Enhancing quantum correlation at zero-IF band by confining the thermally excited photons: InP hemt circuitry effect

Abstract

The microwave quantum correlation as a crucial issue in quantum technology 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. The quantum theory is applied to analyze the system completely. 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, especially the zero-IF band. Nonetheless, the main point is that one can strongly manipulate the quantum correlation in the zero-IF using circuitry engineering. It is established by increasing the operational frequencies in the quantum system leading to dramatically limiting the thermal noise since the zero-IF band remains unchanged.

Appendix 1 The constants related to the Eq. (1) of the main article is defined as:

$$ \begin{gathered} \gamma_{{q_{1} q_{2} }} = \frac{1}{{4\sqrt {Z_{1} Z_{2} } }}\left\{ {\frac{{C_{B} C_{C} C_{A} - C_{C}^{3} }}{{C_{M}^{4} }}} \right\},\,\,\,\gamma_{{q_{1} \varphi_{2} }} = \sqrt {\frac{{Z_{2} }}{{Z_{1} }}} \left\{ {\frac{{3C_{B} C_{C}^{2} g_{m} - 2g_{m} C_{B}^{2} C_{A} }}{{2C_{M}^{4} }}} \right\},\,\,\,\,\gamma_{{\varphi_{1} }} = \overline{{I_{gs}^{2} }} \sqrt {\frac{{Z_{1} }}{2\hbar }} ,\gamma_{{q_{2} \varphi_{2} }} = \left\{ {\frac{{C_{C}^{3} g_{m} + C_{B} C_{C} C_{A^{\prime}} g_{m} - C_{B} C_{C} g_{m} C_{A} }}{{2C_{M}^{4} }}} \right\},\, \hfill \\ \gamma_{{q_{1} }} = \left\{ {\frac{{C_{B}^{2} C_{in} C_{A} V_{RF} - C_{C}^{2} C_{in} C_{B} V_{RF} }}{{C_{M}^{4} }}} \right\}\sqrt {\frac{1}{{2Z_{1} \hbar }}} ,\gamma_{{\varphi_{2} }} = \left\{ {\frac{{g_{m} C_{C}^{2} C_{in} C_{B} V_{RF} - g_{m} C_{B}^{2} C_{in} C_{A} V_{RF} }}{{C_{M}^{4} }} - \overline{{I_{ds}^{2} }} } \right\}\sqrt {\frac{{Z_{2} }}{2\hbar }} ,\, \hfill \\ \gamma_{{q_{2} }} = \left\{ {\frac{{0.5C_{B} C_{C} C_{in} C_{A^{\prime}} V_{RF} + C_{B} C_{C} C_{in} C_{A} V_{RF} - C_{C}^{3} C_{in} V_{RF} }}{{C_{M}^{4} }}} \right\}\sqrt {\frac{1}{{2Z_{2} \hbar }}} ,\gamma_{{q_{1} q_{1} \varphi_{2} }} = \frac{{g_{N2} }}{{C_{M}^{4} }}C_{B}^{2} \sqrt {\frac{{\hbar Z_{2} }}{2}} \frac{1}{{2Z_{1} }},\,\,\gamma_{{q_{2} q_{2} \varphi_{2} }} = \frac{{g_{N2} }}{{C_{M}^{4} }}C_{c}^{2} \sqrt {\frac{{\hbar Z_{2} }}{2}} \frac{1}{{2Z_{2} }}, \hfill \\ \gamma_{{q_{2} \varphi_{2} \varphi_{2} }} = - \frac{{g_{N2} }}{{C_{M}^{4} }}2g_{m} C_{B} C_{c} \sqrt {\frac{\hbar }{{2Z_{2} }}} \frac{{Z_{2} }}{2},\gamma_{{q_{1} \varphi_{2} \varphi_{2} }} = \frac{{g_{N2} }}{{C_{M}^{4} }}2g_{m} C_{B}^{2} \sqrt {\frac{\hbar }{{2Z_{1} }}} \frac{{Z_{2} }}{2},\,\,\,\gamma_{{\varphi_{2} \varphi_{2} \varphi_{2} }} = \frac{{g_{N2} }}{{C_{M}^{4} }}g_{m}^{2} C_{B}^{2} \sqrt {\frac{{\hbar Z_{2} }}{2}} \frac{1}{{2Z_{2} }},,\gamma_{{q_{1} \varphi_{1} \varphi_{2} }} = \frac{{g_{N2} }}{{C_{M}^{4} }}2g_{m} C_{B} C_{c} \sqrt {\frac{\hbar }{{2Z_{1} }}} \frac{{\sqrt {Z_{1} Z_{2} } }}{2} \hfill \\ \end{gathered} $$

(4)

where g_N2 = g_m2 + 6g_m3[∂φ₁/∂t]_DC, C_M² = C_B(C_A + C_N)-C_c², Z₁ = √( L₁/C_q1), Z₂ = √( L_2’/C_q2), C_C = C_gd, C_B = C₂ + C_gd, C_A = C_in + C₁ + C_gs + C_gd, C_A’ = C_A + C_N, C_N = g_m2[φ₂]_DC + 6g_m3[φ₂]_DC*[∂φ₁/∂t]_DC, Ī_gs² = I_g²-I_j², Ī_ds² = i_ds² + I_d² + I_j². The thermally generated noises by the resistors and the current source are defined as Ī_g² = 4K_BT/R_g, Ī_d² = 4K_BT/R_d, Ī_j² = 4K_BT/R_j, i_ds² = 4K_BTγg_m, and Ī_i² = 4K_BT/R_i, where K_B, T, and γ respectively are the Boltzmann constant and operational temperature (Salmanogli 2023). C₁ and C₂ are the total capacitors generated due to the external oscillators coupling to the InP HEMT. The full information about the details of the circuit and the contributed constants can be found in Salmanogli (2023). For a clear and intuitive view about the quantities and their relations, a figure is directly taken from Salmanogli (2023), and presented in this section. Figure 

Fig. 7

Complete system model; L_C1 coupling to L_C2 through InP HEMT Transistor operating at 5 K (Salmanogli 2023)

7.