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SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC)

Approaching Single-Photon Pulses with Weak Coherent States and Nonlinear Phase Modulation

Jonathan Rodrigues da Silva, João Batista Rosa Silva, Rubens Viana Ramos

Published Oct 24, 2021• 1 citation
Publisher

Abstract

Single-photons sources are crucial devices in the development of practical quantum communication and quantum computation. However, such sources are still a technological challenge. One option is to use weak coherent states to mimic single-photon pulses or to produce a pair of photons with parametric down conversion and to detect one of them to herald the presence of the other. In this direction, the present work shows how to produce better approximations of single-photon pulses by using a nonlinear phase modulator in a Mach-Zehnder interferometer. The proposed scheme is explained and applications are discussed.

DOI
10.1109/imoc53012.2021.9624833

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Single-photons sources are crucial devices in the development of practical quantum communication and quantum computation. However, such sources are still a technological challenge. One option is to use weak coherent states to mimic single-photon pulses or to produce a pair of photons with parametric down conversion and to detect one of them to herald the presence of the other. In this direction, the present work shows how to produce better approximations of single-photon pulses by using a nonlinear phase modulator in a Mach-Zehnder interferometer. The proposed scheme is explained and applications are discussed.
Single photons are the smallest excitation states of the elctromagnetic field. They can be experimentally created but there is no apparatus that performs this task with 100% efficiency. Many techniques and theorems of optical quantum information theory use single photons. In order to utilize them for information processing, it is reasonable to know if they had been successfully produced. In other words: One needs heralded single photons. How to achieve this, is the main result of this diploma thesis. The task has been to improve the efficiency of already existing single photon sources. An apparatus had to be found which postprocesses the output of such sources in order to either herald the photons or at least to improve the efficiency. This apparatus is explicitly allowed to use other optical sources, for example coherent states (laser). The situation has been formally represented by the assumption that single photon sources produce a mixture of vacuum and the single photon state. It is known that experimental set-ups also create higher photon contributions. These contributions are considered to be small in corresponding publications. For some cases they even seem to vanish at all. One can distinguish two regimes concerning the techniques which have been used in this work: linear and nonlinear optics. Linear optical tools, for example the beam splitter, do not absorb photons in the ideal case, but it is not easy to implement useful transformations by their means. Absorption and weak coupling are drawbacks which arise mainly in nonlinear optical media. This work shows that the interactions two-photon absorption and cross phase modulation can be used in schemes, which enable the heralding of single photons. Already there are some linear optical quantum gates which manipulate optical states by means of single photons. Photons do not interact with each other directly, in contrast to electrons for example. Therefore quantum gates which act on more than one mode are interesting. The effective interaction of these gates is not quitecomparable to unitary dynamics. Moreover, these gates do not function in each case. Measurements required in auxiliary modes yield different results for each single case and in order to obtain the desired effect the cases have to be selected according to the measurement results. It has been investigated, how such gates perform if they have statistical mixtures as a resource instead of perfect single-photon states. Yet, no improvement of the single-photon contribution has been accomplished by means of these apparatuses. Hereby it has not been disproved that it is possible to achieve this goal using other apparatuses and techniques of linear optics. Yet, it has been shown that an enhancement is possible but then a non-vanishing two-photon contribution is appended. One of the most basic quantum gates is the conditional sign flip. The optical 8 interaction cross phase modulation acts in quite the same way considering only single photons. This effect enables the heralding of single photons in the ideal case. Within this work it has been shown that a Mach-Zehnder interferometer, a cross phase modulating medium and a photo-detector can be employed for this purpose. One could use any source of light as input to the interferometer but a strong coherent state (laser) may be preferred for the purpose of enhancing the interaction. The absorption of two-photon states is another non-linear effect. Astonishingly this effect serves to generate a heralded single-photon state given two imperfect single-photon sources. First the photon adding tool is employed which consists of a beam splitter and a photo-detector. By means of that and the statistical mixtures of two single-photon sources one creates a mixture which contains vacuum, the single-photon state and additionally the two-photon Fock state. This mixture propagates through a Mach-Zehnder interferometer. The interferometer is adjusted such that it is transparent for incoming light. In addition to the interferometer alone a two-photon absorbing medium is placed in one of its arms. For this reason there is a chance that the two-photon contribution entering the interferometer is absorbed within this medium. We cannot exclude this unfortunate case. A detector is placed in one of the two output modes. The interferometer is adjusted such that the single photon state does not leave in the mode in which the detector is placed, but always in the other mode. The detector can only click if the two-photon state propagates through the interferometer and if it is not destroyed in the absorbing medium. If the detector then receives one photon it is obvious that another one must leave in the other mode. The whole phenomenon is very similar to the concept of null measurement. Although not a main result, it has been shown here that the so-called Hong-Ou-Mandel effect can be generalized. It has been proven that the beam splitter transforms Fock states with equal Fock number into superpositions of Fock numbers which are even in each mode. Another effect on special odd Fock states is conjectured.
Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states $\ensuremath{\mid}1⟩$ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross-phase-modulation (XPM). We present a scheme that announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM-related phase shift with a Mach-Zehnder interferometer.
Application of quantum sources in communication and information processing are believed to bring a new revolution to the on-going information age. The generation of applicable quantum sources such as single photon state and two-photon state, appears to be one of the most difficult in experimental quantum optics. Spontaneous Parametric Down-Conversion (PDC) is known to generate two-photon state, but bandwidth problem makes it less applicable in quantum information processing. The aim of this work is to generate a narrow band two-photon state and apply it to quantum information processing. We start by developing a cavity enhanced PDC device to narrow the bandwidth of the two-photon state. Direct measurement of the bandwidth of the generated state has been made and the quantum theory of such a device has been investigated. An application of this narrow band two-photon state is to generate anti-bunched photons for quantum cryptography, based on the quantum interference between the two-photon state and a coherent state. The feasibility of this scheme for pulsed pump is also investigated. When applying the concept of mode locking in lasers to a two-photon state, we have mode-locked two-photon state which exhibits a comb-like correlation function and may be used for engineering of quantum states in time domain. Other applications such as demonstration of single photon nonlocality, nonlinear sign gate in quantum computation, and direct measurement of quantum beating, will also be addressed.
Abstract We report on a novel phase-locking technique for fiber-based Mach–Zehnder interferometers based on discrete single-photon detections, and demonstrate this in a setup. Our interferometer decodes relative-phase-encoded optical pulse pairs for quantum key distribution applications and requires no locking laser in addition to the weak received signal. Our new simple locking scheme is shown to produce an Ornstein–Uhlenbeck dynamic and achieve optimal phase noise for a given count rate. In case of wavelength drifts that arise during the reception of Doppler-shifted satellite signals, the arm-length difference gets continuously readjusted to keep the interferometer phase stable.
The memory-assisted measurement device-independent quantum key distribution (MDI-QKD), which requires less stringent conditions on the memory modules than that of quantum repeaters scheme, offers a practical mid-term solution to long-distance quantum key distribution. In this paper, considering the high cost and the high multi-photon probability, respectively, of single-photon source (SPS) and weak coherent source (WCS), we present schemes on implementing the parametric down-conversion sources, including the heralded single-photon source (HSPS) and single-photon-added coherent source (SPACS), in the memory-assisted MDI-QKD. By numerical simulations, we show that HSPS and SPACS scheme have apparent superiorities both in the key generation rate and the required minimal coherence time of quantum memory compared to WCS scheme. Moreover, we find that the robustness of SPACS against intensity fluctuations is better than WCS, but still worse than HSPS.