Quantum Beat of Two Single Photons

The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect two-photon coalescence even for nonperfect photons.

Figure 1

Fourth-order interference. Single photons emerge from $A$ and $B$ and impinge simultaneously on a beam splitter. The photons are so long that they give rise to distinct photodetections. The first detection projects the system into a superposition, which then determines the probability of detecting the second photon with either one or the other detector.

Figure 2

Atoms and photons. (a) Triggered by laser pulses, an atom-cavity system emits unpolarized single photons. They are randomly directed by a polarizing beam splitter along two paths towards a nonpolarizing beam splitter (BS). A photon traveling along path $A$ gets delayed so that it impinges on the BS simultaneously with a subsequent photon that travels along path $B$. (b) Number of coinciding photodetections in the two output ports as a function of the time difference between the detections: If only a single path is open, a Hanbury-Brown–Twiss measurement of the intensity correlation is performed, showing antibunching (solid line). If both paths are open but have perpendicular polarization, no interference takes place and the BS randomly directs the photons to $C$ and $D$. This leads to coincidences at $\tau \approx 0$ (dashed line). All traces result from a convolution with a 48 ns wide square time-bin function.

Figure 3

Quantum beat. Number of coinciding photodetections as a function of the time difference $\tau$ between the detections [only the central peak is shown; see Fig. 2b]. Both paths are open and have parallel polarization (circles). The solid lines represent a numerical fit to the data [8]. A Gaussian fit to the reference signal (perpendicular polarization, dashed line) is also shown. (a) Photons of identical frequencies lead to a 460 ns wide central minimum. This lack of coincidences is caused by coalescing photons that leave the BS through the same port. Depth and width of the minimum indicate the initial purity of the superposition and the mutual coherence time of the photons, respectively. (b) The atom-cavity system is driven by a sequence of laser pulses with a frequency difference $\Delta =|{\omega }_1-{\omega }_2|=2\pi \times 3\mathrm{M}\mathrm{H}\mathrm{z}$ between consecutive pulses (see level scheme). This gives rise to a frequency difference between consecutive photon emissions, which leads to a quantum beat in the correlation function starting at $\tau =0$.