Bimodal behavior of microlasers investigated with a two-channel photon-number-resolving transition-edge sensor system

We explore the photon-number distribution of bimodal quantum-dot micropillar lasers with a two-channel transition-edge sensor (TES) detection system. The two channels of the photon-number-resolving TES system simultaneously detect light emission of two orthogonal components of the micropillar's fundamental emission mode. The applied experimental scheme provides unprecedented access to the joint photon-number distribution and enables a profound insight into the dynamics and photon statistics of the gain-coupled mode components. In particular, the two-channel TES measurements reveal an optical bistability of the correlated laser modes leading to temporal hopping between emission associated with Poissonian and thermal-like emission statistics. The experimental data and theoretical modeling based on Monte Carlo simulations are in good agreement and reveal the anticorrelated behavior of the mode hopping, which results in intensity fluctuations and superthermal values of the autocorrelation function. Our investigations clearly demonstrate the great benefit of using photon-number-resolving detectors in nanophotonics to explore the rich physics of multimode micro- and nanolasers.

Figure 1

Sketch of the used microelectroluminescence ($\mu \mathrm{EL}$) setup: The bimodal micropillar is operated at $T=20\mathrm{K}$ inside a continuous-flow helium cryostat. The two linearly polarized fundamental mode components are separated with a half-wave plate (HWP) and a polarizing beam splitter (PBS). The spectral properties are measured with two grating spectrometers each equipped with a charge-coupled device (CCD) camera. The joint PND is measured using two fiber-coupled transition-edge sensors (TESs) read out by a superconducting quantum interference device (SQUID) current sensor. The TES detectors are placed in an adiabatic demagnetization refrigerator (ADR) and are operated at a temperature of 100 mK. The laser excitation is synchronized with the data acquisition (DAQ), which digitizes the analog TES output signal for further processing.

Figure 2

Signal response of a single transition-edge sensor (TES). (a) Exemplary TES output signal of a microlaser under pulsed excitation (40 time traces are shown); zero to six photons can be clearly distinguished by the pulse height at wavelength of 850 nm. (b) The photon count distribution is extracted by analyzing the time integral for red individual pulses in (a) of 200 800 detection events. The area of a Gaussian peak determines their photon-number probability. (c) The corresponding photon-number distribution of (b) is plotted.

Figure 3

Pulsed microelectroluminescence spectrum of a 4-$\mu \mathrm{m}$-diameter micropillar laser above threshold ($V_{\mathrm{pulse}}=3.25\mathrm{V}$). The two linearly polarized fundamental mode components split to 30 $\mu \mathrm{eV}$ due to the slightly elliptical cross section; $E_0=1.4595\mathrm{eV}$.

Figure 4

(a) Input-output characteristics of the bimodal microlaser under pulsed excitation. The strong mode dominates the emission intensity before the weak mode becomes the superior mode above the crossing point $V_{\mathrm{pulse}}\approx 4.85\mathrm{V}$ (vertical gray strip). (b) At the laser threshold $V_{\mathrm{pulse}}\approx 2.7$ V (vertical orange strip), the linewidth of both modes decreases strongly, indicating the onset of temporal coherence. (c)–(e) Excitation strength-dependent autocorrelation functions [$g^{\left(2\right)}\left(0\right), g^{\left(3\right)}\left(0\right), g^{\left(4\right)}\left(0\right)$] for both modes. The horizontal lines indicate the expected values $(2,6,24)$ and $(1,1,1)$ for thermal and coherent emission, respectively. (f), (g) The cross correlations are well below 1 over a wide range across the input-output characteristics, which indicates a strong anticorrelation of the two modes. The crossing points in (c), (d), (e), and (g) also fall into the gray strip. (Error bars shown if larger than symbol size.)

Figure 5

The joint PND is shown for a pulse voltage of $5.0\mathrm{V}$ with the individual PND for the strong mode at the bottom and for the weak mode at the left axis calculated via a sum over the respective columns and rows. Remarkable are the two concentrations (dark red) of probabilities, which are also visible in the double-peak structure of the individual PNDs.

Figure 6

Decomposed joint PND and original joint PND: (a)–(c) show the joint PNDs for state (a) $l=1$, (b) $l=2$, and (c) $l=1,2$ reconstructed from the original joint PND in (d) (same data as in Fig. 5) using Eq. (7) and the non-negative matrix factorization in Eq. (8). In (e) the single distributions of strong ($P_i^{\left(1\right)}$) and weak ($Q_j^{\left(1\right)}$) modes for $l=1$ and in (f) the single distributions of strong ($P_i^{\left(2\right)}$) and weak ($Q_j^{\left(2\right)}$) modes for $l=2$ are shown.

Figure 7

Mixing parameters $a_l$ and the related autocorrelation functions $g^{\left(2\right)}$ in dependence of the pulsed voltage excitation. (a) The mixing parameters and the summation. The horizontal line marks the center where the mixing parameter is $1/2$. (b) The four combinations (strong and weak, state 1 and 2) of autocorrelation functions that result from NMF. The gray vertical strip marks the crossing point using the same voltage value as in Fig. 4.

Figure 8

(a) Intensities of the two modes given by the average number of photons recorded by the TES, (b)–(d) autocorrelation functions, and (e) cross-correlation functions of the bimodal laser under pulsed excitation. Dashed curves result from the extended Monte Carlo simulations and symbols represent the experimental data in Fig. 4. [Error bars shown if larger than symbol size. The orange (gray) strip indicates the laser threshold (intensity crossing point).]

Figure 9

The left (right) column shows from top to bottom the joint PND from experiments (Monte Carlo simulations) for $V_{\mathrm{pulse}}$ being 5.0, 4.85, 4.7, 3.8, and $3.2\mathrm{V}$; cf. Fig. 8.