Overview of system

The single-photon source which has been described in the previous sections is used to implement the BB84 protocol for quantum key distribution using polarisation encoding on the photons. A free space polarisation modulator (Newport 4102 NF broadband

polarisation modulator) is used to produce the four polarisation states for the BB84 protocol using vertical and horizontal polarisation encoding for one basis set and left and right circular polarisation for the other basis set. The polarisation modulator works by the electro-optic effect. When an electric field is applied across an optical medium the refractive index of the medium changes anisotropically [61]. This optic-electric effect can introduce new optic axes into naturally refracting crystals or to make naturally isotropic crystals doubly refracting. The change in refractive index Dn due to an applied electric field E in the_z z direction is given by

3 0

2 ^z n n rE

D = Equation (3.8)

where r is the linear electo-optic coefficient and n is the refractive index. The device₀ operates when an optical beam, which is polarised at 45° to the crystal’s principle axis, propagates parallel to the crystals optic axis. When there is no applied electric field the crystal acts as a retarding waveplate. When an electric field is applied, the electro-optic effect changes the indices of refraction along the two crystal directions by different amounts, which changes the retardation of the waveplate. The optical layout shown in Figure 3.18 forms a Pockel’s electro-optic modulator and is used for the results shown in Figure 3.21.

Figure 3.18. Components of a Pockels electro-optic modulator. The modulator is placed between crossed polarisers. The crystal acts as a variable waveplate which changes the polarisation of the output beam from linearly polarised to circular, to linear to circular etc. as the applied voltage is increased which controls the amount of light that is finally transmitted [61].

A high extinction ratio input polariser (10000:1) guarantees that the unpolarised output from the quantum dot [27] is polarised at 45° to the crystal’s principal axes. The crystal acts as a variable waveplate, changing the exit polarisation from linearly polarised (0°

rotated from the input) to circularly polarised, to linearly polarised (90° rotated), to circular, etc., as the applied voltage is increased. As in the case of Figure 3.18, when the modulator crystal is placed between crossed polarisers the transmitted intensity I is given by

where V_p is the voltage required for a phase retardation of p , V is the applied voltage on the crystal and f is the phase. The polarisation modulator required that the input optical beam had a maximum diameter of 500 µm across the entire 56 mm length of the crystal [62]. The optical arrangement to achieve this is shown in Figure 3.19. For the launch optics a 16 mm focal length lens (f₁) is used to collimate the photons emitted from the 9 µm core diameter fibre from Alice and a 500 mm focal length lens (f₂) is used to focus the photons through the modulator. The collection optics comprises of one 300 mm (f₃) and one 8 mm (f₄) focal length lens. The loss of the launch/collection optics and the modulator was 9.5 dB.

Figure 3.19. Optical layout to ensure the maximum beam width across the polarisation modulator is 500 µm. The loss of this stage including the collection loss into the 9 µm diameter core fibre is 9.5 dB.

The Newport 4102 NF broadband polarisation modulator containing a crystal of LiNO3

is a resonant device which operates at a clock frequency of 40 MHz which limited the maximum clock rate in the experiment. The crystal is part of a resonant LCR circuit which ensures that energy is efficiently transferred to the crystal and is not lost across

the internal resistance, R, of the modulating source. The inductance L is chosen such that 4p²f₀² =1 LC, where f is the modulation frequency. This enables crystals with₀ lower values of V_p [61]. The driving electronics for the crystal allows an external analogue voltage (0 to 5V) to modulate the output RF level. Figure 3.20 shows the gain curve for the Newport (Model 3363) resonant modulator driving electronics. A pulse pattern generator provided the input voltage signal. The polarisation modulator can be driven at a maximum of 25 V (peak to peak) [62] which is an issue when trying to produce the final fourth polarisation state for BB84. Figure 3.21 shows how the transmitted optical power varies with the applied voltage when the polarisation modulator is placed between crossed polarisers similar to the arrangement inFigure 3.18. In Figure 3.21 it is possible to see that the first linear state occurs at 0 V, the first circular occurs at 9.6 V indicated by the 50% transmission and the second linear at 17.67 V. The voltage which is required to generate the second circular state is predicted to occur at 27.27 V which exceeds the maximum safe driving voltage for the crystal and also exceeds the maximum output of the modulator driving electronics. This means that the polarisation modulator is unable to provide the four polarisation states for a fully working implementation of the BB84 system.

Figure 3.20. The gain curve for the amplitude modulator driving electronics.

Figure 3.21. Shows the normalised power measured at the output of the polarisation modulator after passing through an analyser polariser. The analyser is orientated such that when there is zero applied voltage the transmitted intensity is zero. The two linear states are achieved at a driving voltage of 0 and 19.67 V. The first circular state occurs at 9.6 V indicated by 50% transmission. After obtaining maximum transmission the transmitted power never decreases to 50% again indicating that the second circular state is not achievable. The expected power is obtained using Equation (3.9).

Figure 3.22. One period of the electrical driving signal to the polarisation modulator to generate the 4 states. A DC offset means that while the second linear state is achievable in the first half cycle it is not obtainable in the second half cycle.

Figure 3.22 shows a typical period of the electrical driving signal for the polarisation modulator. It becomes obvious from the figure that while the first linear, first circular and second linear voltage levels are achievable on the first half cycle of the wave the second linear is not achievable on the second half due to the DC offset in the electrical signal. In theory a bias Tee, which adds a DC offset to an AC source, could have been inserted into the electrical circuit to compensate for this offset but the additional electrical loss induced and electrical ringing issues made this impossible.

It is necessary to synchronise the optical light pulse travelling through the polarisation crystal with the electrical signal driving the crystal to ensure that the light pulse is modulated with the correct polarisation state. To achieve this, the electrical signal used to pulse the laser is delayed with respect to the modulator signal. A schematic of the experiment is shown in Figure 3.23.

Figure 3.23. Experimental arrangement to synchronise the optical light pulse travelling through the polarisation crystal with the electrical signal driving the crystal to ensure that the light pulse is modulated with the correct polarisation state. The Agilent 811134A PPG is used as the master clock for the system and drives the laser driver with a 64 bit data pattern at 40 MHz. The HP 8110A PPG, which is clocked by the master clock frequency divided by 64, is used to drive the modulator driver.

The Agilent 81134A pulse pattern generator (PPG) is used as the 2.56 GHz master clock in the system. The output is frequency divided by 64 to provide the 40 MHz

larger amplitude signals and is used to provide the source for the modulator internal oscillator and also the AM modulation input. The laser is triggered by the data output channel on the Agilent 81134A PPG, which is a 64 bit pattern that repeats every 25 ns and whose electrical width is 390.625 ps. It is evident from Figure 3.21 that linear polarisation modulation is only achievable over a limited operating range. This results in the polarisation states in Figure 3.24 being unequally spaced in time. To compensate for this the laser has to be pulsed non-periodically to coincidence with the polarisation states produced by modulator. This has security implications as an eavesdropper can measure the time interval between pulses to gain full information about the states.

Figure 3.24. The variation in the polarisation extinction ratio is plotted as the active bit in a 64 bit pattern, which is used to trigger the laser is swept across one period of the 40 MHz clock signal for the modulator.

The diagram shown in Figure 3.25 shows the outline of the test bed for the implementation of the BB84 protocol. The polarisation encoding system which includes the polarisation modulator in Alice and the beamsplitter, polarisation beamsplitters (PBS) and static polarisation controllers (SPC) in Bob was a relatively uncomplicated system to build and to more importantly to maintain its alignment. For example the SPC in Bob needed adjustment to correctly align the polarisation with the PBS but this was found to remain stable for at least a day. If a phase encoding system was employed using fibre interferometry, active and more frequent feedback is required to ensure path length changes in the arms of the interferometer is minimised. The

importance of the stability of the polarisation encoding system can be understood when considering the alignment of the optical components that make up the single-photon source (SPS). The SPS system required much more frequent adjustment to ensure the highest photon flux was achieved and therefore having an encoding system which had a stable alignment made data acquisition easier. A PicoQuant LDH series excitation diode laser at 784 nm, operating at 40 MHz, excites the quantum dot sample through the custom microscope. The emitted light at a wavelength of 904.5 nm is collected by the microscope and focused through the polarisation modulator which sets the polarisation state of the light. Two orthogonal linear states were used in the course of the experiment. These states occur at bit positions 30 and 50 in Figure 3.24. The pulse pattern generator then outputted a 128 bit pattern with bits 30 and 114 active (one period of 64 bits + 50 in the next). This ensures that a laser pulse train is created which has a mean frequency of 40 MHz. The light then travels through standard telecommunications fibre to Bob. To ensure the light propagates in the fundamental mode short lengths of 5 µm diameter core fibre are spliced onto the ends of the 9 µm fibre which removes higher order longitudinal modes which is a form of spatial filtering [63].

Figure 3.25. Schematic diagram of the QKD system. The box labelled “single-photon source” contains the custom microscope used to optically excite the quantum dot and to collect its emission. The quantum channel is telecommunications optical fibre. To ensure light at 895 nm propagates in the fundamental mode 5 µm core diameter optic fibre is spliced onto the ends of the standard telecom fibre. Static polarisation controllers (SPC) compensate for polarisation evolution in the fibre and return the light into its input polarisation state to ensure either reflection or transmission at the polarisation beam splitters (PBS). The photons are detected using silicon single-photon avalanche photodiodes (Si-SPAD).

The light is then incident on a 50:50 fibre coupled beam splitter in Bob which randomly routes the photon to one of two polarisation beam splitters (PBS) which are used to make measurements of the polarisation state of the photon in either the linear or circular polarisation basis set. These PBS cubes separate the S polarisation (electric field perpendicular to plane of incidence) and P polarisation (electric field parallel to plane of incidence) components by reflecting the S component at the dielectric beamsplitter coating, while allowing the P component to pass [64], [65]. A static polarisation controller (SPC) then directs the photons onto either the designated detector for measuring a binary 0 or binary 1 value via the PBS in each basis set. This is achieved by the controlled bending of the fibre which introduces birefringence [66]. The change in the refractive induced by bending is given by the following expression

2

0.136 r

n R

d = - ´ç ÷^{æ ö}è ø Equation (3.10)

where r is the radius of the fibre and R is the bend radius [67]. Before any key is transmitted, Alice sends an alignment optical pulse to Bob which ensures that the polarisation axes between the two parties are correctly aligned. Unambiguous discrimination is only achieved when Alice encodes and Bob measures in the same polarisation basis set. Imperfections in Bob’s optical components resulted in a loss of 4.76 dB in his measurement apparatus.

Figure 3.26. Schematic of the in-line fibre optic polarisation controller. Using Equation (3.10) it can be shown that the induced phase change due to bending is given by D =f 0.136´ ´N 8p lr² R,where N is the number of loops. If the bend radius is given by R=0.136 8´ p lr² Rthen 1 loop creates a quarter waveplate (QWP) and two loops creates a half wave plate (HWP) [68].