3 CAPÍTULO III DIAGNÓSTICO
4. CAPÍTULO IV PROPUESTAS
4.2 Cambios deseados y factibles 2
This chapter has looked at the issue of generating single photons which exhibit sub-Poissonian statistics using a quantum dot embedded in a micropillar cavity with an
implementation of the BB84 protocol for QKD. Autocorrelation measurements were performed to characterise how closely the quantum dot behaves like a true single-photon emitter at a series of different excitation powers. The lowest measured g( )2
( )
0value was 0.32 at an excitation power of 0.25 µW rising to 085 at the highest excitation power of 5 µW. The highest photon emission rate from the quantum dot sample was 4 MHz which was calculated assuming an 11% coupling efficiency of the microscope into 9 µm diameter core fibre and a detector efficiency of 38% at a wavelength of 895 nm.
Due to difficulties with the polarisation modulator only three of the four states required for the BB84 protocol could be generated. The modulator was also a resonant device which meant that the only clock rate at which the system could be operated at was 40 MHz. The maximum observed value for the primary excited state lifetime was 563 ps which would limit the maximum excitation pulse repetition rate to several hundred megahertz. This would allow a much higher photon flux. In addition if the free space modulator could be replaced by an in-line fibre coupled version the loss of the system could be significantly reduced.
As a result of the non-equally spaced bit locations for the four polarisation states as seen in Figure 3.24 it was necessary to pulse the laser non-periodically to ensure that the optical pulse when inside the polarisation crystal was synchronised with the electrical signal for each of the polarisation states. This leaves the system vulnerable to a potential eavesdropper who can measure the temporal separation between pulses to gain information on the state sent by Alice. In a more realistic scenario the laser pulse repetition frequency should be kept constant.
A series of measurements investigating how the QBER and the net bit rate varied as the excitation power was varied is shown in Figure 3.28 and Figure 3.29 for a transmission distance of 0 km and 2 km. The net bit rate was calculated using both the Cascade error correction protocol and the GLLP security analysis. The highest bit rate obtainable using the GLLP analysis was 65 bits/sec for 2km and 396 bits/sec for 0 km. The net bit rate obtained using Cascade error correction is higher as it does not take into account those extra bits which must be sacrificed because of the PNS. The highest bit rate obtainable using Cascade error correction was 179 bits/sec for 2km and 453 bits/sec for 0 km. Other research groups have used single-photon sources in a QKD system. The Toshiba research group used an InAs quantum dot operating at ~1.3 µm over 35 km of
optical fibre using phase encoding with a Mach Zehnder interferometer [72]. They reported ag( )2
( )
0 value of 0.16 and a secure bit rate of ~2 bits/sec at 35 km using GLLP analysis. The reported single-photon efficiency was 4.6% at a clock rate of 1 MHz. In 2010 researchers in Japan reported the lowest g( )2( )
0 value of 0.055 obtained at a wavelength of 1.5 µm using a quantum dot structure [75]. The single photon efficiency was 5.8% corresponding to a single photon per pulse of 1.2 MHz. Using simulations based on Waks et al. [53] a single photon source with a g( )2( )
0 of 0.055 can distribute secure keys over 6 dB more channel loss compared to a SPS with a g( )2( )
0 value of0.85. One of the highest reported emission rate for a quantum dot microcavity was made by Strauf et al. with a emission rate of 31 MHz after correction for detection efficiency, displaying a g( )2
( )
0 value of 0.4 [59]. If this single-photon source could be integration into the QKD system described here, which has an emission rate of ~7.75 times the source used in this chapter then a calculated secure bit rate of 1653 bits/sec could be expected using a g( )2( )
0 of 0.4.The issue of source efficiency and collection efficiency for a single-photon source was examined by Gérard et al in 2010 [76]. They used self-assembled InAs quantum dots embedded in a GaAs Photonic nanowire which was carefully tapered at one end and with a metal-dielectric mirror at the other. Using a 0.7 NA collection lens they obtained a source efficiency, defined by the probability of collecting a photon into the first lens in the system, of 0.72 (72%). This corresponded to a single-photon emission rate into the first lens of 55 MHz when optically pumped at saturation using a Ti:sapphire laser at a repetition rate of 76 MHz. The emission wavelength of the source was 915.2 nm which was maintained at 5 K. A g( )2
( )
0 value of less than 0.008 was obtained. They stated that photonic nanowires have an advantage over quantum dot cavity single-photon emitters as cavities which are detuned from the QD can contribute to the cavity mode via coupling to the continuum of states leading to multiphoton pulses under non-resonant excitation, thereby increasing the g( )2( )
0 value. The addition of a source similar to the one developed developed by Gérard et al., which is at least an order of magnitude more efficient than the source presented in this chapter, into the QKD system here would be a huge benefit to the bit rate which could be obtained from the system.The necessity for operating the QKD system described in this chapter with liquid helium places restrictions on the practicality of such a system. Already demonstrations of single-photon emission at room temperature has been demonstrated in molecules
[77], colour centres in diamonds [78] and nanocrystals [79]. Philip Grangier’s group in Paris, used the nitrogen-vacancy colour centre in a diamond nonocrystal in a free-space QKD system employing polarisation encoding at 1.55 µm. They obtained a g( )2
( )
0value of 0.15 and a bit rate of 1.67 kbits/sec at 30.5 metres [80].
Recently the interest in using quantum dots in a QKD system has dropped due to the development of decoys states which can deliver superior bits rates with lasers offering a much simpler solution [81]. In 2008 Dixon et al. demonstrated a gigahertz clocked decoy-protocol quantum key distribution system [82]. A secure bit rate of 1.02 Mbits/s was obtained over a fibre distance of 20 km while 10.1 kbit/s was achieved for 100km.
By simply sending decoy pulses, Alice and Bob are able to prevent the photon number splitting attack. However interest in single-photon sources could be reinvigorated for applications in distributing entangled states over long distances using quantum repeaters which require single-photon sources [83].