Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies

Abstract

Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order crossand auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5]. Presently, HOM two-photon interference has been demonstrated exclusively using photons at optical or telecom wavelengths. Experiments were performed with photons emitted from a single source using parametric downconversion [1], trapped ions [3], atoms [6], quantum dots [7] and single molecules [8]. The HOM effect has also been observed with two independent sources [9–15] realizing indistinguishable single-photon states which are required as a resource in quantum networks or linear optics quantum computation. Such experiments have also been performed using donor impurities as sources [16] including NV-centers in diamond [17, 18]. Furthermore, the HOM effect has been employed to create entanglement between ions [19] in spatially separated traps, and to realize a controlled-NOT gate in a small-scale photonic network [20]. Here, we demonstrate the HOM interference of two indistinguishable microwave photons emitted from independent triggered sources realized in superconducting circuits. In each source A (B) a transmon-type qubit is strongly coupled with rate g/2π = 169 (177) MHz to a transmission line resonator, see Fig. 1a. To create a single photon using one of the sources, we coherently excite the qubit into a state α |g〉 + β |e〉 using a resonant microwave pulse. Then, we swap the qubit state into the resonator mode  (B̂) by tuning the qubit transition frequency for half a vacuum-Rabi period into resonance with the resonator. This creates the state α |0〉 + β |1〉 in the resonator, which for β = 1 corresponds to a single-photon Fock state [22]. The photon then decays exponentially with Lorentzian spectrum through the strongly coupled output port of the resonator into the input mode â′ (b̂′) of the beam splitter at a rate κ/2π = 4.1 (4.6) MHz, see Fig. 1. The two photons then interfere at the beam splitter and are emitted into the output modes â and b̂, see Fig. 1a. Using the dispersive interaction between qubit and resonator, we tune the emission frequencies of the two sources to an identical value of νr = 7.2506 GHz. This is achieved by adjusting the qubit transition frequencies νa to 8.575 (8.970) GHz with a static magnetic flux applied to the SQUID-loop of each qubit. For our experiments, we sequentially create 20 single photons in each source at a rate 1/tr = 1/512 ns ∼ 1.95 MHz in a sequence repeated every 12.5μs.