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Abstract
A high-performance resonant balanced homodyne detector is a key element for the measurement of picosecond pulsed squeezed light, which is an important quantum resource in quantum-enhanced microscopic imaging. In this paper, we design and demonstrate a resonant photodetector for homodyne measurement with a maximum signal-to-noise ratio of 22.42 dB at resonant frequency of 20 MHz. Using this detector to pulsed regime, a maximum signal-to-noise ratio at resonant frequency is 10.02 dB, where a 40 dB subtraction capability at 80 MHz repetition rate of pulsed laser is obtained. With this design, the quantum noise of picosecond pulsed squeezed light is measured and the best squeezing level −1.7 dB below the shot noise level is clearly observed at 20 MHz.
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1. Introduction
As two important quantum resources, squeezing and entanglement play key roles in the rapidly developing fields of quantum information science [1,2], quantum precision measurement [3] and quantum imaging technology [4]. For example, a gate sequence based on a six-mode entangled state for continuous-variable one-way quantum computation [5], multipartite entanglement swapping [6] and orbital angular momentum multiplexed quantum teleportation [7] for constructing quantum networks, have been demonstrated experimentally. Besides, squeezed states of light provide a way to increase the sensitivity by reducing the quantum noise in gravitational wave observatories [8,9]. Moreover, because of the high peak power and particular pulsing shape, the pulsed squeezing and entanglement have attracted more attention [10–12]. The prepared ultrashort pulsed squeezed light is confirmed to realize quantum-enhanced microscopic imaging [13,14] by improving signal-to-noise ratio (SNR).
In the experiment of preparing squeezed and entangled states [15–17], a high-performance detector is required besides a high-quality squeezer [18–23]. Since a balanced homodyne detector proposed by Yuen et al. [18], it becomes one of main methods for measuring the amplitude/phase quadrature variances of squeezed states [11,24]. The balanced homodyne detector is preferred to measure the weak signal beam since the interference with a local oscillator (LO) boost the shot-noise of the signal beam above the electronic noise of the detector, where both the quantum and excess noises of the LO can be eliminated by coherent subtraction of the two outputs of a 50:50 beam splitter [18]. The three main criteria of balanced homodyne detector are SNR not less than 10 dB, the common mode rejection ratio more than 30 dB and high bandwidth [25]. So far, a maximum common mode rejection ratio of 75.2 dB [21] and a bandwidth up to GHz [25,26] are obtained.
However, a resonant detection, which has a high transimpedance gain at the resonant frequency and filters the undesired frequency component, is an alternative approach in the measurement of squeezed states [14,27–30]. For instance, a high-power, low-noise and multiply resonant photodetector has been used to gravitational wave detection [28]. Recently, Casacio et al. have experimentally reported that quantum correlations allow a SNR beyond the photodamage limit of conventional microscopy by using a 20 MHz resonant detector [14]. In addition, a tunable resonant detector over a frequency range of more than 100 MHz [30] and a resonant balanced homodyne detector at 500 MHz [29] are designed respectively.
In this paper, we develop a 20 MHz resonant balanced homodyne detector by combining the advantages of resonant and homodyne detections. Firstly, by choosing a pair photodiodes with near-identical dark current, capacitance and quantum efficiency, we obtain a resonant balanced homodyne detector that the quantum noise is approximately linear relationship with power of LO and a maximum SNR at resonant frequency is 22.42 dB. Then, when a pulsed LO is seeded, a maximum SNR is up to 10.02 dB, where a 40 dB subtraction capability at 80 MHz repetition rate of the pulsed laser is obtained. Finally, by utilizing a second-order nonlinear periodically poled potassium titanyl phosphate (PPKTP) crystal, we successfully detect the noise power of picosecond pulsed squeezed light with −1.7 dB squeezing, which provides a quantum resource for future quantum-enhanced microscopic imaging with a small number of photons.
2. Design and construction
Figure 1 shows the electronic circuit schematic of the resonant balanced homodyne detector, where a pair of similar performance photodiodes are installed by replacing the single photodiode in Ref. [14]. There are three steps to amplify the photocurrent subtraction signal, which flows out from the series node (a) of the pair of photodiodes. Firstly, the subtracted photocurrent is converted into a voltage signal and amplified by a transimpedance amplification, which reduces the input impedance and improves SNR [29]. Secondly, the DC photocurrent is separated from the AC branch by filter circuit. AC signal is used to measure the noise power connected to spectrum analyzer (SA), and DC branch connected to a digital oscilloscope (OSC) provides a monitor signal for laser beam alignment and the relative phase between the LO and signal. Finally, in order to amplify the separated signals, a second amplification is designed. Low-noise operational amplifiers (OA) LMH6624 (Texas Instruments) and OP27 are used to amplify AC and DC signals, respectively.
Then, we discuss the detailed circuit construction. The transimpedance amplifier (TIA) circuit, composed of OA (OPA690 with input capacitance 2.9 pF in typical, TI Company) and feedback network (consisting of $L_{\text {1}}$, $R_{\text {1}}$, $C_{\text {1}}$ and $R_{\text {2}}$), is used to convert the input current into a voltage signal. Compared with a bipolar junction transistor (BJT) OA, low input noise could be achieved by connecting in series a junction field-effect transistor (JFET) buffer into the inverting input part of BJT. In the design, a BF862 with high input impedance, low input voltage noise density (0.8 nV/$\sqrt {\text {Hz}}$) at 100 kHz and input capacitance 10 pF in typical at 1 MHz is chosen as the JFET buffer running at unity gain [31,32].
The resonant structure consists of parallel inductance $L_{\text {1}}$ and a feedback capacitance $C_{\text {1}}$. The resonance frequency is expressed as
The bandwidth (cut-off frequency) around $f_{\text {res}}$ is given by
Based on the Eqs. (1) and (2), we can see that the resonance frequency and the bandwidth are determined by choosing the parallel inductance $L_{\text {1}}$, resistance $R_{\text {1}}$ and the capacitance $C_{\text {1}}$. In our design, by setting $L_{\text {1}}=4.70\,\mu$H, $R_{\text {1}}=50\,\Omega$ and $C_{\text {1}}=12.25$ pF, we calculate $f_{\text {res}}=20.97$ MHz and $\Delta f=2.30$ MHz, respectively. Thus, the resonance frequency and the bandwidth are chosen according the requirement by adjusting the parameters of L-C resonant circuit.The SNR of feedback TIA is calculated as [29]
In addition, in the circuit schematic (Fig. 1), an inductance $L_{\text {2}}$ and a capacitance $C_{\text {3}}$ are connected in series to form a frequency selection circuit. After that, only the signal at resonance frequency is passed through, and the desired stable frequency is further formed. Finally, in order to limit signal loss at the detector output, a 50 $\Omega$ resistance is used for impedance matching.
For protecting the internal transmission signal from disturbance and minimizing the parasitic capacitance and inductance, three main efforts are done in the design of printed circuit board (PCB). At first, the tracks on the PCB are kept as short as possible. Second, a bi-layer board is designed, where electronic components and signal lines are on one layer, and power lines and ground lines are on the other layer. Final, to ensure a maximally balance of the detector with two photodiodes, the layout of the two photodiodes are required as symmetrical as possible. Eventually, a metal box with electromagnetic shielding function is used to fix the whole PCB for avoiding any environmental noise.
3. Experimental descriptions and results
Based on the design of the detector, a resonant balanced homodyne detector is built by picking the electronic components meticulously. The experimental setup is shown in Fig. 2. Our LO is seeded into a 50:50 beam splitter, and then are focused into two photodiodes with two lens. To optimize the balance of the homodyne detector, three steps are necessary. The first step is to rotate accurately the angle of the beam splitter so that the splitting ratio is 50:50, compensating the possible differences caused by electronic components and quantum efficiencies. The second setp is to equalize the path lengths of the two beams entering the photodiodes. The final step is to optimize the position of the lens in order to equalize the responses of photodiodes. After that, the DC output is connected with a OSC to verify the balance of homodyne detector, and the AC output is connected with a SA to measure the noise power.
Fig. 2. Experimental set-up for measuring performance of the detector. The performance of the detector is characterized when LO is seeded. Then, the quantum noise of pulsed squeezing is measured by seeding the pulsed squeezed light and LO simultaneously. LO, local oscillator; PZT, piezoelectric transducer; BS, 50:50 beam splitter; $\text {L}_{\text {1}}$ and $\text {L}_{\text {2}}$, lens 1 and lens 2; DC, direct current; AC, alternating current; OSC, digital oscilloscope; SA, spectrum analyzer.
3.1 Results with continuous wave local oscillator
We firstly characterize performances of the resonant balanced homodyne detector in continuous regime, where LO is generated by semiconductor laser with a center wavelength of 852 nm and maximum output power of 900 mW (TA Pro). Two photodiodes S5971 produced by Hamamatsu with high quantum efficiency of 88% at 852 nm are used in the detector. When the reverse voltage of photodiodes 5 V is supplied, the terminal capacitance and dark current of photodiodes are 4 pF and 36 pA, respectively.
The SNR of the resonant balanced homodyne detector at a SA is shown in Fig. 3. The black curve is internal noise of SA. The blue and red curves are the electronic noise and shot noise, respectively. When the LO power is 128 mW, the resonant frequency appears around 18 MHz and the bandwidth is about 3.1 MHz, which are different from the theoretical results. This is because the value of actual capacitance $C_{\text {1}}$ is unequal to the value calculated by Eqs. (1) and (2), which is caused by two possible reasons. One is the influence of parasitic capacitance of the PCB pattern. And the other is that the actual capacitance $C_{\text {1}}$ increases with the increase of LO power. The inset of Fig. 3 shows the dependence of noise variance on the LO power at a bi-logarithmic scale. With the increase of LO power doubly, a SNR about 3 dB at 20 MHz is increased. The experimental data confirms that linearity agrees with the expected manifestation of quantum vacuum variance as Gaussian-distributed white noise. When the total LO power is up to 128 mW, the maximum SNR of 22.42 dB is obtained at resonant frequency of 20 MHz.
Fig. 3. Performances of the resonant balanced homodyne detector in the continuous regime. Black curve: internal noise of SA; Blue curve: electronic noise; Red curves: shot noise with total LO power of 128 mW. The dependence of noise variance on different LO powers is shown in inset. The black dashed line is electronic noise variance. The red dots correspond to raw noise variance, which is measured directly in the experiment. The blue squares represent noise variance when the electronic noise variance is subtracted.
3.2 Results with pulsed local oscillator
In order to measure the noise power spectrum of a pulsed squeezed light at 20 MHz Raman modulation frequency, we also characterize performances of the resonant balanced homodyne detector in pulsed regime, in which the LO is generated by a tunable two-color picosecond laser with a pulse width of 2 ps and a repetition rate of 80 MHz (picoEmerald). The central wavelength and maximum peak power are 1031 nm and 25 kW, respectively. Different from photodiodes in continuous regime, two InGaAs photodiodes (FD100) with 95% quantum efficiencies at 1031 nm are chosen. The terminal capacitance and dark current of photodiodes at 5 V reverse voltage are 1.1 pF and 0.5 nA in typical, respectively.
The noise power and noise variance in pulsed regime are shown in Fig. 4. The measured results are similar to that in continuous regime. Limited by high noise power of 80 MHz repetition rate, a maximum SNR 10.02 dB is obtained with mean LO power of 3 mW at 20 MHz. In order to decrease the influence of 80 MHz repetition rate on pulsed squeezing, the undesired 80 MHz repetition rate should be minimized. As shown in Fig. 5, black curve is the electronic noise spectrum of the resonant balanced homodyne detector without any injected light. Blue curve shows the noise spectrum of the unbalanced resonant detector, when one photodiode is blocked and the other is illuminated at the power of 0.25 mW. At this low power, the unbalanced detector reaches saturation, because the noise power is near −32 dBm at 80 MHz. When two photodiodes are illuminated simultaneously at the equal power of 0.25 mW, the noise power of 80 MHz is reduced to −72.5 dBm (red curve). Comparing the red curve in Fig. 4 with the blue curve in Fig. 5, the maximum SNR and saturated power of resonant balanced homodyne detector surpass that of unbalanced resonant detector.
Fig. 5. The typical results of the balancing process. Black curve: the electronic noise power (two photodiodes blocked); Blue curve: the noise power of the unbalanced detector (one photodiode blocked, one photodiode illuminated); Red curve: the noise power of the balanced detector with total LO power of 0.5 mW (two photodiodes illuminated).
4. Application
We have characterized the performances of the resonant balanced homodyne detector with SNR 10.02 dB at 20 MHz resonant frequency, where the effect of noise power at 80 MHz repetition rate is reduced. Given this practical resonant balanced homodyne detector, we measure the noise power spectrum of pulsed squeezed light. In the experiment, the prepared pulsed squeezed light and the pulsed LO light are interfered on 50:50 beam splitter, and then they are detected with our photodetector. The resolution bandwidth and video bandwidth of SA are set to 300 kHz and 300 Hz, respectively.
In Fig. 6, red curve is the normalized noise powers of pulsed squeezed vacuum states obtained experimentally, when the relative phase between the signal and LO is scanned to show both squeezing and anti-squeezing. Black curve is the shot-noise level (SNL), which is obtained by blocking the signal light. The measured squeezing and anti-squeezing levels are −1.7 dB below the SNL and 3.4 dB above the SNL with a fixed radio frequency of 20 MHz.
Fig. 6. The normalized noise power of the pulsed squeezed state with pump power of 200 mW. Black curve is shot noise level with total LO power 3 mW. Red curve is relative noise power when the relative phase between signal and LO is scanned. The squeezing of −1.7 dB and anti-squeezing of 3.4 dB are observed. The results are analyzed by SA directly at a sideband frequency of 20 MHz.
5. Discussion and conclusion
In conclusion, by combining the advantages of balanced and resonant detection, we develop a resonant balanced homodyne detector at a resonant frequency of 20 MHz. The design not only detects a quantum noise of weak signal beam, but also filters the effect of undesired frequency component by using resonant feedback construction. In addition, by adjusting the parameters of electric components, the resonant frequency and bandwidth are changed conveniently according to custom’s requirements. In this paper, maximum shot noises of about 22.42 dB and 10.02 dB are obtained under continuous wave and pulsed LO, respectively. Compared with the unbalanced resonant detector, a 40 dB subtraction capability at 80 MHz repetition rate of the pulsed laser is obtained in a resonant balanced homodyne detector. The results present that the performances of the resonant balanced homodyne detector meet the normal criteria. As a demonstration, we measure squeezing and anti-squeezing of pulsed squeezed vacuum states obtained experimentally by scanning the relative phase between the signal and LO. A pulsed squeezed vacuum state with −1.7 dB squeezing and 3.4 dB anti-squeezing is obtained at a resonant frequency of 20 MHz.
Funding
National Natural Science Foundation of China (11974227, 61905135); Applied Basic Research Project of Shanxi Province, China (20210302122002); Shanxi Scholarship Council of China (2021-03).
Disclosures
The authors declare no conflicts of interest.
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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