Generation of photon-number squeezed light or sub-Poissonian light has attracted a great deal of interest in recent years. The use of such nonclassical light makes it possible to beat the standard quantum limit (SQL) of classical light. This is now strongly needed in the field of high precision measurements and optical communications. A variety of schemes has been proposed and demonstrated to manipulate the quantum statistical properties of photons. The scheme utilizing semiconductor light emitters driven by a constant-current source is one of the most attractive ways because of the simple experimental configuration, the low energy consumption, and the possibility of significantly reducing noise by using high-quantum-efficiency devices. Photon-number fluctuations as much as 4.5 dB below the SQL have been obtained with a pump-noise-suppressed laser diode (LD).[1]

An alternative approach using a light-emitting diode (LED) has further practical importance. The thresholdless mode operation of the LED has an advantage over the lasing mode of an LD for generating weak sub-Poissonian light because the LED has a higher quantum efficiency even in the low-injection-current regime compared with the LD. Shinozaki et al. reported the largest intensity squeezing of 3.1 dB in 1997.[2] In recent work, Kobayashi et al. measured the broadest squeezing bandwidth by using an integrated LED-detector system specially designed for expanding the squeezing bandwidth,[3] although there was excess noise in the low-frequency region below 100 MHz.

To make further progress in this direction, it is essential to investigate the generation mechanism of sub-Poissonian light.[4] Our method of generating sub-Poissonian light using a commercial LED is so stable and highly reproducible that we can investigate and discuss the generation mechanism, such as the pump-current dependence of the squeezing bandwidth. In this paper, we demonstrate wideband squeezing over a 200 MHz frequency range at low temperature. The experimental result was compared with the unified model[5] that explains the regulation mechanism of emitting photons in terms of the backward pump (BP) process in a heterojunction. The ratio of the BP current to the forward injection current, α, is a key parameter of the model.

The unified model was proposed by Kobayashi et al. in Ref. [5]. The model reduces to the thermionic emission limit[6] at α=0 and to the diffusion limit[7] at α=1. They also investigated the pump-current dependence of the squeezing bandwidth for a p-n heterojunction LED at room temperature. Their result, however, cannot be explained by the definite values of α. The result shows that α is an increasing function of the pump-current at room temperature. At the low-temperature limit, however, the BP process is supposed to less occur than that at room temperature. Therefore, the experimental result should be explainable by the unified model at the thermionic emission limit (α=0), and the effect of the BP process can be clearly shown.

The generation of sub-Poissonian light is based on pump-current-noise suppression by a constant current source.[8, 9] The noise-suppressed electrons reduce photon-number fluctuations to below the shot-noise limit. However, the noise suppression of pump currents alone does not guarantee the regulation of carrier electrons injected into an active layer and the following photon emissions because the electrons injected into a depletion layer randomly go through a potential barrier in a heterojunction by thermionic emission or the tunneling process. Hence, there should exist other regulation mechanisms to compensate for the random process.

Fortunately, for conventional LEDs, this regulation mechanism is the junction voltage fluctuations owing to the thermionic emission of a large number of carrier electrons and to the continuous electron supply by a constant current source.[5, 6, 7] The electrons injected into the active layer are considered to be regulated if the measurement time is much longer than the thermionic emission time, ${\tau }_{\mathit{te}}=\frac{k_{B}T{C}_{\mathit{dep}}}{eI}=r_d{C}_{\mathit{dep}}$, where C_dep is the junction capacitance and r_d is the differential resistance of the LED. This negative feedback mechanism of a macro-size LED or LD is called the collective or macroscopic Coulomb-blockade effect.

According to the above explanation, the regulation bandwidth due to this feedback mechanism is given by $f_{\mathit{te}}=\frac{1}{2\pi {\tau }_{\mathit{te}}}$ and is proportional to the pump-current I. Another effect that limits the squeezing bandwidth is the radiative recombination of the carrier electrons. Thus, an expression for the total squeezing bandwidth must include the effects of the radiative lifetime, τ_rad, and τ_te, and the unified model takes both effects into account.

Let us now consider two extreme cases of the unified model. First, when there is no BP process (i.e., α=0), the thermionic emission process at the band-gap and the radiative recombination process at the active layer occur independently. We can then treat each process separately. Therefore, the Fano factor[10] is described by the product of two Lorentzians,[5]

where η is the quantum efficiency of the LED and f is the noise frequency of interest. This is called the thermionic emission limit[6]. In contrast, if α=1, the two processes are strongly coupled. The backward transport of conduction electrons from active region may exist on a microscopic level. Therefore, these two processes are then regarded as an inseparable single system. Thus, the Fano factor is described by the single Lorentzian,

This is called the diffusion limit[7], and the experimental results were explained by Eq. (2) in Refs. [11] and [12]. The squeezing bandwidth f_c is defined as the frequency where $W=1-\frac{1}{2}\eta$ and is obtained from Eq. (1) or (2) by a simple calculation.[5] Note that f_c is mainly determined by τ_te in the low-current regime, while the influence of τ_rad becomes dominant in the high-current regime.

The experimental setup is shown schematically in Fig. 1. We used a high-speed, high-quantum efficiency GaAlAs LED (Hitachi HE8812SG) with a double-heterojunction structure. The LED was connected through a metal-film resistor (R_S) to a constant voltage power supply. R_S was chosen to be much higher than the differential resistance of the LED (R_S≫r_d).[8, 9] The overall quantum efficiency η, which is determined by the ratio of the photocurrent from the photodiode (PD) to the LED injection current, reached 0.41 at low temperature when LED₁ was placed just in front of a high-efficiency PD (Hamamatsu S6040). To calibrate the shot-noise level, the PD was weakly coupled to another LED (LED₂). When the coupling efficiency was sufficiently small, the emitted photons from LED₂ were approximately considered as Poissonian light. To keep the overall efficiency of LED₂ to be less than 1%, the maximum available Poissonian photocurrent was limited to 1.5 mA. Therefore, we intentionally reduced the coupling efficiency of LED₁ in the high pump-current regime. This does not affect the observed squeezing bandwidth, but restricted the maximum amount of squeezing. The noise signal was amplified by an ultralow noise preamplifier (NF SA-430F5) and was fed into a spectrum analyzer (ADVANTEST R3261C). The Fano factor was given by the ratio of the sub-Poissonian noise power to the Poissonian noise power. The whole measurement system including the spectrum analyzer was installed inside an electromagnetically shielded room.

 

Fig. 1. Schematic of the experimental setup. LED₁ (sub-Poissonian mode) and LED₂ (Poissonian mode) were driven by a constant current source. LED2 was weakly coupled with the photodiode (PD) (η_p<1%).

Download Full Size | PDF

Figure 2 shows the dependence of the squeezing bandwidth on the pump-current at 40 K (cryostat temperature). The device temperature was estimated to be 96 K, which was determined by measuring of the differential resistance (~ k_BT/e_I). In the low-current regime, the squeezing bandwidth increases linearly as the pump-current increases due to the influence of τ_te. In the high-current regime, however, the squeezing bandwidth approaches the constant limited by τ_rad. This result demonstrates clearly the two kinds of contribution to the generation dynamics of sub-Poissonian light.

 

Fig. 2. Pump-current dependence of the squeezing bandwidth. Theoretical curve for the thermionic emission limit (trace a, solid-red line) and for the diffusion limit (traces b, c, and d, dashed-blue lines). Trace a (C_dep=310 pF, τ_rad=0.72 ns) and trace b (C_dep=270 pF, τ_rad=0.62 ns) are chosen to fit the data in the lower and higher pump-current regime with 96 K. Trace c (C_dep=300 pF, τ_rad=0.42 ns) is the fit in the lower I_LED, and trace d is the fit in the higher I_LED.

Download Full Size | PDF

 

Fig. 3. Wideband squeezing observed at 48 K (lower) (I_LED=4.1 mA, η=0.37). The squeezing bandwidth was estimated to be 165 MHz. For comparison, the data at room temperature (297 K) (upper) (I_LED=5.6 mA, η=0.27) was also shown.

Download Full Size | PDF

Trace a in Fig. 2 is the theoretical curve for the thermionic emission limit. C_dep=310 pF and τ_rad=0.72 ns are chosen to fit the data only in the lower and higher pump-current regime with 96 K, because the squeezing bandwidths at lower and higher pump-current regimes must correspond to τ_te (C_dep) and τ_rad, respectively. Nevertheless, trace a is fairly close to the experimental values in the whole pump-current range. For comparison, three theoretical curves for the diffusion limit (b, c, and d) are shown as dashed-blue lines in the same figure; they fit only in the lower pump-current region (trace c) and in the higher pump-current (trace d). We see that no theoretical curve for the diffusion limit can explain the experimental result in the whole range of the pump-current.

Figure 3 shows one example of the experimental result of wideband squeezing at 48 K (lower trace). The pump current was 4.1 mA. The quantum efficiency was 0.37, and the observed Fano factor at the low-frequency limit was very close to the expected value of 0.63. Obviously, the noise suppression was obtained over a 200 MHz frequency range. For comparison, the experimental data at room temperature (upper trace) is also shown in Fig. 3. The pump-current was 5.6 mA, and the quantum efficiency was 0.27. Each data set is well fit with a single Lorentzian, which Eqs. (1) and (2) reduce to in the high I_LED (solid-red lines). The squeezing bandwidths were estimated to be 165 MHz and 79 MHz. In order to obtain this wideband squeezing, we used a relatively high pump-current so that the total squeezing bandwidth was determined only by τ_rad. Therefore we believe that the dramatic expansion of f_c was caused by the difference of τ_rad between the two temperatures.[13]

In conclusion, we have demonstrated wideband amplitude squeezing over 200 MHz from a high-speed LED, and have investigated the pump-current dependence of the squeezing bandwidth at the low-temperature limit. The result is well explained by the unified model of the pump and recombination process at the thermionic emission limit. Our simple configuration using commercially available LEDs will be easily applicable to a quantum optical repeater technique[14, 15] or other experimental demonstration of the nature of light.

The authors thank Y. Kadoya and H. Sumitomo for helpful discussions. This work was supported by the Core Research for Evolutional Science and Technology (CREST) of JST, and JSPS Research Fellowships for young scientists.