Generation of frequency sidebands on single photons with indistinguishability from quantum dots

Generation and manipulation of the quantum state of a single photon is at the heart of many quantum information protocols. There has been growing interest in using phase modulators as quantum optics devices that preserve coherence. In this Rapid Communication, we have used an electro-optic phase modulator to shape the state vector of single photons emitted by a quantum dot to generate new frequency components (modes) and explicitly demonstrate that the phase modulation process agrees with the theoretical prediction at a single-photon level. Through two-photon interference measurements we show that for an output consisting of three modes (the original mode and two sidebands), the indistinguishability of the mode engineered photon, measured through the second-order intensity correlation $\left[g^2\left(0\right)\right]$ is preserved. This work demonstrates a robust means to generate a photonic qubit or more complex state (e.g., a qutrit) for quantum communication applications by encoding information in the sidebands without the loss of coherence.

Figure 1

(a) Normalized second-order intensity correlation of a single QD. At $\tau =0$ the raw coincidence count drops to $g^{\left(2\right)}\left(0\right)=0.039\pm 0.01$, confirming the single-photon nature of the emitted stream of photons. The red curve is the theoretical fit to the data obtained using Eq. (1). (b) Semilog plot of resonantly excited time tagged fluorescence emission of a single QD. The red curve is a single exponential with an offset fitted to the data, which gives the emission lifetime to be $745\pm 5$ ps. All error bars plotted in this Rapid Communication are standard error of the mean.

Figure 2

(a) Experimental setup for the two-photon interference measurements. The quantum dot is resonantly excited by a cw laser and the collected photons are sent through a fiber phase modulator (turned off for this measurement) and an unbalanced fiber Mach-Zehnder interferometer. The same setup with the first BS removed is used to measure the statistics of the emitted photons as seen in Fig. 1. (b) Two-photon interference measurements with dot 1 for linearly copolarized and (c) linearly cross-polarized photons with the phase modulator off. For copolarized photons, the $g_{\text{HOM}}^{\left(2\right)}(\tau =0)$ goes to $0.19\pm 0.03$. In the case of the cross-polarized photons, the value is 0.5, which is the classical correlation value. The two side dips at $\tau =\pm 35$ ns correspond to the relative path-length difference of the Mach-Zehnder interferometer where the coincidence count is reduced due to the classical counting probability for single-photon source, and not due to the interference. Therefore, the magnitudes of these dips are equal for the copolarized and cross-polarized cases. (d) and (e) are interference visibilities measured for dot 1 and dot 2. The red curve on (b), (c), and (d) and (e) are obtained from the theoretical fit given by Eqs. (2), (3) and (4) respectively.

Figure 3

(a) Scanning Fabry-Pérot spectrum of single photons after sending through the electro-optic phase modulator for various modulation indices ($\beta$). The solid lines are the Lorentzian fit to the data. The phase modulator is driven with a 5-GHz microwave driver. The relative variance of the intensity of the sidebands is due to the finite discrete stepping resolution of the scanning étalon. (b) Integrated counts as a function of modulation index for the central peak and the average of the first two sidebands obtained for the fit. The data are normalized by taking the integrated count for the unmodulated case to be one. The solid lines are the square of the zeroth-, first-, and second-order Bessel coefficients plotted as a function of the modulation index. The inset of (b) shows suppression of the carrier component within the extinction contrast with a modulator driven at $3\pi /4$ modulation index.

Figure 4

Two-photon interference measurements for linearly copolarized photons modulated at (a) 7 GHz, (c) 5 GHz, and (e) unmodulated case. The interference visibility for each driving frequency is plotted with the same order in the right column. For (a)–(d), the modulator is driven at $\beta \sim \pi /3$ index and all frequency components are used in the HOM measurements. The red curves are obtain from the theoretical fit given by Eqs. (2, 3, 4) for the unmodulated case. The dashed blue lines in the left figures are the classical correlation limit; the normalized coincidence counts below the line indicate the quantum interference between the two photons. The interference visibility, and thus the indistinguishability, are well preserved for the modulated photons.