In classical digital communications two main families of “M-ary” modulation schemes are generally distinguished: bandwidth limited and power limited. The canonical comparison of these modulation methods is based on normalized data rate (R/W) (bits per second per hertz of bandwidth) and the signal to noise rate per bit required to achieve a given error probability for different M. In a classical picture, the two families reside in two separate semi-plains R/W < 1 and
R/W > 1, i.e. energy efficiency and bandwidth efficiency cannot be optimized at the same time. However,
we find an alphabet family that can be paired with a quantum receiver to simultaneously optimize bandwidth and power efficiency of a communication channel. Particularly we found that coherent frequency shift keying (CFSK) gives rise to a family of communication protocols that are bandwidth limited in nature, but whose bandwidth usage can be optimized so that R/W>1 for a range of alphabet lengths M, while power sensitivity beats that of power-limited protocols. We will report our theoretical findings and experimental progress towards implementation of this protocol family.
The efficient use of communication channels motivates extensive research in novel communication protocols. Modern communication protocols use large alphabets contain up to a few thousand symbols, thus optimizing the use of power and available frequency space. To date, quantum receivers that discriminate up to approximately 20 symbols were theoretically investigated and receivers with as many as 4 nonorthogonal coherent states have been experimentally demonstrated. However, all heretofore explored quantum receivers suffer from the sensitivity degradation with the alphabet size. Particularly, their Helstrom Bound (HB) nearly reaches the classical standard quantum limit (SQL).
Here we introduce an M-ary quantum receiver based on a coherent frequency shift keying (CFSK) protocol with a record power sensitivity, free of the above deficiency. The CFSK not only provides better accuracy for longer alphabets but also allows discrimination with a practically attainable symbol error rate (SER) situated much below the HBs of other encodings for large alphabets. Our receiver operates with a classical transmitter, and with any communication channel, including the existing global fiber network. It can be used to increase the amplification-free range in a network and/or reduce power requirements on the transmitter by more than 1000 times. In addition, the quantum measurement advantage can significantly optimize the use of the frequency space in comparison to classical frequency keying protocols. This advantage can be used in deep-space telecom links to enhance the satellite power budget. In existing fiber network links, quantum CFSK receivers can improve the amplification-free range by approximately the factor of 2.
We characterize an efficient and nearly-noiseless parametric frequency upconverter. The ultra-low noise regime is reached by the wide spectral separation between the input and pump frequencies and the low pump frequency relative to the input photons. The background of only ≈100 photons per hour is demonstrated. We demonstrate phase preservation in a frequency upconversion process at the single-photon level. We summarize our efforts to measure this ultra-low noise level, and discuss both single-photon avalanche photodiode measurements and a photon-counting transition edge sensor (TES) measurements. To reach the required accuracy, we supplemented our TES with a dark count reduction algorithm. The preservation of the coherence was demonstrated by simultaneously upconverting the input of each arm of a Mach-Zehnder interferometer through high interference fringe contrast. We observe fringe visibilities of ≥0.97 with faint coherent input.
The non-stationary problem of electron-molecular ion scattering is solved analytically in the frame of the perturbation
theory on the scattering potential and without the plane wave approximation for the incident electron. The influence of
the parameters of the incident electron wave-packet on the observed diffraction images is studied. Effect of interference
between incident and scattered wave packets is analyzed in details and shown to result in dramatic changes of the