This study significantly concentrates on cryogenic InP HEMT high-frequency circuit analysis using quantum theory to find how the transistor nonlinearity can affect the quantum correlation of the modes generated. Firstly, the total Hamiltonian of the circuit is derived, and the dynamic equation of the motion contributed is examined using the Heisenberg-Langevin equation. Using the nonlinear Hamiltonian, some components are attached to the intrinsic internal circuit of InP HEMT to address the circuit characteristics fully. The components attached are arisen due to the nonlinearity effects. As a result, the theoretical calculations show that the states generated in the circuit are mixed, and no pure state is produced. Accordingly, the modified circuit generates the two-mode squeezed thermal state, which means one can focus on calculating the Gaussian quantum discord to evaluate quantum correlation. It is also found that the nonlinearity factors (addressed as the nonlinear components in the circuit) can intensely influence the squeezed thermal state by which the quantum discord is changed. Finally, as the primary point, it is concluded that although it is possible to enhance the quantum correlation between modes by engineering the nonlinear components; however, attaining quantum discord greater than unity, entangled microwave photons, seems a challenging task since InP HEMT operates at 4.2 K.
This study significantly concentrates on cryogenic InP HEMT high-frequency circuit analysis using quantum theory to find how the transistor nonlinearity can affect the quantum correlation of the modes generated. Firstly, the total Hamiltonian of the circuit is derived, and the dynamic equation of the motion contributed is examined using the Heisenberg-Langevin equation. Using the nonlinear Hamiltonian, some components are attached to the intrinsic internal circuit of InP HEMT to address the circuit characteristics fully. The components attached are arisen due to the nonlinearity effects. As a result, the theoretical calculations show that the states generated in the circuit are mixed, and no pure state is produced. Accordingly, the modified circuit generates the two-mode squeezed thermal state, which means one can focus on calculating the Gaussian quantum discord to evaluate quantum correlation. It is also found that the nonlinearity factors (addressed as the nonlinear components in the circuit) can intensely influence the squeezed thermal state by which the quantum discord is changed. Finally, as the primary point, it is concluded that although it is possible to enhance the quantum correlation between modes by engineering the nonlinear components; however, attaining quantum discord greater than unity, entangled microwave photons, seems a challenging task since InP HEMT operates at 4.2 K.
This study focuses on generating and manipulating squeezed states with two external oscillators coupled by an InP HEMT transistor operating at cryogenic temperatures. First, the small-signal nonlinear model of the transistor at high frequency at 5 K is analyzed using quantum theory, and the related Lagrangian is theoretically derived. Subsequently, the total quantum Hamiltonian of the system is derived using Legendre transformation. The Hamiltonian of the system includes linear and nonlinear terms, by which the effects on the time evolution of the states are studied. The main result shows that the squeezed state can be generated owing to the nonlinearity of the transistor, and more importantly, it can be manipulated by some specific terms introduced in the nonlinear Hamiltonian. In fact, the nonlinearity of the transistors induces some effects such as capacitance, inductance, and second-order transconductance, by which the properties of the external oscillators are changed. These changes may lead to squeezing or manipulation of the parameters related to squeezing in the oscillators. In addition, it is theoretically derived that the circuit can generate two-mode squeezing. Finally, second-order correlation (photon counting statistics) is studied as a complementary task, and the results demonstrate that the designed circuit exhibits antibunching, where the quadrature operator shows squeezing behavior.
Abstract This study focuses on generating and manipulating squeezed states with two external oscillators coupled by an InP HEMT operating at cryogenic temperatures. First, the small-signal nonlinear model of the transistor at high frequency at 5 K is analyzed using quantum theory, and the related Lagrangian is theoretically derived. Subsequently, the total quantum Hamiltonian of the system is derived using Legendre transformation. The Hamiltonian of the system includes linear and nonlinear terms by which the effects on the time evolution of the states are studied. The main result shows that the squeezed state can be generated owing to the transistor’s nonlinearity; more importantly, it can be manipulated by some specific terms introduced in the nonlinear Hamiltonian. In fact, the nonlinearity of the transistors induces some effects, such as capacitance, inductance, and second-order transconductance, by which the properties of the external oscillators are changed. These changes may lead to squeezing or manipulating the parameters related to squeezing in the oscillators. In addition, it is theoretically derived that the circuit can generate two-mode squeezing. Finally, second-order correlation (photon counting statistics) is studied, and the results demonstrate that the designed circuit exhibits antibunching, where the quadrature operator shows squeezing behavior.
The quantum correlation between microwave modes in an RF electronic circuit is analyzed and studied. An open quantum system operating at 4.2 K is designed in which InP HEMT as the nonlinear component couples two external oscillators to each other. The quantum theory is applied to completely analyze the system, by which the related quantum Hamiltonian containing all noise sources is derived. The Lindblad Master equation is used to analyze the time evolution of the expanded closed system that covers the environmental effects. In the following, the state of the system defined is determined in terms of the ensemble average state using the density matrix; then, the ensemble average of the different operators is calculated. Accordingly, the covariance matrix of the quantum system is derived, and the quantum discord as a key quantity to determine the quantum correlation is calculated. As an interesting point, the results show that InP HEMT mixes two coupling oscillator modes so that the quantum correlation is created at different frequency productions such as 2nd, 3rd, and 5th. The harmonics suitable for sampling and digitalization is the zero-IF (downside of 2nd harmonics) band at which the quantum correlation is generated. Another point is that there is no quantum correlation at the frequency resonance of each oscillator coupled to InP HEMT.
Abstract This article mainly focuses on important quantum phenomenon called entanglement arising the nonlinearity property. This study uses a unique approach in which transistor nonlinearity effect (third-order nonlinearity) entangled microwave photons are created in a cryogenic low-noise amplifier (LNA). For entanglement analysis, the Hamiltonian of the designed cryogenic LNA (containing two coupled oscillators) is derived, and then, using the dynamic equation of motion, the oscillator’s number of photons and the phase-sensitive cross-correlation factor are calculated in the Fourier domain to calculate the entanglement metric. The oscillators are coupled to each other through the gate–drain capacitor, and nonlinear transconductance is as an important factor strongly manipulating the entanglement. As a main conclusion, the study shows that the designed circuit using transistor third-order nonlinearity has the ability to generate the entangled microwave photons at very low intrinsic transconductance and more importantly when the noise figure (NF) is strongly minimized. As a complementary task, the printed circuit board of the cryogenic LNA is designed and simulated to verify the ability of the circuit to achieve an ultralow NF, by which the probability of the generation of entangled microwave photons is increased.
In this study, we present the design and analysis of a Low Noise Amplifier tailored specifically for quantum applications. We selected the HEMT for its unique noise reduction properties, crucial for quantum engineering. The main goal is to minimize the noise figure within the C-band frequency range (4-8 GHz) to induce nonclassicality in quantum signals. While achieving a noise figure of less than 0.065 dB within this band, we recognized the trade-off with gain, mitigated by incorporating additional stages to maintain noise figure at optimal levels. Quantum analysis of the circuit, employing a simplified model of HEMT due to its complexity, revealed insights into its nonlinear properties and interactions between circuit components and environmental factors. Leveraging Qutip toolbox in Python, we conducted time-evolution analysis of the system, revealing the circuit's behavior as an open quantum system under cryogenic conditions. Our investigation extends to quantifying quantum correlation (quantum discord) and its relationship with noise figure, posing important questions regarding the direct impact of its minimization on circuit nonclassicality at cryogenic temperatures. This comprehensive study sheds light on the intricate interplay between circuit design, and its influence on the relationship between the noise figure and quantum correlation.
Abstract This study presents the design and analysis of a specialized RF/MW circuit named the Quantum Non-classicality Enhancing Circuit, specifically developed for quantum applications. The primary objective is to reduce the noise figure within the operational frequency range of 4–8 GHz to enhance non-classical properties in quantum signals. To achieve this, a HEMT was chosen due to its exceptional noise reduction capabilities, which are critical for quantum engineering. While targeting a noise figure of less than 0.065 dB within the specified frequency band, a trade-off with gain was identified. This issue was addressed by introducing additional amplification stages to stabilize the noise figure without compromising overall performance. Quantum analysis of the circuit, based on a simplified HEMT model, provided valuable insights into its nonlinear behavior and the interaction between circuit components and environmental factors. Using the QuTiP toolbox in Python, a time-evolution analysis of the system was conducted, revealing the circuit’s response as an open quantum system under cryogenic conditions. The study also explores the relationship between quantum correlation (measured by quantum discord) and the noise figure, raising significant questions about the impact of noise minimization on enhancing non-classicality at low temperatures. Alongside the quantum analysis, a detailed circuit layout was designed and optimized to minimize the noise figure. The findings from the quantum analysis demonstrated that non-classicality generation and noise minimization share a common foundation, reinforcing the design approach. This comprehensive study highlights the complex interplay between circuit design and quantum properties, offering a strategic path toward improved quantum signal processing at cryogenic temperatures.