Experimental Fock-State Superradiance

Superradiance in an ensemble of atoms leads to the collective enhancement of radiation in a particular mode shared by the atoms in their spontaneous decay from an excited state. The quantum aspects of this phenomenon are highlighted when such collective enhancement is observed in the emission of a single quantum of light. Here we report a further step in exploring experimentally the nonclassical features of superradiance by implementing the process not only with single excitations, but also in a two-excitation state. Particularly, we measure and theoretically model the wave packets corresponding to superradiance in both the single-photon and two-photon regimes. Such progress opens the way to the study and future control of the interaction of nonclassical light modes with collective quantum memories at higher photon numbers.

Figure 1

(a) Experimental setup. PBS stands for polarizing beam splitter; IM for in-fiber intensity modulator; TMD for time-multiplexing detection; and $\lambda /2$ and $\lambda /4$ for half- and quarter-wave plates, respectively. The inset shows the effective configuration of detectors of the TMD apparatus. (b) Pulse sequence for each measurement cycle. (c) and (d) provide the level scheme and fields for single- and two-photon superradiance, respectively.

Figure 2

Probabilities $P_{i,j}$ to detect $j$ photons in field 2 conditioned on the detection of $i$ photons in field 1 as a function of the probability $p_1$ to detect one photon in field 1, with (a) $i=1$ and (b) $i=2$. Circles, squares, and diamonds plot the probabilities of detecting one, two, and three photons in field 2. Solid lines are linear fits. Black dashed lines provide the values for the plateau of $P_{i,1}$ [0.0085 for (a) and 0.0170 for (b)]. Red and blue dashed lines give the square and cube, respectively, of the black one, corresponding to the Poisson levels for two- and three-photon components.

Figure 3

Single-photon wave packets—Conditional probability $p_c(t)$ for a single detection in field 2 at time $t$, normalized by $P_c$. (a) For ${\mathrm{OD}}_1$, wave packets for $P_{R1}$ (black curve) and $P_{R2}$ (red curve). (b) For $P_{R1}$, wave packets for ${\mathrm{OD}}_1$ (black curve) and ${\mathrm{OD}}_2$ (red curve). The insets plot the corresponding theoretical curves according to Eq. (4) along with the respective pure exponential decays (dashed lines).

Figure 4

Biphoton wave packets—Panels (a) and (b): Probability $p_{c1}(t_1)$ to detect the first field-2 photon at $t_1$, normalized by $P_{c1}$. Panels (c) and (d): Probability $p_{c\tau }(\tau )$ to detect the second photon at time $\tau$ after the first detection, normalized by $P_{c\tau }$. Data in panels (a) and (c) [(b) and (d)] resulted from the same measurements as for the experimental black [red] curve in Fig. 3. Solid lines provide the theory from Eqs. (5) and (6), for the same parameters as the inset in Fig. 3. Dashed lines plot the respective pure exponential decays.