Efficient Multiphoton Generation in Waveguide Quantum Electrodynamics

Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a long-standing goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling.

Figure 1

(a) [(c)] Setup for the first [second and third] protocol: $N$ target atoms [one source and $N_d$ detector atoms] are coupled to the waveguide. Photon detection [atomic detection in the detector ensemble] heralds the addition of collective excitations. (b) Atomic level structure for the first protocol: Waveguide modes are coupled to $e\leftrightarrow s$ transition with an emission rate ${\mathrm{\Gamma }}_{1\mathrm{D}}$. Transition $g\leftrightarrow e$ is driven by a Raman laser $\mathrm{\Omega }$ and the spontaneous emission rate to other modes is denoted by ${\mathrm{\Gamma }}^{*}$. (d) Atomic level structure for second and third protocols: Waveguide modes are coupled to the $e_1\leftrightarrow g$ and $e_2\leftrightarrow s$ transition with an emission rate ${\mathrm{\Gamma }}_{1\mathrm{D}}$. A two-photon transition $a_1\leftrightarrow e_1$ is driven by laser light via level $a_2$ with effective Rabi frequency ${\mathrm{\Omega }}_a$. Transition $a_1\leftrightarrow e_2$ is driven by another laser with Rabi frequency ${\mathrm{\Omega }}_b$. Coupling between levels $s\leftrightarrow s_n$ is given by a Rabi frequency ${\mathrm{\Omega }}_c$.

Figure 2

Steps for the second protocol, with ${\pi }_{c,t,d}$ denoting the $\pi$ pulses for the population transfers within the source, target, or detector atoms. The driven transitions to the excited states are indicated by the Rabi frequencies ${\mathrm{\Omega }}_{a,b}$. The final state is highlighted in yellow.