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.
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.
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.
This thesis presents the experimental achievements of (1) generating entangled-microwave fields propagating on two physically separate transmission lines and (2) verifying the entangled states with efficient measurements. Shared entanglement between two parties is an essential resource for quantum information processing and quantum communication protocols. Experimentally, entangled pairs of electromagnetic fields can be realized by distributing a squeezed vacuum over two separated modes. As a result, entanglement is revealed by the strong cross-correlations between specific quadratures of the two modes. Although it is possible to verify the presence of entanglement with low-efficiency quadrature measurements, higher detection efficiencies are desired for performing protocols that exploit entanglement with high fidelity.\nIn the microwave regime, Josephson parametric amplifiers (JPAs) fulfill the two major tasks mentioned above: JPAs prepare the required squeezed states to generate entanglement and enable us to perform efficient quadrature measurements. Therefore, for the purposes of entanglement generation and verification, ultralow-noise--frequency-tunable JPAs have been developed. Additionally, to increase the efficiency of entanglement generation, we integrate JPAs with two on-chip microwave passive components, a directional coupler and a quadrature hybrid, to form an entangler circuit. The two-mode entangled states are created at the two output modes of the entangler and are measured with a two-channel measurement apparatus where each of the two channels incorporates a JPA as a single-quadrature preamplifier. By employing this measurement scheme, the two measured quadratures of the two output modes can be chosen independently of each other, enabling a full characterization of the two-mode state. To definitively demonstrate the two-mode entanglement, I prove that the measured quadrature variances satisfy the inseparability criterion.
Quantum illumination has been suggested as a way to improve the sensitivity of remote target detection by taking advantage of quantum entanglement between a traveling electromagnetic beam of light interrogating the target, and a second beam kept in the lab. In the microwave domain, superconducting quantum circuit utilizing superconducting Josephson tunnel junctions can be used as quantum-limited amplifiers of faint microwave signals, as well as bright sources of quantum entangled signals. These Josephson parametric amplifiers (JPAs) are poised to become fundamental building block in a future quantum illumination radar operating in the microwave domain. Demonstrating a practical advantage of quantum illumination with ambient temperature signals is, however, challenging. Indeed, current quantum protocols are not practical as they require a complex receiver with stringent phase-matching conditions, which cannot be met in the field. Notably, it is also not currently known how one can transfer faint microwave signals out of cryogenic systems without destroying their fragile entanglement. In this article, we discuss the recent progress and challenges regarding the development of an all-microwave quantum illumination radar using the recently developed and implemented quantum-enhanced noise radar protocol. This quantum illumination protocol is simpler to implement and procures a quantum enhancement over its classical analog. Finally, we discuss different strategies that may resolve the issue of transmitting microwave entanglement under ambient conditions. We, thus, conclude that successful transmission of entangled microwaves can be done in the near future, with possible demonstrations of practical quantum advantage over short distances.
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.
Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.
We propose and demonstrate a scheme to stably generate quadrature-entangled optical pulses using a ring interferometer composed of an optical parametric amplifier and a dispersive media. The entangled light pulses at telecommunication wavelength are generated by combining two squeezed beams. In our scheme, the relative phase between the two beams is kept stable by the ring interferometer and is controllable using dispersive media. The amplitude and phase quadratures of the entangled beams are measured using two time-domain pulsed homodyne detectors. When the relative phase is fixed at $\ensuremath{\pi}/2$, we verify the inseparability of the states by a sufficient criterion $⟨{\ensuremath{\Delta}}^{2}[{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{a}({\ensuremath{\phi}}_{0})+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{b}(\ensuremath{\pi}\ensuremath{-}{\ensuremath{\phi}}_{0})]⟩+⟨{\ensuremath{\Delta}}^{2}[{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{a}({\ensuremath{\phi}}_{0}^{\ensuremath{'}})\ensuremath{-}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}_{b}(\ensuremath{-}{\ensuremath{\phi}}_{0}^{\ensuremath{'}})]⟩=0.64<1$ where ${\ensuremath{\phi}}_{0}^{\ensuremath{'}}\ensuremath{-}{\ensuremath{\phi}}_{0}=\ensuremath{\pi}/2$.