Nandan gun

Nandan gun is proposal by Nandan Birst for the source of equally spaced photons.

This page is at the very early stage of development. (P.S. And, perhaps, never will be written as follows.)

=Approach to the photon machine gan.=

Abstract. The gedanken experiment with generation of regular sequence of single photons (machine gun) is suggested. The use of array of parametric down converters is aassumed; each of them procuces the entangles pair of photons, and one photon in each pair is detected. On the bade of signals from the detectors, the router dispatches one and only one photon to the output. Perdormance of such a scheme is considered. Abilities of the realization with commercially available devices are estimated.

1. Introduction.
Problem od generation of regular sequence of single photons ("machine gun") in a single mode gate (polarization-preerving single-mode fiber) is discussed since century 20 [1-9].

This problem is believed to be very important because of the ideas of the application in the quantum communications and quantum computing [10-20].

In this article, the proposal dor such a machine gun is suggested, Figure 1. It is based on the array of sources of entangled photons, Each detector determines weather the pair is generated or not; if the photon is detected, this indicates the existence of its twin.

If at least one photon in one of the elements of the array is detected, it is routed to the output, without considering other channels.

If no one photon is detected, then, for this cicle of operatin, the generation is declared to fail.

Due to non-perfectness of generators of twin photons, splitters, routers, not always there will be exactly one photon at the output. Such events are considered as errors. Optimization of the scheme means reduction of the probability of errors. However, this probability should be estimated assuming gien propertiers of the devices available for 21 century.

2. Basic formulas
Performance of the suggested scheme is characterized with the following parameters:

A. Probability of having exactly one photon in the output mode of the device.

B. Probability of failure, that is sum of probability to have zero photons and probability to have more than one photon at the outout.

C. Intelligence, id est, product of uncertainty of frequecy to that of the arrival time.

These parameters can be (and shouls be) evaluates, estimated, assuming that given properties of the devices involved.

Assume, at the input, we have pulses of light of some fixed energy, duration and the repetition rate. Assume that the repetirion rate \(r\) is low enough compare to allow the detectors to recover between pukses, id est,

\( r t < 1\)

where \(t\) is dead time of the detector.

Since here, we do not care about structure of pulses, the repetition rate and other properties of input pulses, but we assume that each of the dounconverters in Figure 1 produces the pares of photons with Poissonian distribution of number of pairs.

\(\rho_n = b^n \exp(-b)/n!\)

Parameter \(b\) should not be very high in order to prevent sending of several photons to the outout; so, asume \(b<1\).

The efficincy of polarizers can be of order of 0.99 or even higher (less than one percent of photons are lost in polarizers) [21,22]. This efficiency is high compared to the efficiency of detectors, that is typically of order of \(\eta=0.2\) [23,24], so, we neglect the loss at the polarizeds.

The efficiency of detectors \(\eta\) is low. This efficiency seems to set the most important limitation of the performance of the machine gun suggested.

In addition, sometimes detectors say "klick" even if no photon arrive. Probability \(rho_{\rm d}\) of such event is called false alarm expectation.

Once the photon is detected it is supposed to be treated numerically withot errors, in order to elaborate signal for the switches in Figure 1. However, the switches are not ideal. Let each switch be characterized with probability \(p_{\rm s}\) of sending the input to the wrong output channel. So,

\(p_{\rm s} \ll 1\)

3. Calculus.
Assume, we have \(2^m\) sources of entangled photon pairs.

As soon as any of tetectors does "click" the router arranges the way for its wtin to the detector.

5. Polarizers and detectors
Typically, the polarization analyzeds have essiciency .99, id est with probability of order of 1%, the phorons to to the wronf channel (For example, both go to the detector, or both go to the delay line). [].

6. Delay line
Typically, the reponse time of the switches is about \(10^{-9}\) second [26,27]. While the computer and switches form the root for the twin of the detected photon, this photon should wait in the delay shown in figure 1. However, while the photon is waiting, it may get absorbed. Denote the probability of the absorption of photon in the delay line with \(p_d\).

8. Conclusions.
The new scheme of teslization of the photon machine gun is considered. This scheme uses the array of sources of entangled photons; one photon of each pair goes to the detector. If at the first elementof the array, there is photon and it is detected, then ist twin photon is routed to the output. It no photon is detected, the same operation is performed for the second element ans so on.

The efficiency of such a photon machine gun depends on the following parameters:

For realistic devices [

On the base of the results of the detectoin, the outp

rerefences
Quantum Computation

1. Andreas, ..