We propose a heralded single-photon source based on injecting a superposition of oppositely squeezed states onto a beam splitter. Our superposition of squeezed states is composed of only even photon number states (the number of photons is equal to $2,6,10,...$) meaning the probability for an emitted single photon given as a heralded single-photon event is higher than what one can achieve from the usual two-mode squeezed state. This enables one to realize an enhanced heralded single-photon source. We discuss how to create this superposition of squeezed states utilizing a single-mode squeezed state and the cross-Kerr nonlinearity. Our proposed method significantly improves the probability of emitting the heralded single photon compared to spontaneous parametric down-conversion.
We propose a heralded single-photon source based on injecting a superposition of oppositely squeezed states onto a beam splitter. Our superposition of squeezed states is composed of only even photon number states (the number of photons is equal to 2,6,10,...) meaning the probability for an emitted single photon given as a heralded single-photon event is higher than what one can achieve from the usual two-mode squeezed state. This enables one to realize an enhanced heralded single-photon source. We discuss how to create this superposition of squeezed states utilizing a single-mode squeezed state and the cross-Kerr nonlinearity. Our proposed method significantly improves the probability of emitting the heralded single photon compared to spontaneous parametric down-conversion.
Abstract We study implementing a heralded single-photon source with second-order nonlinear photonic crystals. Injecting pump and signal light beams into a one-dimensional photonic crystal composed of a material with a large second-order nonlinear optical susceptibility χ ( 2 ) , we can transform the coherent incident signal light into squeezed light. Preparing two squeezed light beams by this method and input them into two ports of a 50-50 beam splitter independently, we can transform them into a two-mode squeezed state. Because those two modes of photons share entanglement, a single photon of the one mode is emitted with a high probability on the condition of the single-photon detection of the other mode as a heralding signal. We evaluate the efficiency and the second-order intensity correlation function g ( 2 ) ( 0 ) for this heralded single-photon source. Moreover, we examine changes in the efficiency and g ( 2 ) ( 0 ) when we assume that the single-photon detector for the heralding signal is imperfect. For a specific concrete example, we consider a case where the nonlinear medium is lithium niobate LiNbO 3 and the frequency of the incident signal light is on the order of 1014 Hz.
We show that superpositions of oppositely squeezed states -- non-Gaussian Schr{ö}dinger-cat-like states -- exhibit enhanced nonclassical features and provide an entanglement advantage in the small-squeezing regime. These states possess photon-number structures distinct from conventional coherent-state cat states, and we analyze their Wigner functions and the entanglement generated when they are injected into a 50-50 beam splitter. As a practical application, we demonstrate that they enable a high-quality heralded single-photon source whose second-order intensity correlation function is smaller than that obtained from a pure two-mode squeezed vacuum state. We further propose a linear-optical heralding scheme that approximates these superpositions without requiring strong Kerr nonlinearities. Our results indicate that the superposition of oppositely squeezed states is a promising non-Gaussian resource for quantum information processing, particularly for single-photon generation.
Abstract Quantum secure direct communication (QSDC) promises unconditional security for direct information transmission without pre-shared keys. However, practical implementations using weak coherent sources face critical challenges from device imperfections, such as emitting vacuum states and multiphoton states. Here, we introduce a heralded QSDC protocol leveraging squeezed-state superposition in a cross-Kerr nonlinear medium, where single-mode squeezed states interfere with coherent states to generate superposition states via post-measurement selection. We have considered three detector models to analyze the heralding performance of light sources under different conditions, including the ideal photon number detector, the practical photon number detector, and the practical photon detector. Our proposed protocol dramatically reduces the vacuum state ratio compared to weak coherent pulse sources, and the multiphoton ratio is still maintained at a low level, significantly enhancing the security information capacity and the maximum secure communication distance. We perform numerical simulations and compare our protocol with the optical single-photon-based QSDC protocol. At 7.5 km with an average photon number of 0.01, the security information capacity improves by 13.42 times, 12.20 times, and 8.64 times for three detector models. Extending to 17.5 km, these gains will be to 277.59 times, 251.58 times, and 172.91 times. Our work provides a robust framework for high-capacity, long-distance, secure quantum communication systems. PACS numbers: 03.67.Pp, 03.67.Hk, 03.65.Ud
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.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down-conversion combined with a heralding photon detection. The heralded light pulse from such a source is typically treated as single mode; this treatment, however, is incomplete. We develop a full multimode description based on the exact Bogoliubov treatment of the down-conversion process. We then provide a perturbative and effective treatment, which illustrates the most important physical mechanisms and permits analytical estimates of the success probability and purity of single-photon states under practical heralding conditions, both without relying on the precise detection time of the heralding photon and when accepting photons only in a narrow window around the time of the detection. This permits us to characterize the emitted light under three different assumptions for the pump pulse. For spontaneous parametric down-conversion with a very short pump pulse, we find the single-mode description to be accurate, while for longer pump pulses and continuous pumping, a multimode description is necessary. Our findings can be used to guide the design of quantum information protocols based on heralded single-photon sources, as their performance may depend on the multimode nature of the sources.