Dielectric layer roughness

During the fabrication of the second-generation of devices, it was noticed that the surface of the MoSi nanowires was rougher compared to the first-generation devices. It is believed that this is due to the increased roughness of the sputtered SiO2 compared to thermally-oxidized SiO2. Indeed, during the investigation of the RIE process, samples were fabricated on both thermally-oxidized SiO2(see Figs. 3.11a and 3.11b) and sputtered SiO2(see Figs. 3.11c 34

3.3. Fabrication imperfections

(a) Loss inducing materials, only the nanowire is as-sumed to play a part in the detection mechanism (la-belled).

(b) Extra-fine mesh generated by Comsol for the finite-element analysis.

Figure 3.14: Structure of the simulated nanowire with the addition of lossy elements which do not take part in the detection process.

(a) Absorption as a function of nanowire width and fill-factor.

(b) Slice through at a nanowire width of 150 nm.

Figure 3.15: Simulated absorption inside the nanowire for a structure that includes intra-cavity loss originating from etch residue and layer intermixing.

Chapter 3. Superconducting nanowire single-photon detectors

and 3.11d). It’s clear from the SEM images that the devices deposited on thermal oxide are much smoother. In addition, the sputtered oxide exhibited large particles from time to time, which occasionally completely broke the nanowire, as shown in Fig. 3.11d.

The roughness was also measured with an AFM, comparing the MoSi deposited on thermal oxide and sputtered oxide, which is shown in Fig. 3.16. The average roughness was almost a factor of two larger for MoSi deposited on sputtered oxide. It is believed that this could be the cause for the detector operating temperature which was lower than expected for the 6.5 nm thick, second-generation devices.

A possible solution is to change the deposition conditions of the SiO2sputtering, which will require further investigation. For example, the use of an alternating bias during magnetron sputtering of SiO2 has been shown to produce smoother films [89]. Another possibility would be to try SiO2deposition by evaporation with ion assistance [90] or plasma-enhanced chemical vapor deposition (PECVD).

(a) MoSi on thermal oxide. Average roughness, Ra= 0.67 nm.

(b) MoSi on sputtered oxide. Average roughtness, Ra= 1.15 nm.

Figure 3.16: Comparison of roughness for MoSi deposited on thermal oxide and sputtered oxide.

3.4 Summary

The focus of this chapter has been the development of in-house fabricated SNSPDs. This project was launched mid-way through this thesis, and within two years, very promising device performance has already been achieved. The latest generation devices have demonstrated a SDE of 65%, exhibiting a saturated internal efficiency at 1550 nm and are capable of operating at temperatures up to 1.9 K.

I have discussed the fabrication procedure of two types of devices, one being a simple nanowire structure and the second being a micro-cavity-enhanced version. For the latter, I have de-scribed a method for numerically simulating the optical properties of the structure, in order to 36

3.4. Summary

optimized the design, using Comsol software. These simulations have also been used to study potential sources of efficiency reduction in these devices.

The superconducting material of choice was MoSi, which is a reasonably new material for SNSPD development. To this end, a thorough characterization of the material properties was carried out, including critical temperature, crystallography and ellipsometry. It is a promising material system due to its amorphous nature, leading to very uniform films and subsequently, good fabrication yield. In addition, its critical temperature is relatively high, meaning it will be compatible with practical and low-cost cryogenic systems operating at 2.5 K.

Interesting insights have been found during a spectral response characterization of the devel-oped devices, namely that there is a nonlinear relation between the incident photon energy and the current required for unity internal efficiency. This is contrary to previous investi-gations based on other material systems. This opens up the possibility of investigating and contributing to the study of the detection mechanism in these devices, which is an open question in the SNSPD community.

The final part of this chapter was dedicated to discussing the current imperfections in the second-generation devices as well as the latest developments aimed at overcoming them. The most important factor to be improved was the nanowire etching technique, which will be used in the next generation devices.

A significant part of the thesis also involved the thorough characterization of state-of-the-art devices fabricated by NIST (SDE=87% at 1550 nm), which has helped the understanding of the operation of these devices and sets a benchmark for the in-house detector development.

Throughout the completion of the thesis, these detectors have been used in several demanding quantum-optics experiments [47, 91, 48], which demonstrates the impact that they can have on the community and highlights the importance of further development. Overall, these detectors carry great promise in that they can achieve high SDE, low DCR, high count rates and low temporal jitter, all at the same time. Moreover, thanks to the highly-broadband internal spectral-response, they could be optimized and utilized at a vast set of wavelengths.

4 Long-distance and high-rate quantum key distribution

Proposed in 1984, quantum key distribution (QKD) allows two users to exchange provably secure keys via a potentially insecure quantum channel [92]. Since then, QKD has attracted much attention and significant progress has been made both in theory and practice [1, 2, 93, 94], such that even commercial solutions have existed for some time now. QKD is seen as an upgrade to key distribution protocols which rely on computational complexity, which are at threat of future advances in decryption technology.

The main challenge that faces QKD is its ability to integrate into the existing communications infrastructure. In order to guarantee perfectly secure encryption, one must use a protocol known as the one-time pad (OTP), which requires a secret key as long as the message and the key cannot be reused. Unfortunately, there is still a significant gap between the achievable QKD secret key generation rates (megahertz) compared to the speed of classical communi-cation systems (gigahertz), meaning that the use of the OTP is limited for the time being. An intermediate and transitory solution would be to use AES based key expansion, with the seed key being provided by QKD, which can be seen as an enhancement over the current encryption schemes. The second challenge is the increase of the maximum distribution distance between the two users, in order to enable the spread of a QKD network over large areas.

A natural choice for the quantum channel in a QKD system is an optical fiber, and the use of quantum states of light at telecom wavelengths as the information carriers. A popular family of protocols form the discrete-variable QKD systems, where the quantum states are encoded in a discretely modulated degree-of-freedom of a single photon (ideally). This calls for high performance single-photon detectors and it is typically this part of the QKD system that limits the ultimate performance. Indeed, on the source side, it is possible to make use of standard telecom components which are very well developed. This means that technological advances in single-photon detection can be directly transfered into improvement in QKD systems. In this chapter we shall discuss the application of the single-photon detectors developed in the earlier part of this thesis to high performance QKD systems in order to push the current capabilities.

Chapter 4. Long-distance and high-rate quantum key distribution

In Sec. 4.1 I shall outline the use of low-noise InGaAs/InP NFAD detectors, discussed in Chapter 2, for long distance QKD. The following sections will discuss further methods for performance and security improvement, with Sec. 4.3.1 and 4.3.2 outlining numerical simula-tions of protocols looking at increasing the achievable secret key rate (SKR) and transmission distance, respectively, both through the use of SNSPDs.

Figure 4.1: Dark count rate versus detector temperature (blue circles). The required deadtime for each temperature to keep the afterpulse probability low enough to not impact the QBER in a QKD system (green squares. Solid lines are best fit functions.

4.1 Long distance QKD with free-running InGaAs/InP detectors.

In Chapter 2 we have demonstrated that InGaAs/InP NFAD detectors can simultaneously achieve extremely low dark count rate (DCR), good afterpulse probability (AP) and timing jitter whilst operating with detection efficiencies approaching 30%. This makes them ideal for appli-cation in high-speed QKD systems. In particular, the low-noise nature of the detectors makes them particularly attractive for long distance QKD implementations, since the transmission probability of the photons carrying the encoded information become very low and hence the DCR has to be kept well below the photon arrival rate, otherwise the quantum bit error rate (QBER) increases too much. Moreover, as the photon detection rates become rather small, a deadtime on the order of tens ofµs can be tolerated, reducing the AP sufficiently. Thanks to the two orders of magnitude reduction of DCR in InGaAs/InP detector presented during this thesis, such detectors can, for the first time, play a role in long distance QKD experiments, alongside SNSPDs.

The QKD system investigated in this section is described in detail in App. A.2. It incorporates all of the necessary components for full QKD, including real-time post-processing for error correction, privacy amplification and authentication. The implementation is based on the coherent one-way (COW) protocol [95, 96] which uses two detectors, one know as the data detector used for measuring the bit value encoded in the photon arrival time (early or late time-bin) and a second one called the monitor detector to measure the visibility of the coherent state 40

4.1. Long distance QKD with free-running InGaAs/InP detectors.

Figure 4.2: (a) Shaded region shows the theoretical detector temperatures that would yield a positive SKR at each fiber length. Experimentally used detector temperatures are shown with black squares. (b) Experimentally measured sifted key rates at each distance (red circles) as well as a theoretically calculated values for the required deadtimes (solid red line). Theoretical sifted key rate for a detector with no deadtime is shown by a dashed black line.

Figure 4.3: Secret key rates versus quantum channel loss using the coherent one-way QKD system at four different temperatures. The QBER for each point was around 2%

Chapter 4. Long-distance and high-rate quantum key distribution

interference, which guarantees security. The data detector is the most crucial in terms of low DCR requirements, since it is used to generate the correlated bit string between Alice and Bob, hence any QBER in this string has to be corrected in the subsequent information reconciliation protocol. The monitor detector on the other hand is used to bound the eavesdropper’s information through a measure of the visibility, hence the DCR component of the erroneous detections can be subtracted from the visibility calculations, which is justified in a trusted detector scenario.

The first goal is to analyse the effect of detector temperature on the performance of the QKD system. For simplicity of the first investigation, we tested the system performance using only the data detector, whilst assuming a constant visibility of 96.0%. The transmission link between Alice and Bob consisted of two 25 km spools of standard single-mode fiber (SMF), one for the quantum channel and the second for the classical channel used for synchronization and classical communication between the two systems. To simulate additional losses a variable optical attenuator was added in the quantum channel.

At each detector temperature, the SKR was maximized by adjusting the detection efficiency and deadtime, whilst the maximum threshold for the QBER was fixed to 2%. With high channel loss, a higher detection efficiency was preferable since a longer deadtime could be tolerated.

With less channel loss the detectors would start to saturate, therefore it was beneficial to reduce the detection efficiency to facilitate a shorter deadtime, which led to a higher SKR.

Figure 4.3 shows the final SKR as a function of the quantum channel loss, with a comparison of the effect of the detector temperature. The optimum temperature, in terms of maximum loss budget, was found to be 183 K. In this case up to 32 dB of loss could be tolerated, whilst generating around 400 bit/s of secret key. At higher temperatures, the maximum tolerated channel loss was reduced due to the increased DCR, however at lower channel loss, the SKR was higher due to reduced afterpulsing and hence the ability to operate with less deadtime. It should be noted that adapting the error correction protocol for lower throughput and higher error rates (not to be limited at 2% QBER) would significantly increase the loss budget. The message of this result is that there indeed exists an optimum detector temperature for a given channel loss.

To find the optimum temperature for each channel loss we tested the detector with the QKD system and set the lowest possible deadtime such that the afterpulsing contribution to the QBER was negligible. Figure 4.1 shows the resulting DCR and deadtime relation as a function of detector temperature. Subsequently, the performance of the COW protocol was numerically simulated in Python. For each fiber length, the maximum tolerated DCR resulting in a positive SKR, was extracted. At the maximum theoretical distance the SKR starts to drop to zero, therefore, in reality, it is not possible to operate the system at this distance, since it would require a very long acquisition time to take the finite key effects into account, during which time the system needs to remain stable. Because of this, an overhead of 10 dB in channel loss was added to the simulation. After calculating the tolerated DCR, this was translated into the maximum detector temperature by using the fit function found in Fig. 4.1. Figure 4.2(a) shows

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