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Acta Physica Sinica

Squeezing angle locking of entangled microwave based on photon counting

Tianli Wei, De-Wei Wu, Chunyan Yang, Junwen Luo, Xiang Li, Haonan Zhu

Published Jan 1, 2019• 1 citation
Publisher

Abstract

Quantum entanglement possesses important applications in quantum computation, quantum communication, and quantum precision measurement. It is also an important method to improve the performance of quantum radar and quantum radio navigation. However, the penetration of light wave is poor due to the high frequency, which leads to detecting limitations in bad weather. In this context, quantum entanglement in the microwave domain has been extensively studied, and it is hopeful to overcome the above-mentioned defects in quantum optics. Although the entangled microwave preparation of continuous variable is achievable at present, there exist still some problems such as poor entanglement performance, low entanglement efficiency, complex signal processing and control, which restrict the development of entangled microwave sources. In order to improve the entanglement performance in microwave domain, a squeezing-angle locking scheme based on single photon counting is proposed. First, two Josephson parametric amplifiers (JPAs) are driven respectively by two pump signals to generate two single-mode squeezed states which are uncorrelated to each other. Next, the squeezing angle difference between the two single-mode squeezed states is adjusted to 180°, and then the two signals are mixed in a superconducting 180° hybrid ring coupler for two entangled microwave outputs. The outputs are single photon detected, and the results are sent to the data processor for solution. The squeezing angle difference between the input single-mode squeezed microwaves is estimated by Bayesian criterion and compared with the target value to calculate the error. Finally, the squeezing angle correction information is fed back into the JPA pump to control the squeezing angle of the single-mode squeezed microwave of the JPA output as well as the relative squeezing angle to reach the target value. Thus, the dual-path entangled microwave with the optimal entanglement performance is output. Comparing with the existing entangled microwave preparation schemes, a single photon counter is utilized in the scheme of this paper, which leads to a detection efficiency of 90%. In addition, the Bayesian criterion is used to estimate the output result, and the theoretical precision reaches the quantum Cramer-Rao lower bound. Meanwhile, the introduced noise level and operation difficulty are reduced, which greatly improves the property of dual-path entangled microwave preparation.

DOI
10.7498/aps.68.20182077

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Quantum entanglement possesses important applications in quantum computation, quantum communication, and quantum precision measurement. It is also an important method to improve the performance of quantum radar and quantum radio navigation. However, the penetration of light wave is poor due to the high frequency, which leads to detecting limitations in bad weather. In this context, quantum entanglement in the microwave domain has been extensively studied, and it is hopeful to overcome the above-mentioned defects in quantum optics. Although the entangled microwave preparation of continuous variable is achievable at present, there exist still some problems such as poor entanglement performance, low entanglement efficiency, complex signal processing and control, which restrict the development of entangled microwave sources. In order to improve the entanglement performance in microwave domain, a squeezing-angle locking scheme based on single photon counting is proposed. First, two Josephson parametric amplifiers (JPAs) are driven respectively by two pump signals to generate two single-mode squeezed states which are uncorrelated to each other. Next, the squeezing angle difference between the two single-mode squeezed states is adjusted to 180°, and then the two signals are mixed in a superconducting 180° hybrid ring coupler for two entangled microwave outputs. The outputs are single photon detected, and the results are sent to the data processor for solution. The squeezing angle difference between the input single-mode squeezed microwaves is estimated by Bayesian criterion and compared with the target value to calculate the error. Finally, the squeezing angle correction information is fed back into the JPA pump to control the squeezing angle of the single-mode squeezed microwave of the JPA output as well as the relative squeezing angle to reach the target value. Thus, the dual-path entangled microwave with the optimal entanglement performance is output. Comparing with the existing entangled microwave preparation schemes, a single photon counter is utilized in the scheme of this paper, which leads to a detection efficiency of 90%. In addition, the Bayesian criterion is used to estimate the output result, and the theoretical precision reaches the quantum Cramer-Rao lower bound. Meanwhile, the introduced noise level and operation difficulty are reduced, which greatly improves the property of dual-path entangled microwave preparation.
The entangled state of continuous variables of microwave frequency is an important resource in the field of quantum. In order to apply it to quantum communication protocol and quantum radar, the entanglement between two spatially separated subsystems, namely dual-path entangled quantum microwave is needed. However, for the circuit that generates the entangled quantum microwave, there is no suitable method to indicate whether the quality of the entangled microwave signal is good or not. Aiming at this problem, we put forward a method of evaluating the quality of dual-path entangled quantum microwave signals generated based on von Neumann entropy. The origin of the entangled quantum microwave is that vacuum state signals are transformed into squeezed state signals in driven pump, so in this paper we use a two-mode squeezed vacuum state to describe the formation of dual-path entangled quantum microwave signal, thus providing the function relation between the photon number and the squeezed parameter. In a communication system, the signal-noise ratio is usually used to express the reliability of system. Entropy is a measure of disorder degree in information. If both of them can be made the analogy, the entropy is used to evaluate the proportion of entangled state signals, the quality of original signals will be evaluated and the relationship among the entropy and squeezed parameter and the photon number will be analyzed. The simulation results show that the photon number in the entangled quantum microwave signal is determined by the squeezed parameter, and there is an index change with the square rule between them. Entropy decreases with the increase of squeezed parameter: its minimum value is 0, and its maximum value can be found from 0.9 to 1. The slope of curve is steep near the maximum, which reflects that the influence of squeezed parameter on the degree of entanglement is obvious, and that the range of optimal value choices in squeezed parameter is very narrow. The optimal value of squeezed parameter is dependent on photon number; it increases with the increase of the photon number. Entropy tends to decrease smoothly with the increase of squeezed parameter and it approximately has a negative exponent relation. The photon number in an actual signal is limited, so the limit value of entropy is estimated to be about 65%. The research shows that the quality of the entangled microwave signal can be improved by choosing appropriate squeezed parameter in different circuits that generate dual-path entangled quantum microwave signals for meeting the actual needs. Therefore, the research can provide the method of choosing the parameters of dual-path entangled quantum microwave circuit and improve the availability of system.
In recent years, the great progress of studying the quantum entanglement has been made. In the field of optics, the great success has been achieved in quantum entanglement theory and technology. Then researchers concentrate on the microwave frequency band whose frequency is lower than that of optical frequency band. The signal in the microwave frequency band has a longer wavelength, and it has the diffraction capability that the optical signal does not possess. Furthermore, it can spread further in complex environments. Now it is possible to experimentally produce squeezed state of microwave signals and spatially separated path-entangled microwave signals. It is an important issue to judge whether the microwave signals received through dual paths are in entanglement state. In this paper, we firstly introduce the method of using squeezed state of microwave and microwave beam splitter to prepare path-entangled microwave signals. Then we use entanglement witness method to detect entanglement. Through constructing the entanglement witness operator in path-entangled microwave signals, the entanglement of path-entangled microwave signals can be effectively detected. We decompose the expression of the continuous variables path-entangled microwave signals into a large number of 2 2 entangled superposition states, deduce an entangled witness operator of path-entangled microwave signals based on the principle of partial transpose criterion and entanglement witnessing, and prove that the entangled witness can be used to detect the path-entangled microwave signals. Finally, we propose a physical verification of path-entangled microwave signal entanglement. The verification can be realized as follows:firstly, we reverse the phase of a received quantum-state microwave signal by utilizing continuous variable controlled phase gate in a range of 0-, then we send two microwave signals into the two input ports of the microwave beam splitter, and we operate coincidence counting of microwave photons on the two output ports after entanglement microwave signals have passed through the microwave splitter. By analyzing the results of the whole process, we have the following conclusions:if the coincidence rate of two input signals is higher than that of non-entangled microwave signals under the same power, signals can be counted as entanglement. The proposed method can detect the entangled microwave signals more efficiently than the conventional methods, such as quantum state reconstruction, and thus reduce the detection and computational complexity. The entanglement of the two microwave quantum state signals can be observed directly by using this method. This paper provides a new idea for detecting the path-entangled microwave signals.
Abstract Entanglement has attracted great attention in the past few decades due to its potential applications in the field of quantum information protocols. From now, achieving excellent phase locking in entanglement generation is significant yet a challenging task in cryogenic quantum technology. In this work, we propose and demonstrate a comprehensive paradigm of phase locking protocol for quadrature entanglement at the microwave wavelengths. We carry out a theoretical derivation of the quadrature entangled microwaves generated based on Josephson parametric amplifiers (JPAs), and the phase locking error signal, which is used to lock the relative phase of zero between the two quadrature squeezed microwaves. Simulating data for the phase locking scheme are shown under different parameter settings for comparison. Finally, we use the proposed phase locking scheme to enable a stable output of quadrature entangled microwave.
The creation of high-quality cluster states in superconducting microwave circuits is a relevant ingredient in continuous-variable quantum computing. Although large-scale cluster states have been established in optical systems, dissipation prevents their direct applicability to the microwave realm. Recent improvements in superconducting parametric circuits, in particular Josephson parametric amplifiers (JPA) and traveling wave parametric amplifiers (TWPA), have permitted substantial progress in producing entangled states using microwave photons. In this paper, we examine experimentally and theoretically the effects of numerous parametric pump tones on the degree of two-mode squeezing in a quantum circuit and apply it to the JPA. We find that additional pumps diminish the initial two-mode correlations achieved with a single pump by redistributing it among a larger network of modes and by introducing entanglement with additional idler frequencies. Taking into account the actual heterodyne measurement conditions, the experimental results are consistent with theoretical expectations.
Detection of low-reflectivity objects can be improved by the so-called Quantum Illumination (QI) procedure. However, quantum detection error probability exponentially decays with the source bandwidth. The Josephson Parametric Amplifiers (JPAs) technology utilized as a source, generating pairs of entangled signals called two-mode squeezed vacuum states, shows a very narrow bandwidth limiting the operation of the Microwave Quantum Illumination (MQI) systems. In this paper, for the first time, a microwave quantum radar setup based on quantum illumination protocol and using a Josephson Traveling Wave Parametric Amplifier (JTWPA) is proposed. We experimentally demonstrate the generation and control of three-wave mixing modes produced by a JTWPA, key enabler radiation source for MQI schemes. Measurement results of the developed JTWPA, pumped at 12 GHz, show the capability to generate entangled modes in the X-band, making our MQI system a promising candidate for the detection of stealth objects.
A scheme of parametrically enhanced cavity electro-opto-mechanical converter is proposed in this paper, which utilizes Josephson parametric amplifier and optical parametric amplifier. Basic principles of typical cavity electro-opto-mechanical converter and parametrically enhanced version are introduced briefly. We have probed the squeezing and microwave-optical entanglement performance of the scheme with one or both of the amplifiers. The Wigner distribution of the optical output is obtained to analyze the squeezing effect. Meanwhile, quadrature variances and time domain waveforms of output signals are compared and discussed. The results show that microwave-optical entanglement has been enhanced via nonlinear parametric effects no matter when there is one or two amplifiers. However, single mode squeezing only occurs in the cavity which the amplifier is placed in, and this squeezing effect would not transmit to another cavity which hasn’t been amplified. When both amplifiers are introduced simultaneously, each output of cavity electro-opto-mechanical converter is squeezed independently. Our research provides another way to prepare squeezed microwave or optical signal and proves that microwave-optical entanglement can be well enhanced by introducing parametric amplifiers.