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Coherent Detection of High-Rate Optical PPM Signals

A method of coherent detection of high-rate pulse-position modulation (PPM) on a received laser beam has been conceived as a means of reducing the deleterious effects of noise and atmospheric turbulence in free-space optical communication using focal-plane detector array technologies. In comparison with a receiver based on direct detection of the intensity modulation of a PPM signal, a receiver based on the present method of coherent detection performs well at much higher background levels. In principle, the coherent-detection receiver can exhibit quantum-limited performance despite atmospheric turbulence. The key components of such a receiver include standard receiver optics, a laser that serves as a local oscillator, a focal-plane array of photodetectors, and a signal-processing and data-acquisition assembly needed to sample the focal-plane fields and reconstruct the pulsed signal prior to detection. The received PPM-modulated laser beam and the local-oscillator beam are focused onto the photodetector array, where they are mixed in the detection process. The two lasers are of the same or nearly the same frequency. If the two lasers are of different frequencies, then the coherent detection process is characterized as heterodyne and, using traditional heterodyne-detection terminology, the difference between the two laser frequencies is denoted the intermediate frequency (IF). If the two laser beams are of the same frequency and remain aligned in phase, then the coherent detection process is characterized as homodyne (essentially, heterodyne detection at zero IF). As a result of the inherent squaring operation of each photodetector, the output current includes an IF component that contains the signal modulation. The amplitude of the IF component is proportional to the product of the local-oscillator signal amplitude and the PPM signal amplitude. Hence, by using a sufficiently strong local-oscillator signal, one can make the PPM-modulated IF signal strong enough to overcome thermal noise in the receiver circuits: this is what makes it possible to achieve near-quantum-limited detection in the presence of strong background. Following quantum-limited coherent detection, the outputs of the individual photodetectors are automatically aligned in phase by use of one or more adaptive array compensation algorithms [e.g., the least-mean-square (LMS) algorithm]. Then the outputs are combined and the resulting signal is processed to extract the high-rate information, as though the PPM signal were received by a single photodetector. In a continuing series of experiments to test this method (see Fig. 1), the local oscillator has a wavelength of 1,064 nm, and another laser is used as a signal transmitter at a slightly different wavelength to establish an IF of about 6 MHz. There are 16 photodetectors in a 4 4 focal-plane array; the detector outputs are digitized at a sampling rate of 25 MHz, and the signals in digital form are combined by use of the LMS algorithm. Convergence of the adaptive combining algorithm in the presence of simulated atmospheric turbulence for optical PPM signals has already been demonstrated in the laboratory; the combined output is shown in Fig. 2(a), and Fig. 2(b) shows the behavior of the phase of the combining weights as a function of time (or samples). We observe that the phase of the weights has a sawtooth shape due to the continuously changing phase in the down-converted output, which is not exactly at zero frequency. Detailed performance analysis of this coherent free-space optical communication system in the presence of simulated atmospheric turbulence is currently under way.

Vilnrotter, Victor↗

Optical communication with two-photon coherent states. II - Photoemissive detection and structured receiver performance

In a previous paper (1978), the authors developed a method of analyzing the performance of two-photon coherent state (TCS) systems for free-space optical communications. General theorems permitting application of classical point process results to detection and estimation of signals in arbitrary quantum states were derived. The present paper examines the general problem of photoemissive detection statistics. On the basis of the photocounting theory of Kelley and Kleiner (1964) it is shown that for arbitrary pure state illumination, the resulting photocurrent is in general a self-exciting point process. The photocount statistics for first-order coherent fields reduce to those of a special class of Markov birth processes, which the authors term single-mode birth processes. These general results are applied to the structure of TCS radiation, and it is shown that the use of TCS radiation with direct or heterodyne detection results in minimal performance increments over comparable coherent-state systems. However, significant performance advantages are offered by use of TCS radiation with homodyne detection. The abstract quantum descriptions of homodyne and heterodyne detection are derived and a synthesis procedure for obtaining quantum measurements described by arbitrary TCS is given.

Shapiro, J. H.↗

Laser Truss Sensor for Segmented Telescope Phasing

A paper describes the laser truss sensor (LTS) for detecting piston motion between two adjacent telescope segment edges. LTS is formed by two point-to-point laser metrology gauges in a crossed geometry. A high-resolution (<30 nm) LTS can be implemented with existing laser metrology gauges. The distance change between the reference plane and the target plane is measured as a function of the phase change between the reference and target beams. To ease the bandwidth requirements for phase detection electronics (or phase meter), homodyne or heterodyne detection techniques have been used. The phase of the target beam also changes with the refractive index of air, which changes with the air pressure, temperature, and humidity. This error can be minimized by enclosing the metrology beams in baffles. For longer-term (weeks) tracking at the micron level accuracy, the same gauge can be operated in the absolute metrology mode with an accuracy of microns; to implement absolute metrology, two laser frequencies will be used on the same gauge. Absolute metrology using heterodyne laser gauges is a demonstrated technology. Complexity of laser source fiber distribution can be optimized using the range-gated metrology (RGM) approach.

Liu, Duncan T.↗

A near-optimum receiver structure for the detection of M-ary optical PPM signals

A class of receivers called conditionally nulling receivers is defined for quantum noise limited optical communications. These receivers have the ability to decide at each moment in time whether or not to coherently combine a predetermined local oscillator field with the received optical field, prior to performing an energy measurement (photodetection) on the combined field. Conditionally nulling receivers are applicable to pulse position modulation and related modulation schemes, which have the property that, at each moment in time, the transmitted signal is in one of only two states, on or off. The local oscillator field which may or may not be added by the receiver is an exact replica of the negative of the received on field; hence, the receiver can exactly null the on signal if the on signal is present and the receiver chooses to use the local field. An ideal conditionally nulling receiver achieves very nearly the same error probability (within a multiplicative factor varying froom 1 to 2.15) as the optimum quantum measurement for quantum noise limited detection of M-ary PPM signals. In contrast, other known receiving methods, such as direct, heterodyne, and homodyne detection, are exponentially suboptimum.

Dolinar, S. J., Jr.↗

Enhancing Qubit Readout with Autoencoders

In addition to the need for stable and precisely controllable qubits, quantum computers take advantage of good readout schemes. Superconducting qubit states can be inferred from the readout signal transmitted through a dispersively coupled resonator. Here, this work proposes a readout classification method for superconducting qubits based on a neural network pretrained with an autoencoder approach. A neural network is pretrained with qubit readout signals as autoencoders in order to extract relevant features from the data set. Afterward, the pretrained-network inner-layer values are used to perform a classification of the inputs in a supervised manner. We demonstrate that this method can enhance classification performance, particularly for short- and long-time measurements where more traditional methods present inferior performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Field test of continuous-variable quantum key distribution with a true local oscillator

A continuous-variable quantum key distribution (CV QKD) using a true local (located at the receiver) oscillator (LO) has been proposed to remove any possibility of side-channel attacks associated with transmission of the LO as well as reduce the cross-pulse contamination. Here we report an implementation of true LO-CV QKD using “off-the-shelf” components and conduct QKD experiments using the fiber optical network at Oak Ridge National Laboratory. A phase reference and quantum signal are time multiplexed and then wavelength division multiplexed with the classical communications that “coexist” with each other on a single optical network fiber. Importantly, this is the first demonstration of CV QKD with a receiver-based true LO over a deployed fiber network, a crucial step for its application in real-world situations.

97 MATHEMATICS AND COMPUTING↗

Bayesian homodyne and heterodyne tomography

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties—including uncertainty quantification and optimality in mean-squared error—Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian quantum state tomography workflow capable of inferring generic CV states measured by homodyne or heterodyne detection, with no assumption of Gaussianity. As examples, we demonstrate our approach on experimental coherent, thermal, and cat state data, obtaining excellent agreement between our Bayesian estimates and theoretical predictions. Our approach lays the groundwork for Bayesian estimation of highly complex CV quantum states in emerging quantum photonic platforms, such as quantum communications networks and sensors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Complete spectroscopy in the attosecond regime

Harnessing light waveforms at attosecond time scales provides information of the structure and dynamics of matter on it's natural time scales. For this reason attosecond metrology has been at the forefront of the optical sciences for more than a decade, and it represents the latest time-domain frontier of the quantum world. Attosecond light pulses are commonly generated using higher-order harmonic generation (HHG) , a process capable of generating XUV coherent pulses. In addition to generate attosecond pulses, HHG can be used to study the structure and dynamics of atoms and molecules by analyzing the spectral content of the XUV pulses. This approach is known as HHG spectroscopy and it provides a coherent, time-dependent approach to study structure and dynamics in the quantum world. In this proposal we will generate harmonics from two optical foci produced by a system of a two-dimensional spatial light modulator (SLM) and a lens. In the far eld the train of attosecond pulses will interfere creating harmonic-dependent fringes. The position of such fringes is a direct measurement of the relative phase between the two foci and they also carry information about the quantum state of the target atom or molecule. Therefore, by measuring the amplitude and relative phase of the emitted harmonics we will have access to both, the amplitude and phase of the dipole moments of the studied target. Because the two beams are completely indistinguishable from each other up to a few millimeters from the focus, both driving pulses share the exact beam path. So far we have measured a jitter of 700 zeptoseconds with a 12.5 attosecond resolution in the delay control of the two foci. These two time scales represent some of the best time controls ever achieved to date.

74 ATOMIC AND MOLECULAR PHYSICS↗

Optical antenna gain. II - Receiving antennas

Expressions are developed for the gain of a centrally obscured, circular optical antenna used as the collecting and focusing optics in a laser receiver, involving losses due to (1) incoming light blockage by central obscuration, (2) energy spillover at the detector, and (3) the effect of local oscillator distribution in the case of heterodyne or homodyne detection. Numerical results are presented for direct detection and for three types of local oscillator distribution (uniform, Gaussian, and matched).

Degnan, J. J.↗

Homodyning and heterodyning the quantum phase

The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.

Dariano, Giacomo M.↗

Efficient Trainability of Linear Optical Modules in Quantum Optical Neural Networks

The existence of “barren plateau landscapes” for generic discrete-variable quantum neural networks, which obstructs efficient gradient-based optimization of cost functions defined by global measurements, would be surprising in the case of generic linear optical modules in quantum optical neural networks due to the tunability of the intensity of continuous variable states and the relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light in m modes can be generically compiled efficiently if the total intensity scales sublinearly with m, and extend this result to cost functions based on homodyne, heterodyne, or photon detection measurement statistics, and to noisy cost functions in the presence of attenuation. Here, we further demonstrate efficient trainability of m mode linear optical quantum circuits for variational mean field energy estimation of positive quadratic Hamiltonians for input states that do not have energy exponentially vanishing with m.

47 OTHER INSTRUMENTATION↗

Time-Resolved Ultrafast Transient Polarization Spectroscopy to Investigate Nonlinear Processes and Dynamics in Electronically Excited Molecules on the Femtosecond Time Scale

Here, we report a novel experimental technique to investigate ultrafast dynamics in photoexcited molecules by probing the third-order nonlinear optical susceptibility. A non-colinear 3-pulse scheme is developed to probe the ultrafast dynamics of excited electronic states using the optical Kerr effect by time-resolved polarization spectroscopy. Optical heterodyne and optical homodyne detection are demonstrated to measure the third-order nonlinear optical response for the S 1 excited state of liquid nitrobenzene, which is populated by 2-photon absorption of a 780 nm 35 fs excitation pulse.

47 OTHER INSTRUMENTATION↗

Fiber optic links for microwave/millimeter-wave systems

Recent advances in device technology for microwave/mm-wave (M/MMW) analog fiber-optic communication systems are surveyed, with discussion of system parameters, design optimization methods, and hardware selection and manufacturing considerations. Particular attention is given to 1-km-link systems operating at 21, 30, and 12 GHz for satellite-communication, electronic-warfare, and radar applications. The design and fabrication simplicity of direct modulation is weighed against the wide bandwidth, low distortion, and mm-wave and frequency operation advantages of external modulation. Homodyne or heterodyne coherent detection is shown to improve system S/N by 10-20 dB over conventional detection methods. Diagrams, drawings, photographs, and graphs of typical performance data are included.

Pan, J. J.↗

Optical communication theory.

An introduction is provided to the important ideas involved in the design and the evaluation of optical communication systems which transmit digital or analog data. Field representations are discussed together with background noise, a detector statistical model, quantum receivers, and turbulent and scatter channels. Free-space channels are considered, taking into account heterodyne systems, preamplifier and homodyne systems, direct-detection systems, and optimum quantum systems.

Hoversten, E. V.↗

Conceptual radiometer design studies for Earth observations from low Earth orbit

A conceptual radiometer design study was performed to determine the optimum design approach for spaceborne radiometers in low Earth orbit. Radiometric system configurations which included total power radiometers, unbalanced Dicke radiometers, and balanced Dicke, or as known as noise injection, radiometers were studied. Radiometer receiver configurations which were analyzed included the direct detection radiometer receiver, the double sideband homodyne radiometer receiver, and the single sideband heterodyne radiometer receiver. Radiometer system performance was also studied. This included radiometric sensitivity analysis of the three different radiometer system configurations studied. Both external and internal calibration techniques were analyzed. An accuracy analysis with and without mismatch losses was performed. It was determined that the balanced Dicke radiometer system configuration with direct detection receivers and external calibrations was optimum where frequent calibration such as once per minute were not feasible.

Harrington, Richard F.↗

Optical communication with two-photon coherent states. III - Quantum measurements realizable with photoemissive detectors

Homodyne detection is shown to achieve the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes linear modulation TCS performance gain. The full equivalence of homodyne detection and single-quadrature field measurement is established. A heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. Results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.

Yuen, H. P.↗

Spectrally Resolved Synthetic Aperture Imaging Interferometer: Final Report of NASA Innovative Advanced Concepts - Phase 1 Study

The Spectrally Resolved Synthetic-Aperture Imaging Interferometer (SRSAII) is a system proposed to provide high-resolution and high-sensitivity measurements of astronomical objects. SRSAII uses long baseline interferometric methods to achieve the resolution and low-noise, high time-precision detection to achieve the sensitivity. The primary goal of the SRSAII study was to lay out a framework for using new optical physics technologies to directly resolve, both spatially and spectrally, the disk of an exoplanet. In addition to the ambitious goal of directly resolving an exoplanet, the SRSAII team also sought to identify science opportunities achievable with intermediate system configurations which may offer resolution significantly higher than the current state of the art, but insufficient for direct resolution of an exoplanetary disk. An operational SRSAII system can function with essentially arbitrarily large baselines, achieving correspondingly high angular resolution. The primary limitation occurs in the system sensitivity, which became the major technical focus for study. In this report, we compare the predicted performance (sensitivity in SNR (Signal-to-Noise Ratio) along with angular resolution) of three interferometric techniques: direct detection (also known as homodyne interferometry), multi-channel intensity interferometry (using the Hanbury Brown and Twiss effect), and multi-channel heterodyne interferometry (using an optical frequency comb as a local oscillator). Additionally, quantum-assisted interferometry is also explored as a prospective enhancement of established methods. This report presents a survey of the technologies that enable the SRSAII techniques - optical frequency combs, single photon detectors, and photonic integrated circuits. These technologies are the basis of methods critical to SRSAII's success: precision timing, length and frequency metrology, sensitive photodetection, fine-scale wavelength filtering, and dense multi-channel operation. Lastly, we give some notional performance metrics and propose some possible experimental observations.

High Resolultion↗

Optical communications and a comparison of optical technologies for a high data rate return link from Mars

The important principles of direct- and heterodyne-detection optical free-space communications are reviewed. Signal-to-noise-ratio (SNR) and bit-error-rate (BER) expressions are derived for both the direct-detection and heterodyne-detection optical receivers. For the heterodyne system, performance degradation resulting from received-signal and local oscillator-beam misalignment and laser phase noise is analyzed. Determination of interfering background power from local and extended background sources is discussed. The BER performance of direct- and heterodyne-detection optical links in the presence of Rayleigh-distributed random pointing and tracking errors is described. Finally, several optical systems employing Nd:YAG, GaAs, and CO2 laser sources are evaluated and compared to assess their feasibility in providing high-data-rate (10- to 1000-Mbps) Mars-to-Earth communications. It is shown that the root mean square (rms) pointing and tracking accuracy is a critical factor in defining the system transmitting laser-power requirements and telescope size and that, for a given rms error, there is an optimum telescope aperture size that minimizes the required power. The results of the analysis conducted indicate that, barring the achievement of extremely small rms pointing and tracking errors (less than 0.2 microrad), the two most promising types of optical systems are those that use an Nd:YAG laser (lambda = 1.064 microns) and high-order pulse position modulator (PPM) and direct detection, and those that use a CO2 laser (lambda = 10.6 microns) and phase shifting keying homodyne modulation and coherent detection. For example, for a PPM order of M = 64 and an rms pointing accuracy of 0.4 microrad, an Nd:YAG system can be used to implement a 100-Mbps Mars link with a 40-cm transmitting telescope, a 20-W laser, and a 10-m receiving photon bucket. Under the same conditions, a CO2 system would require 3-m transmitting and receiving telescopes and a 32-W laser to implement such a link. Other types of optical systems, such as a semiconductor laser systems, are impractical in the presence of large rms pointing errors because of the high power requirements of the 100-Mbps Mars link, even when optimal-size telescopes are used.

Spence, Rodney L.↗