An optically reconfigurable photon source

As described by Eq. 3.5 the propagation of two-photons in a non- linear waveguide array is essentially linear. So if driving the waveguide np with unity pump amplitude produces the quan-

§3.2 An optically reconfigurable photon source 35

duces the state _|Ψ_i = _∑nN_p=1 Anp

ψ_np

. Therefore by varying the

Nclassical laser inputs, Anp, we can reconfigure the device in real

time to produce any state in an N dimensional quantum space. Thus, a nonlinear waveguide array is an optically reconfigurable on-chip photon source.

We first demonstrate this experimentally, for the simplest type of nonlinear waveguide array, an array of just two coupled waveguides. Thus we will refer to this device as a nonlinear coupler. I assisted with the optical alignment, data analysis and quantum tomography system design for the nonlinear coupler experiment presented in this section, as published in.27 I also showed how the result can more generally applied to arrays of larger numbers of waveguides as I will present in Sec. 3.3.

The nonlinear coupler used in the experiment was fabricated using Titanium in-diffused waveguides on a Lithium Niobate chip. In this experiment the on-chip waveguides where sin- gle mode at the down-converted photon wavelength of around 1342nm filtered to a 12nm bandwidth, and multi-mode at the pump wavelength of 671nm. The pump laser was always cou- pled into the chip so as to only excite the lowest order waveguide mode. The evanescent field overlap between the two waveguides was chosen to be very small for the pump wavelength so that light from the pump laser does not couple significantly out of the waveguide it is originally coupled into. In contrast there is a large overlap between the waveguide modes at the longer wavelength of the down-converted photons, so they will couple between waveguides. The length of the waveguides is optimized so that the CL = π/2 at the down-converted photon wavelength

range, so photons created at the very start of the waveguide will exit in a superposition of both waveguides.

For this device the two-photon wavefunction as a function of propagation distance can be described by the differential equa- tion,82 ∂Ψ1,1(z) ∂z = A1de i∆β(0)z_−iC[Ψ 1,2+Ψ2,1]. (3.9) ∂Ψ1,2(z) ∂z = −iC[Ψ1,1+Ψ2,2] (3.10)

Figure 3.4:a) Diagram of the nonlinear waveguide coupler. The two input pump lasers have a tunable phase shift ∆φbetween them. b) The single photon eigenmodes of the coupler. c) Tunability of the

two-photon state by adjusting the phase mismatch (via temperature tuning) or pump phase difference.

∂Ψ2,2(z)

∂z = A2de

i∆β(0)z

−iC[Ψ1,2+Ψ2,1]. (3.11) Which is simply Eq. 3.5 for the case where n_{i(s) ∈ {}1, 2_}. For the simple case of two waveguides the supermode phase-matching term βkski will have values β1,1 = 2C, β1,2 = β2,1 = 0 and β2,2 =

−2C. Thus the nonlinear coupler differential equations have so- lution, ψ1,1(L) = Ld 4 A1 + A2eiδφ eiL∆β20+πsinc L∆β0 −π 2π (3.12) ψ1,2(L) = ψ2,1(L) = − Ld 4 A1 + A2eiδφ eiL∆2β0sinc L∆β0 2π (3.13) ψ2,2(L) = Ld 4 A1 + A2eiδφ eiL∆β20−πsinc L∆β0 +π 2π (3.14) where sinc(x) = sin(πx)/x, and we have used the fact that

LC = π/2 for this particular coupler. From these equations it

§3.2 An optically reconfigurable photon source 37

Figure 3.5: Tunability of output two-photon wavefunction from the nonlinear coupler. a) Two photon correlations measured for in phase pumps (∆φ = 0) pumps at various temperatures, b) and c) for

∆φ=π/2 and∆φ=πrespectively.

A1 and A2, or phase between them, eiδφ, will change the out- put wavefunction. Adjusting the phase mismatch, ∆β0, can add another degree of freedom to allow the wavefunction to be var- ied over a larger range of states as demonstrated in reference.27 However, control of the phase mismatch can not be achieved all optically in any straightforward way, thus here we focus our at- tention of exerting control purely with the pump lasers A1 and

A2 and their phase difference.

The temperature of the chip was set to around 370°C in order to achieve phase matching with∆β(0) = 0. In this case the output

wavefunction can be expressed as,

Ψ(L) = ₋idπA 2C e i∆φ/2 sin(∆φ/2) cos(∆φ/2) cos(∆φ/2) −sin(∆φ/2) , (3.15) where the matrix element m,n corresponds to the wavefunction element ψn,m and we have set A1 = A2 = A. From this we see that by tuning ∆φ between 0 and π the output wavefunc-

tion can switch from an anti-bunched state (where both pho- tons are in the opposite waveguides), to a bunched state (where both photons are in the same waveguide). This switching can

be seen in the experimentally measured two-photon correlations produced by the nonlinear coupler [Fig. 3.5]. Specifically for the temperature of 370.6°C a pump phase difference of 0 results in the two-photon correlations between photons in waveguides 1 and 2 being the strongest. Where as, simply switching the pump phase difference to π changes the two photons correlations to be

strongest between photons emerging from the same waveguide, corresponding to the bunched state.

Therefore the two-photon wavefunction can be reconfigured all-optically between bunched and anti-bunched states. For prac- tical applications it would be useful to be able to produce more complex states, while still retaining the ability to all-optically those states. Therefore in the next section we consider how a general integrated all-optically reconfigurable source could be developed, which could be engineered produce and switch be- tween any quantum states in any multidimensional space.

3.3 Steering the wavefunction with tailored poling patterns