High-dimensional quantum frequency converter

In high-dimensional quantum communication networks, the quantum frequency converter (QFC) is indispensable as an interface in the frequency domain. For example, many QFCs have been built to link atomic memories and fiber channels. However, almost all QFCs work in a two-dimensional space. It is still a pivotal challenge to construct a high-quality QFC for some complex quantum states, e.g., a high-dimensional single-photon state that refers to a qudit. Here, we firstly propose a high-dimensional QFC for an orbital-angular-momentum qudit via sum-frequency conversion with a flat-top beam pump. As a proof-of-principle demonstration, we realize quantum frequency conversions for a qudit from infrared to visible range. Based on the qudit quantum state tomography, the fidelities of a converted state are 98.29(95.02)%, 97.42(91.74)%, and 86.75(67.04)% for a qudit without (with) accidental counts in 2, 3, and 5 dimensions, respectively. The demonstration is very promising for constructing a high-capacity quantum communication network.

Figure 1

The conversion efficiency (CE) for HD-QFC. (a) The simple regime of a sum-frequency generation. (b) The normalized CEs (n-CEs) vs different OAM laser pump of Gaussian and flat-top beam, respectively. (c, d) The distributions of the c-CEs vs different beam waist ratio $\gamma$, where the inputs are the Gaussian and flat-top beams, respectively. In the simulation, the wavelengths are 794, 1550, and 525 nm for the pump, input, and output, respectively; the beam waist is 100 $\mu \mathrm{m}$ for the input signal photon; for the strong pump laser, the beam waist for the Gaussian or beam size of flat-top sets is 100 $\mu \mathrm{m}$; and the length of the crystal (PPKTP) is 10 mm.

Figure 2

Schematics of a HD-QFC. (a) Generation of an infrared heralding single-photon state. (b) the HD-QFC for a qudit preparation, conversion, and projection measurement, where the pump is a flat-top beam shaped by a $\pi$ shaper. (c) The electronic logic modules for correlation measurement. (d) The simple frame for the HD-QFC. PBS: polarization beam splitter; DM: dichromatic mirror; HWP1 (2, 3): half-wave plate for infrared (pump, visible) photon; Len1(2, 3): lens work in infrared (1550 nm), pump (794 nm), and visible (525 nm) bands. SLM1(2): a spatial light modulator for infrared (visible) photons; BPF: bandpass filter; D1: D2: single-photon avalanche diode detector; C.C.: correlation coincidence logic. The classical strong pumps in SPDC and sum-frequency generation are continuous waves.

Figure 3

The mode conversion efficiency of HD-QFC and interference curves for the qudit in the dimension of 2 and 3. (a) The mode conversion efficiencies vs the input pump power for inputs of $|0\rangle$, $|1\rangle$, and $|2\rangle$. (b) The coincidence between infrared and visible photons for single OAM eigenstates in subspace $\left\{-3,\cdots ,3\right\}$, where the accidental count is 6. (c, d) Coincidences minus the accidental counts are recorded by scanning the phase angle in a spatial light modulator (SLM2), where the projection states are ${\left(e^{i{\theta }_0}\left|-1\right.〉+\left|1\right.〉\right)}^{†}$ and ${\left(\left|-1\right.〉+e^{i{\theta }_0}\left|0\right.〉+\left|1\right.〉\right)}^{†}$ for a two- and a three-dimensional qudit state, respectively. Each coincidence data for (b), (c), and (d) are recorded by 30, 60, and 150 s.

Figure 4

The reconstructed density matrix and the fidelity for a qudit in three- and five-dimensional space via quantum state tomography. (a, b) The real and imaginary parts of the density matrix for a qubit state $\left(\left|-1\right.〉+\left|1\right.〉\right)/\sqrt{2}$. (c, d) The real and imaginary part of the density matrix for a three-dimensional state ${\left|\phi \right.〉}_{\Re =3}=\left(\left|-1\right.〉+\left|0\right.〉+\left|1\right.〉\right)/\sqrt{3}$. (e, f) The situations of a qudit ${\left|\phi \right.〉}_{\Re =5}=\left(\left|-2\right.〉+\left|-1\right.〉+\left|0\right.〉+\left|1\right.〉+\left|2\right.〉\right)/\sqrt{5}$ in five-dimensional subspace. Each coincidence data for three qudits are recorded at 100 s, 300 s, and 300 s, respectively. The corresponding accidental counts are 16, 20, and 40, where the single counts in idler ports are 0.4, 0.4, and 1 Mhz. In our experiment, the photon counts can be adjusted by increasing the input power in PPKTP1. The inserted table shows the qudit fidelities for $d=2$, 3, and 5 via Gaussian or flat-top beam pump, where the Gaussian-beam-T and flat-top-beam-T are theoretical predictions based on the nonlinear coupling equations. The flat-top-beam-E is the experimental reconstructed results without (with) accidental counts based on the state tomography.

Figure 5

The conversion efficiency and beam profiles for a high-dimensional frequency converter (HD-FC). (a, b) Conversion efficiency for pumps of the Gaussian and flat-top beam in a single-pass configuration, where the $x$ axes are the same for (a) and (b), which represents the topologic number $\ell$ of input OAM states. (c, d) The beam profiles for a theoretical and experimental flat-top beam, where the white lines are the one-dimensional distribution along the vertical center of the beam profile. (e, h) The beam profiles of input OAM states. (i, l) The beam profiles of up-converted OAM states after HD-FC. All of the units in beam profiles (c)–(l) are $\mu \mathrm{m}$.