† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11654002, 61575114, 11874250, and 11804207), the National Key Research and Development Program of China (Grant No. 2016YFA0301401), the Program for Sanjin Scholar of Shanxi Province, China, the Program for Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, China, the Fund for Shanxi “1331 Project” Key Subjects Construction, China, and Key Research and Development Projects of Shanxi Province, China (Grant No. 201903D111001).
We report a low-noise, high-signal-to-noise-ratio (SNR) balanced homodyne detector based on the standard transimpedance amplifier circuit and the inductance and capacitance combination for the measurement of the bright squeezed state in the range from 1 kHz to 100 kHz. A capacitance is mounted at the input end of the AC branch to prevent the DC photocurrent from entering the AC branch and avoid AC branch saturation. By adding a switch at the DC branch, the DC branch can be flexibly turned on and off on different occasions. When the switch is on, the DC output provides a monitor signal for laser beam alignment. When the switch is off, the electronic noise of the AC branch is greatly reduced at audio-frequency band due to immunity to the impedance of the DC branch, hence the SNR of the AC branch is significantly improved. As a result, the electronic noise of the AC branch is close to −125 dBm, and the maximum SNR of the AC branch is 48 dB with the incident power of 8 mW in the range from 1 kHz to 100 kHz. The developed photodetector paves a path for measuring the bright squeezed state at audio-frequency band.
Squeezed states are usually divided into two types: one is the bright squeezed state that has a coherent amplitude, and the other is the squeezed vacuum state that has no coherent amplitude.[1–5] Which type of squeezed light is desirable is dependent on the applications. In interferometer, the squeezed vacuum state is usually used to reduce the cross-interference influence due to no coherent amplitude.[6–10] While the bright squeezed state has a coherent amplitude, which can be used in spectroscopic measurement,[11,12] velocimetry,[13] LIDAR,[14] and quantum key distribution.[15,16]
The detection,[17,18] besides the generation[19–22] and propagation of squeezed states, is another key element for improving their application performances. Many dedicated researches have been carried out to explore a balanced homodyne detector (BHD) with low-noise, high-gain, and high common mode rejection ratio (CMRR).[23–30] Our group has designed a low-noise, high-gain photodetector based on the bootstrap structure with a clearance of 21 dB for 410 μW injected power.[25] Subsequently, by adopting a junction field-effect transistor (JFET) buffering input, we suppressed further the electronic noise of the photodetector, extended the dynamic range to 11.22 mW with a clearance of 36 dB.[29] Furthermore, by adding the differential fine turning circuit between two photodiodes (PDs), a maximum CMRR of 75.2 dB was obtained.[27] A common feature of these detectors described above is to employ a transimpedance amplifier (TIA), which is a natural choice for low-noise, shot-noise detection. In combination with the inductance and capacitance (L–C) circuit, the AC and DC signals are observed individually with different gains. The design, which is usually adopted to detect squeezed states at MHz regime, can not only prevent the DC signal from entering the AC branch that avoids AC branch saturation, but also provide a monitor signal for laser beam alignment. However, as the detection frequency decreases, the AC separation from the DC signal faces a challenge. In order to resolve the trouble, the DC coupled transimpedance detector is widely used to measure squeezed vacuum states at audio-frequency band. Vahlbruch et al. designed a DC coupled transimpedance detector, whose SNR is around 20 dB in the tens of Hertz to tens of thousands of Hertz frequency band for optical power of around 1 mW.[31] Compared with the squeezed vacuum state, the bright squeezed state with coherent amplitude can not be accurately detected by the DC coupled transimpedance detector due to the saturation effect. Therefore, one challenge, that is the particular focus of this paper, is the construction of a detection system for the bright squeezed state at audio-frequency band.
In this paper, we design a low-noise, high-SNR BHD for the bright squeezed state measurement in the range from 1 kHz to 100 kHz. By using a capacitance to isolate the DC photocurrent from the AC amplification branch, the AC amplification branch of the photodetector is immune to saturation at audio-frequency band. By adopting a switch at the DC branch, the electronic noise of the AC branch is significantly reduced. At the same time, the intrinsic shunt of the DC branch at audio-frequency band is eliminated when the switch is off, hence the SNR of the AC branch is significantly increased. In addition, the DC branch does also provide a monitor signal for laser beam alignment when the switch is on. As a result, we obtain a high-performance BHD with the electronic noise of about −125 dBm, the maximum SNR of higher than 48 dB for 8 mW incident power, and the CMRR of higher than 59 dB in the range from 1 kHz to 100 kHz.
The main circuit diagram for the photodetector is shown in Fig.
It is well-known that a large number of classical low-frequency noises[32] from the solid-state laser, external environment, and the BHD will inevitably be coupled into the detection system. Even though the balanced homodyne detection is an effective method to amplify the signal fluctuation and reduce the electronic noise, the electronic noise puts a stringent limit on the achievable SNR in the range from 1 kHz to 100 kHz. The model[27,28] for analyzing the AC output noise response of the BHD with TIA circuit is shown in Fig.
![]() | Fig. 2. The AC output noise response model of the photodetector. Some parameters are as follows: ![]() |
The electronic noise of the photodetector with L–C combination and TIA circuit can be classified into three parts:[33] one is from the feedback resistor, another is from the PD, and the third one is from Op-Amp.
The thermal noise caused by the feedback resistor Rf is given by
The electronic noise of the PD composes of the shot noise caused by the dark current and the thermal noise generated by the shunt resistor. Given that the dark currents of the PD1 and PD2 are Idk1 and Idk2, their induced shot noises ΔiPD1,Dark and ΔiPD2,Dark are written as
The thermal noises of the PD1 and PD2 can be expressed respectively in their current forms as follows:
The electronic noise contribution from the Op-Amp includes two parts: the input current noise and the input voltage noise. If the input current noise of Op-Amp is Inoi, its equivalent contribution after the TIA is given by
![](cpb_29_3_034205/cpb_29_3_034205_ieqn2.gif)
![](cpb_29_3_034205/cpb_29_3_034205_ieqn3.gif)
![](cpb_29_3_034205/cpb_29_3_034205_ieqn4.gif)
![](cpb_29_3_034205/cpb_29_3_034205_ieqn5.gif)
![](cpb_29_3_034205/cpb_29_3_034205_ieqn6.gif)
![](cpb_29_3_034205/cpb_29_3_034205_ieqn7.gif)
When two laser beams with equal power P are respectively injected into the two PDs of the BHD with the same responsivity of ρ, the illuminated photocurrents are given by
Substituting Eqs. (
We design and build the BHD with focus on measuring the bright squeezed light in the frequency range from 1 kHz to 100 kHz. The scheme, shown in Fig.
Firstly, the SNRs of the photodetector with and without the DC amplification branch are measured. Changing the laser power from 125 μW to 8 mW by a factor of two, the measured results with and without the DC amplification branch are shown in Figs.
Secondly, according to Ref. [2], the deviation between the measured and real squeezed degrees grows with the increase of the LO intensity noise, but the CMRR of the photodetector can eliminate the impact of the LO intensity noise, which is dependent on the level of the CMRR. The CMRR is another important factor for the performance evaluation of the photodetector, which shows the performance of eliminating the influence of classical noise from the local oscillator. The CMRR is defined as the ratio between the common mode signal and the differential mode signal. The results of CMRR are shown in Fig.
We have developed a low-noise, high-gain BHD based on the TIA technology and the L–C combination for the measurement of the bright squeezed state in the range from 1 kHz to 100 kHz. A capacitance is mounted at the input end of the AC branch to prevent the DC photocurrent from entering the AC branch and avoid AC branch saturation. By adding a switch at the DC branch, the DC branch can be flexibly turned on and off on different occasions. When the switch is on, the DC output provides a monitor signal for conveniently aligning the laser beams to the PDs. When the switch is off, the electronic noise of the AC branch is greatly reduced at audio-frequency band due to immunity to the impedance of the DC branch, hence the SNR of the AC branch is significantly improved. As a result, the electronic noise of the AC branch is close to −125 dBm, and the maximum SNR of the AC branch is 48 dB for 8 mW incident power in the range from 1 kHz to 100 kHz. The noise power without the DC amplification branch entails a 3-dB shift of the corresponding noise trace when changing the laser power by a factor of two, indicating that the photodetector operates linearly in the measurement regime. The CMRR of the AC branch is higher than 59 dB in the frequency range from 1 kHz to 100 kHz. The developed photodetector paves a path for measuring the bright squeezed state at audio-frequency band.
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