic experimental control. We characterized the full spectral and temporal width of a classical and single-photon-level pulse and successfully tested the applicability of the reconstruction algorithm of the spectral phase and amplitude. The method can be extended by implementing a phase-sensitive measurement and is naturally well-suited to partially-incoherent light.
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Electromagnetically induced transparency in atomic systems involving Rydberg states is known to be a sensitive probe of incident microwave (MW) fields, in particular those resonant with Rydberg-to-Rydberg transitions. Here we propose an intelligible analytical model of a Rydberg atomic receiver's response to amplitude- (AM) and frequency-modulated (FM) signals and compare it with experimental results, presenting a setup that allows sending signals with either AM or FM and evaluating their efficiency with demodulation. Additionally, the setup reveals a detection configuration using all circular polarizations for optical fields and allowing detection of a circularly polarized MW field, propagating colinearly with optical beams. In our measurements, we systematically show that several parameters exhibit local optimum characteristics and then estimate these optimal parameters and working ranges, addressing the need to devise a robust Rydberg MW sensor and its operational protocol.
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Quantum asymmetry is a physical resource that coincides with the amount of coherence between the eigenspaces of a generator responsible for phase encoding in interferometric experiments. We highlight an apparently counterintuitive behavior that the asymmetry may increase as a result of a decrease of coherence inside a degenerate subspace. We intuitively explain and illustrate the phenomena by performing a three-mode single-photon interferometric experiment, where one arm carries the signal and two noisy reference arms have fluctuating phases. We show that the source of the observed sensitivity improvement is the reduction of correlations between these fluctuations and comment on the impact of the effect when moving from the single-photon quantum level to the classical regime. Finally, we also establish the analogy of the effect in the case of entanglement resource theory.
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Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies to fully exploit information already present in the field is to perform a quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ an optical quantum memory with spin-wave storage and an embedded processing capability to implement a time-inversion interferometer for input light, projecting the optical field in the symmetric-antisymmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.
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Single photons exhibit inherently quantum and unintuitive properties such as the Hong-Ou-Mandel effect, demonstrating their bosonic and quantized nature, yet at the same time may correspond to single excitations of spatial or temporal modes with a very complex structure. Those two features are rarely seen together. Here we experimentally demonstrate how the Hong-Ou-Mandel effect can be spectrally resolved and harnessed to characterize a complex temporal mode of a single-photon-a zero-area pulse-obtained via a resonant interaction of a terahertz-bandwidth photon with a narrow gigahertz-wide atomic transition of atomic vapor. The combination of bosonic quantum behavior with bandwidth-mismatched light-atom interaction is of fundamental importance for deeper understanding of both phenomena, as well as their engineering offering applications in characterization of ultrafast transient processes.
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Calibrating the strength of the light-matter interaction is an important experimental task in quantum information and quantum state engineering protocols. The strength of the off-resonant light-matter interaction in multi-atom spin oscillators can be characterized by the readout rate ΓS. Here we introduce the method named Coherently Induced FAraday Rotation (CIFAR) for determining the readout rate. The method is suited for both continuous and pulsed readout of the spin oscillator, relying only on applying a known polarization modulation to the probe laser beam and detecting a known optical polarization component. Importantly, the method does not require changes to the optical and magnetic fields performing the state preparation and probing. The CIFAR signal is also independent of the probe beam photo-detection quantum efficiency, and allows direct extraction of other parameters of the interaction, such as the tensor coupling ζS, and the damping rate γS. We verify this method in the continuous wave regime, probing a strongly coupled spin oscillator prepared in a warm cesium atomic vapour.
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Hyperentangled photonic states-exhibiting nonclassical correlations in several degrees of freedom-offer improved performance of quantum optical communication and computation schemes. Experimentally, a hyperentanglement of transverse-wave-vector and spectral modes can be obtained in a straightforward way with multimode parametric single-photon sources. Nevertheless, experimental characterization of such states remains challenging. Not only single-photon detection with high spatial resolution-a single-photon camera-is required, but also a suitable mode converter to observe the spectral-temporal degree of freedom. We experimentally demonstrate a measurement of full four-dimensional transverse-wave-vector-spectral correlations between pairs of photons produced in noncollinear spontaneous parametric downconversion. Utilization of a custom ultrafast single-photon camera provides high resolution and a short measurement time.
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Laser phase noise remains a limiting factor in many experimental settings, including metrology, time-keeping, as well as quantum optics. Hitherto this issue was addressed at low frequencies ranging from well below 1 Hz to maximally 100 kHz. However, a wide range of experiments, such as, e.g., those involving nanomechanical membrane resonators, are highly sensitive to noise at higher frequencies in the range of 100 kHz to 10 MHz, such as nanomechanical membrane resonators. Here we employ a fiber-loop delay line interferometer optimized to cancel laser phase noise at frequencies around 1.5 MHz. We achieve noise reduction in 300 kHz-wide bands with a peak reduction of more than 10 dB at desired frequencies, reaching phase noise of less than -160 dB(rad2/Hz) with a Ti:Al2O3 laser. These results provide a convenient noise reduction technique to achieve deep ground-state cooling of mechanical motion.
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We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on single excitations and demonstrate a spin-wave analog of the Hong-Ou-Mandel effect, realized via a beam splitter implemented in the spin-wave domain. Our scheme equips atomic-ensemble-based quantum repeaters with quantum information processing capability and can be readily brought to other physical systems, such as doped crystals or room-temperature atomic ensembles.
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Effective and unrestricted engineering of atom-photon interactions requires precise spatially resolved control of light beams. The significant potential of such manipulations lies in a set of disciplines ranging from solid-state to atomic physics. Here we use a Zeeman-like ac-Stark shift caused by a shaped laser beam to perform rotations of spins with spatial resolution in a large ensemble of cold rubidium atoms. We show that inhomogeneities of light intensity are the main source of dephasing and, thus, decoherence; yet, with proper beam shaping, this deleterious effect is strongly mitigated allowing rotations of 15 rad within one spin-precession lifetime. Finally, as a particular example of a complex manipulation enabled by our scheme, we demonstrate a range of collapse-and-revival behaviors of a free-induction decay signal by imprinting comb-like patterns on the atomic ensemble.
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Multiparameter estimation theory offers a general framework to explore imaging techniques beyond the Rayleigh limit. While optimal measurements of single parameters characterizing a composite light source are now well understood, simultaneous determination of multiple parameters poses a much greater challenge that in general requires implementation of collective measurements. Here we show, theoretically and experimentally, that Hong-Ou-Mandel interference followed by spatially resolved detection of photons provides precise information on both the separation and the centroid for a pair of point emitters, avoiding trade-offs inherent to single-photon measurements.
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Parallelized quantum information processing requires tailored quantum memories to simultaneously handle multiple photons. The spatial degree of freedom is a promising candidate to facilitate such photonic multiplexing. Using a single-photon resolving camera, we demonstrate a wavevector multiplexed quantum memory based on a cold atomic ensemble. Observation of nonclassical correlations between Raman scattered photons is confirmed by an average value of the second-order correlation function [Formula: see text] in 665 separated modes simultaneously. The proposed protocol utilizing the multimode memory along with the camera will facilitate generation of multi-photon states, which are a necessity in quantum-enhanced sensing technologies and as an input to photonic quantum circuits.
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Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.