In a number of optical heterodyne systems it may happen that the signal power is so low that only a few, or even fractions of, photons enter the receiver in a characteristic time interval. As the heterodyne receiver basically employs the beating effect, such intricate questions as “is there still a beating between the (many) local oscillator photons and the few return photons?” or “how can a single photon produce an intermediate frequency?” arise. We show that the semiclassical theory, which provides exact results as long as optical fields with an adequate classical description are used, is capable of answering those questions. The term “photon” must thereby be assigned its (semiclassically) correct meaning, which is an abbreviation for “discrete interaction of light and matter.” We illustrate our discussion by providing a numerical example related to a space-borne CO2 Doppler wind lidar instrument.
In a number of optical heterodyne systems it may happen that the signal power is so low that only a few, or even fractions of, photons enter the receiver in a characteristic time interval. As the heterodyne receiver basically employs the beating effect, such intricate questions as “is there still a beating between the (many) local oscillator photons and the few return photons?” or “how can a single photon produce an intermediate frequency?” arise. We show that the semiclassical theory, which provides exact results as long as optical fields with an adequate classical description are used, is capable of answering those questions. The term “photon” must thereby be assigned its (semiclassically) correct meaning, which is an abbreviation for “discrete interaction of light and matter.” We illustrate our discussion by providing a numerical example related to a space-borne CO2 Doppler wind lidar instrument.
Heterodyne interferometry uses beats produced by superposing two light waves with different frequencies at a photodetector. The output from the photodetector then contains a component at the beat frequency which can be processed to obtain information on changes in the optical path difference. We present experimental results which show that beats can be observed down to power levels at which the mean time interval between the arrival of photons at the photodetector is much greater than the transit time from the laser source to the detector and also when the mean time interval between photons is greater than the period of the beat. These results show that the beats are not due to the interference of one photon with another, but arise from a succession of single-photon events. It follows that measurements can be made even at extremely low photon fluxes by using homodyne detection and extending the integration time.
We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.
After reviewing recent work on multiphoton direct detection and single-photon heterodyne detection, we examine the behavior of a multiphoton absorption heterodyne receiver. Expressions are obtained for the detector response, signal-to-noise ratio (SNR), and minimum detectable power for a number of cases of interest. Receiver performance is found to depend on the higher order correlation functions of the radiation field and on the local oscillator (LO) irradiance. Although performance similar to that of the single-photon heterodyne receiver can theoretically be achieved, practical problems would appear to make this difficult. A physical interpretation of the process in terms of the absorption of monochromatic and nonmonochromatic photons is given. The double-quantum case is treated in particular detail; the results of a preliminary experiment are presented and suggestions for future experiments are provided.
Optical heterodyning has been observed at the single-photon level by recording the sinusoidal variation in the probability for detection of a photoelectron from a photomultiplier tube illuminated with a FM laser and a local oscillator laser. The single-photon character of the heterodyne process was demonstrated by observation of beat signals at total power levels down to6 \times 10^{-15}W where the spacing between photons emitted from the source laser was\sim40 000times greater than their transit time through the apparatus.
Photon heterodyning affords the opportunity to single out photon detection events at a designated timing in the otherwise elusive transient interference fringes of single photons. Albeit essentially a time-domain analogue of Young's two-slit interference experiment at a single-photon level, it must be borne out by experiment using true single-photon streams. More importantly, it presents a technical challenge even without a tangible screen unlike space domain. Here, we demonstrate single-photon self-heterodyne beats that are obtained by letting the nonclassical light field associated with a photon interfere with itself. This is made possible by splitting, folding and mapping point-by-point the otherwise only poorly correlated time-series data onto a virtual capture frame. Photon heterodyning is of significance in view of conceivable applications. In fact, it marks a great step forward in benefiting such applications that handle interfering light fields in the time domain. An unmatched immunity to dc noise at an extremely low light level opens up the avenue for single-photon interferometry and interferometric biometrics of a highly light-sensitive target. Super-resolution and quantum optical coherence tomography, which are based on the nonclassical nature of photons, are those which should take full advantage of the photon heterodyning technology. On the other hand, the potential of photon heterodyning is most likely to be manifest in the field of quantum information processing by implementing frequency-encoded photon states. Some of these examples will be discussed in more detail.
Quantum Lidar is a future technology that can mean different things to different people. To some it means detection and identification of classical-type lidar signals reflected from an illuminated target at or near the single photon level. This is facilitated by advances in semiconductor detector technology that allow highly efficient photocounting. To others it is more stringent, requiring exploitation of covertness associated with being essentially undetectable by the target in a thermal background, whilst allowing the lidar operator to filter her own signal from this noise. Again there is nothing specifically quantum about this. Any source that mimics of the energy rate per bandwidth seen by the illuminated object in the direction of the source can appear covert. In order to exploit quantum optics one can use inherent correlations, whether entangled or otherwise between light beams. Simple correlated optical beams can do this in two ways, perhaps by storing one beam as a reference and later performing correlated detection with the return signal in a phase sensitive manner. This is the “gold standard” for quantum lidar, but will be difficult outside of laboratory situations. In microscopy such phase control might be possible, or perhaps in the radio or microwave region for a quantum radar. Less challenging is a scenario in which an immediate local measurement of one beam conditions the beam sent to the target, allowing the return signal to be sifted from noise more easily. Here we will consider such a simple system, providing a range equation for a basic quantum lidar if it is to be operated covertly or openly. Open operation allows increased quantum signal brightness but also provides a quantum advantage, unspoofability – the lidar operator can in principle recognise their own return signal. We will also provide an analysis of quantum lidar detection based on quantum hypothesis testing and use this to perform Monte Carlo simulation of both target detections and false positive avoidance in a noisy background. The theory will be applied to experimental data.