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.
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.
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.
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.
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 recent years, quantum computers have emerged as a disruptive technology capable of solving problems currently intractable for classical systems. Computation is performed using qubits, which exploit quantum properties like superposition and entanglement, and requires them to operate at cryogenic temperatures. As a result, quantum computers are built around cryostats that reach temperatures as low as \qty{10}{\milli\kelvin}. However, to deliver a significant advantage over conventional approaches, quantum computers must increase their qubit count, improve qubit quality, and adopt more sophisticated control and readout architectures. The integration of more complex or improved cryogenic electronics inside the cryostat can enhance the scalability of these systems, and is the topic of this thesis. The primary technology platform used in this work is based on cryogenic InGaAs/InP high-electron-mobility transistors (HEMTs). One objective was the development of cryogenic circuits that enhance the scalability of spin-qubit quantum computers by enabling efficient signal delivery in control and readout paths. To this end, cryogenic multiplexers were demonstrated with threshold voltages as low as \qty{90}{\milli\volt}, subthreshold swing of \qty{5}{\milli\volt\per dec}, and on-off ratio of 107 at \qty{4}{\kelvin}. In addition, a charge-storage array was developed for the local generation of qubit bias signals, using an operation scheme based on pulse trains to program voltage levels on capacitors that can be placed in proximity to qubit gates. A second objective was the fabrication of HEMTs with enhanced performance for use in cryogenic low-noise amplifiers, which are critical for qubit readout. Studies were performed to characterize self-heating, an effect that limits transistor performance at cryogenic temperatures. Moreover HEMTs with improved characteristics were fabricated, which achieved exceptional values in state-of-the-art metrics, including fT= \qty{622}{\giga\hertz}, fMAX= \qty{733}{\giga\hertz}, and a noise indication factor IDS/gm= \qty{0.17}{\sqrt{\volt \cdot \milli\meter / \siemens}} at \qty{4}{\kelvin}. These results represent a new record for the combination of high-frequency and low-noise performance in a cryogenic HEMT. These results establish the InGaAs/InP HEMT technology as a promising platform for the development of cryogenic circuits, and demonstrate its versatility in addressing multiple applications requiring both single-device performance and integration at the circuit level.
The cryogenic indium phosphide (InP) high-electron-mobility transistor (HEMT) low-noise amplifier (LNA) is used for the readout amplification of qubits at4K where cooling capabilities are limited implying that the dc power of the active circuits is an essential design constraint. In this article, the RF and noise performance of the InP HEMT under ultralow-power (ULP) operation at4K has been characterized. The small-signal and noise parameter model of the InP HEMT was extracted down to 1μW. The tradeoff between noise performance and dc power consumption was analyzed in terms of the drain current and drain voltage. A 4–6 GHz hybrid cryogenic HEMT LNA designed for qubit readout and optimized for lowest noise below1mW dc power consumption was fabricated. The measured performance of the LNA at4K attained 23.1 dB average gain and 2.0 K average noise temperature at 200μW dc power.