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Abstract
High-precision cavity locking is crucial for squeezing optical fields. Here, a bootstrapped low-noise photodetector is utilized in the generation process of the squeezed state of light. This process is based on a combination of a modified trans-impedance amplifier (TIA) circuit and a two-stage bootstrap amplifier circuit. This not only achieves high-precision and long-term stable locking of the optical cavity, but it also improves the degree to which the light field is squeezed. The experiment results show that the detector has a high signal-to-noise ratio (SNR) of 26.7 dB at the analysis frequency of 3 MHz when measuring the shot noise with an injection optical power of 800 µW, and the equivalent optical power noise level is lower than 2.4 $\textrm{pW} /\sqrt {\textrm{Hz}} $ in the frequency range of 1–30 MHz. Moreover, the squeezing degree of the quadrature amplitude squeezed state light field can be improved by more than 34.9% when the detector is used for optical cavity locking. The photodetector is useful in continuous variable (CV) quantum information research.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the application of non-classical light, squeezed states break the quantum noise limit of specific components, making them an indispensable part of developing quantum information technology [1,2], such as for detecting gravitational waves [3–5], estimating and tracking phases [6, 7,8], and measuring small displacements [9,10]. In addition, the squeezed state light field can be used to prepare the CV quantum entangled light field [11–13], which is crucial for quantum key distribution [14–16], and quantum communication [17,18]. With the rapid increase in demand for quantum information manipulation indicators, figuring out how to optimize the squeezing degree of optical parameter conversion and lower the noise of the detection system has become an important research topic.
Utilizing the parametric down-conversion process in an optical parametric amplifier (OPA) is one of the most common methods for generating CV squeezed states of light. The important step of this method is the precise locking of the cavity length of OPA [19,20]. Generally, strong locking signals can be obtained by enhancing the seed optical power. Although the power of the seed light is weaker than the pump light, the seed light has a great influence on the parametric down-conversion. As the power of the seed light increases, extra noise increases exponentially, reducing the squeezing degree of the squeezed state of light [1,21]. After collecting the reflected or transmitted light signal, the cavity length or optical phase can be locked using the Pound-Drever-Hall (PDH) technology including a photodetector [22–27]. However, due to the inherent amplitude modulation of the phase modulator in reflected light locking, the error signal of the reflected light will be inaccurate, affecting the locking stability. Moreover, since the OPA system has strict requirements on the optical field loss index when the transmitted light field is used for locking, the power of the transmitted optical signal that can be used for locking is extremely weak, and the extractable error signal is also very weak, easily submerged in the noise signal [28–32]. Thus, the key to improving the accuracy and stability of PDH locking technology is that the detected signal in the feedback loop must have a high SNR. Many studies have focused on improving the performance of the detectors, such as using a low-noise JFET transistor, a two-stage amplifier circuit, a method of combining a JFET buffer with a bootstrap structure or combining a monolithic amplifier with a discrete voltage buffer circuit [33–36]. However, these detectors are limited by noise and bandwidth. The equivalent optical power noise above 15 MHz is greater than 7.90$\textrm{pW} /\sqrt {\textrm{Hz}} $, which will reduce the accuracy and stability of cavity length and phase-locking under low optical power conditions, resulting in a reduction of squeezing degree [37,38].
Here, a low-noise, high-SNR photodetector with an effective frequency range of 1–30 MHz for high-precision locking of optical resonators is designed and evaluated to improve optical field squeezing. By selecting an amplifier LTC6268 with low noise and low input parasitic capacitance after theoretical calculation and combining it with bootstrap amplification, the shunt effect of photodiode junction capacitance can be effectively suppressed. The result is a 41.7% reduction in the noise of the system and a 90% improvement in the SNR of the circuit when locking the optical cavity. Furthermore, the equivalent optical power noise level of the detector is very low, which is below 2.4$\textrm{pW} /\sqrt {\textrm{Hz}} $ at 30 MHz. When measuring the shot noise with an incident optical power of 800 µW, the SNR at 3 MHz is 26.7 dB. After experimental verification, the photodetector can effectively increase optical field squeezing by 34.9%. This is very important for improving the quality of quantum information operations by optimizing the squeezed (entangled) states of light fields in an efficient way.
2. Generation of quadrature amplitude squeezed state of light
The squeezed state is a quantum state that redistributes the noise of the quadrature component without violating the Heisenberg uncertainty principle, so that the noise power of one quadrature component is below the shot noise limit and the other is above the shot noise limit [39,40].
When the OPA runs in parameter de-amplification, the quadrature amplitude squeezed state of the light field can be generated. The experimental generation principle is shown in Fig. 1. The 1342 nm and 671 nm dual-wavelength lasers are separated by a dichromatic beam splitter (DBS) and then passed through two-mode cleaners (MC1, MC2) to filter the spatial mode of the beam and additional noise [41]. The 1342 nm light is used as the seed light and phase-modulated by the EOM modulator. A standing-wave cavity is used as an OPA cavity. The M2 coated with transmission T = 10% for 1342 nm and reflectivity R > 99.9% for 671 nm is used as an output mirror, which is controlled by a piezoelectric ceramic (PZT). The input mirror M1 is coated with reflectivity R > 99.8% for 1342 nm and transmission T = 20% for 671 nm. After passing through the high-reflection mirror, the transmitter part of the output light field is received by the detector (PD) for PDH locking, while the reflected part enters the BHD to measure the quantum fluctuation noise of the quadrature component.
Fig. 1. Schematic of the experimental setup. Laser: Nd:YVO4/LiB3O5. DBS1-2: dichroic beam splitter. PBS: polarization beam splitter. PZT: piezo-electric transducer. HR1-3: high reflection mirror. HR4: mirror with reflectivity higher than 99.5% (for 1342 nm). MC1-2: mode cleaner. M1-2: cavity mirror. BS: beam splitter. OPA: optical parametric amplifier. BHD: balanced homodyne detector. PD: photoelectric detector. SA: spectrum analyzer. OSC: oscilloscope.
The squeezing degree is related to the phase jitter of the quadrature components [41–44]. That is,
Where ${V_{sqz - m^{\prime}}}$ is the actually measured variance of squeezed light noise, ${V_{sqz - in}}$ and ${V_{asqz - in}}$ are the theoretical squeezed noise and anti-squeezed noise, respectively. $\theta $ is phase jitter. The uncontrolled phase jitter will lead to the rotation of the squeezing angle, which will transform the squeezed state into the anti-squeezed state, thus reducing the degree of squeezing. Therefore, it’s necessary to improve the optical locking stability as much as possible to facilitate the preparation of highly squeezing-degree optical fields.3. Accurate Locking of Squeezed State Optical Field Generation System Using Low-noise Bootstrap Photodetector
Since the optical cavity that generates the squeezed light field uses the detector to extract the error signal to ensure stable and high-precision locking, it is necessary to reduce the electronic noise as much as possible [45,46]. The TIA is widely used to convert photodiode current to voltage because of its lower noise and higher bandwidth compared to other resistive and voltage amplifiers. However, the input voltage noise of the operational amplifier in the TIA introduces large noise at high frequencies due to input capacitance [47,48]. As is shown in subgraph (a) of Fig. 2, the noise source of TIA can be represented as [49]:
Fig. 2. The schematic of the bootstrap low noise detector. (a) The total input noise model for the TIA operational amplifier; (b) The schematic of photodiode impedance enhancement based on bootstrap feedback. (c) The complete schematic diagram of the designed detector. J1 and J2 are N-channel heterojunction field effect transistors NE3509M04. PD: photodiode.
A bootstrap-based photodiode impedance improvement technology is used to reduce high-frequency noise, thereby solving the high-frequency noise problem caused by the above-mentioned junction capacitance. The principle of this technology is shown in subgraph (b) of Fig. 2. The input voltage signal with a gain of one is sent back to the other end of the photodiode. This reduces the potential difference between the two ends of the photodiode, decreasing its equivalent input capacitance and increasing the bandwidth of the circuit.
Theoretically, the impedance is greatest when the feedback coefficient is 1, but due to the phase delay of the transistor amplifier, the first-stage bootstrap amplifier cannot achieve the theoretical unity gain. As a result, the detector still has large noise at high frequencies. Here, we use a two-stage bootstrapping amplification technique that we refer to as non-unity gain. This is accomplished by first amplification and then reduction of the signal. The second stage is used to correct for the phase delay created by the first stage while also reducing gain such that the feedback gain is as near to 1 or even 1 and the phase is as close to 0. The gain and phase are independent of frequency at the same time. The red dashed box in Fig. 2 shows the developed two-stage bootstrapping amplifier using the proposed method. The circuit gain calculation formula can be obtained from the small-signal model of the transistor multi-stage amplifier circuit, without considering the parasitic capacitance and inductance of the circuit and the gate and source capacitance of the transistor, as follows:
The complete schematic diagram of the designed detector is shown in subgraph (c) of Fig. 2, which contains a TIA and two-stage bootstrap amplifying parts. The amplifier chip LTC6268-10 is used in the TIA circuit because of its low input current noise (${\textrm{i}_\textrm{n}}\textrm{ = 7 fA/}\sqrt {\textrm{Hz}}$), low input voltage noise (${\textrm{e}_\textrm{n}}\textrm{ = 4}\textrm{.0 nV/}\sqrt {\textrm{Hz}}$), and ultra-low input parasitic capacitance (${\textrm{C}_{\textrm{in}}}\textrm{ = 0}\textrm{.45 pF}$), making it suitable for low-noise TIA photodetectors. The input impedance is further increased by incorporating bootstrap feedback technology, which lowers electrical noise and enhances the SNR of the circuit.
The bootstrap amplifier, which consists of the photodiode PD and the two-stage JFET bootstrap amplifiers J1 and J2, is the most important portion of this study. J1 and J2 are connected by capacitor C2, and R7 is used to improve the input impedance of the circuit. A crucial component of bootstrapping feedback is capacitor C1. Adjusting C1 can not only change the gain of the circuit but also compensate for phase hysteresis at high frequencies of the bootstrap amplification part and improve the bandwidth of the detector. The model of the photodiode is FD100, which has a quantum efficiency of 92% at 1342 nm and a junction capacitance of 1.1pF. NE3509M04 is chosen as the two-stage bootstrap amplifier’s JFET. In the specific experimental research, we find that NE3509M14 has the characteristic of ultra-low noise, and it is also suitable for two-stage bootstrapping circuits.
The PCB design is demanding since the input signal of the detector is extremely sensitive to parasitic capacitance. Figure 3 is the actual PCB layout, the board size is 47.63 mm * 32 mm. Under the premise of reasonable device arrangement, the signal line between the photodiode PD and the two-stage bootstrap feedback should be as short as possible to reduce the parasitic capacitance introduced by the input signal line. In the board we arranged, the length of the input signal line is 4.6 mm. To reduce the parasitic capacitance, the ground layers surrounding the JFET bootstrap amplifiers J1 and J2 as well as the LTC6268-10 are eliminated. Resistors and capacitors should choose smaller patch devices, such as 0402. The layout should prevent interference to reduce the loss in the circuit and introduce noise. Finally, the whole circuit board is shielded from outside noise with a metal shielding box.
4. Experimental results
The electronic noise of the photodetector was measured and compared without bootstrap feedback, with traditional unity gain bootstrap feedback, and with two-stage bootstrap feedback in the frequency range of 1–30 MHz to confirm the benefit of the nonunit gain bootstrap feedback (two-stage bootstrap feedback) in reducing the electronic noise. The results are shown in the curves (i, ii, iii) in Fig. 4. At an analysis frequency of 20 MHz, the electronic noise of the detector is −78.1 dBm without bootstrap feedback (i) and −80.5 dBm with traditional unity-gain bootstrap feedback (ii), which has a reduction of 2.4 dBm. The electronic noise of the detector with two-stage bootstrap feedback (iii) is −83.7 dBm, which has a reduction of 3.2 dBm from the traditional unit-gain bootstrap feedback. Obviously, the two-stage bootstrap amplification based on NE3509M04 has a better suppression effect on circuit noise.
Fig. 4. Electronic noise diagrams of different detectors (without optical power input). Resolution bandwidth: 100 kHz, Video bandwidth: 100 Hz.
The output power spectrum of the photodetector under different optical powers of the 1342 nm laser is shown in Fig. 5 (a). It can be seen that the SNR of the detector at the analysis frequency of 3 MHz is as high as 26.7 dB under saturated power injection near 800 µW, and the SNR is larger than 19 dB between the analysis frequencies of 10 MHz and 20 MHz. The detector also shows good linear responsiveness when the incident optical power range is 50–800 µW. The noise curve increases by 3 dB with the doubling of the laser power. Meanwhile, the equivalent optical signal noise spectrum of the detector is plotted, as shown in Fig. 5 (b). The equivalent optical power noise is less than 1.4 $\textrm{pW} /\sqrt {\textrm{Hz}} $ within 15 MHz and less than 2.4 $\textrm{pW} /\sqrt {\textrm{Hz}} $ within 30 MHz.
Fig. 5. (a) The spectrum of a two-stage bootstrap low-noise detector with different optical powers. (b) The equivalent optical power noise curve of a two-stage bootstrap low noise detector. Resolution bandwidth: 100 kHz. Video bandwidth: 62 Hz.
A test was performed to demonstrate the excellent characteristics of the developed detector using the experimental setup shown in Fig. 2. The result of the test is shown in Fig. 6. The OPA847/LTC6409 chip is utilized in the traditional detector, which has a conventional trans-impedance amplifier circuit. KPDE008A/G8376 is used as the photodiode with a 1A/W responsiveness [33,49]. However, the two-stage bootstrap low-noise detector has obvious advantages, its SNR is 11.8 dB higher than that of the conventional detector when the incident light intensity is 200 nW and the load-modulated signal intensity is 10 pW.
Fig. 6. The locking cavity signals with different detectors. The red curve is the lock cavity signal of the two-stage bootstrap low noise detector. The blue curve is the lock cavity signal of the detector with a traditional circuit structure. The modulation frequency: 15 MHz. Resolution bandwidth: 3 kHz. Video bandwidth: 10 Hz.
The locking stability of the detectors is shown in Fig. 7 (a) and (b). The light field output of the two-stage bootstrap low noise detector has substantially less locking power fluctuation than the traditional circuit structure detector. The root-mean-square (RMS) of power fluctuation for the traditional detector is 3%, whereas the two-stage bootstrap low noise detector is 0.8%. This shows that, under the same conditions, the two-stage bootstrap low-noise detector can achieve more stable locking due to its ability to obtain a high SNR locking signal.
Fig. 7. The locking power curves of OPA with different detectors. (a) The traditional circuit structure detector. (b) Two-stage bootstrap low-noise detector.
The two-stage bootstrap feedback enables the detector to significantly reduce the phase jitter of the quadrature component during the locking process of the OPA, which enhances the squeezing degree of the squeezed optical field. The results are shown in Fig. 8 (a) and (b). Under the same conditions, at the analysis frequency of 3 MHz, the quadrature amplitude squeezed state of light can be measured at -6.2 dB and -7.5 dB. The root mean square (RMS) of phase fluctuation is approximately equal to ${1.4^ \circ }$[43]. The squeezing degree of the light field can be significantly improved by more than 34.9%.
Fig. 8. Quantum fluctuations of the quadrature amplitude squeezed optical beams. (a) Locked by traditional circuit structure detector. (b) Locked by two-stage bootstrap low-noise detector. The analysis frequency is 3 MHz. Resolution bandwidth: 30 kHz. Video bandwidth: 30 Hz.
5. Summary
In this study, a low-noise TIA circuit is integrated with a two-stage bootstrap feedback technique to reduce noise at high frequencies and enable high precision optical locking in the frequency range of 1–30 MHz. The detector can achieve an SNR of 26.7 dB at the analysis frequency of 3 MHz with an incident power of 800 µW, and the input noise level drops to 2.4 $\textrm{pW} /\sqrt {\textrm{Hz}} $ in the frequency range of 1–30 MHz, which is a very low level to date. Additionally, the detector can be used for precise locking of the OPA cavity and has good long-term locking stability, which helps prepare high squeezing degree squeezed light fields. This method can also achieve precise locking of the optical phase, which is of great help in improving the quality of the CV entangled optical fields and the high-sensitivity detection of space gravitational waves. Finally, the method is an important basis to develop the BHD with excellent SNR for the accurate detection of squeezed and entangled light fields, which has great value in the research of CV quantum communication networks.
Funding
National Natural Science Foundation of China (11904218, 62135008, 61775127, 11947133, 12004276, 11804246); National Outstanding Youth Foundation of China (62122044); China National Funds for Distinguished Young Scientists (61925503); Program for Sanjin Scholars of Shanxi Province; Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi; Natural Science Foundation of Shanxi Province (201801D221009); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2019L0092, 2020L0029); Fund for Shanxi Key Subjects Construction, “1131” Project Key Subjects.
Disclosures
The authors have no conflicts of interest to declare.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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