Coherent Control of Population and Quantum Coherence in Superconducting Circuits

Abstract

Quantum mechanics, with its counterintuitive principles and probabilistic nature, has long been confined to the microscopic realm of atoms and photons. Yet, recent breakthroughs have pushed the boundaries of quantum behavior into the macroscopic world, where objects are visible to the naked eye and governed by classical physics. This review article traces the extraordinary progress toward achieving coherent control of population distributions among multiple quantum levels, as well as manipulation of absorption and refractive index, in such large-scale quantum systems, a feat once considered beyond reach.

Figures (15)

• Figure 1: (a) The schematic diagram of a spring-mass system. (b) Schematic illustration of an LC oscillator analogous to a mechanical mass-spring system. In this representation, the charge $q$ accumulated on the capacitor due to the current $I$ flowing through the inductor plays the role of the position coordinate, while the magnetic flux $\Phi$ through the inductor acts as the conjugate momentum. (b) Alternative description in terms of circuit flux variables, where the generalized coordinate is the node flux $\phi = \int V\,dt$, defined as the time integral of the voltage $V$ across the capacitor, and the conjugate momentum is the charge $Q$. The charge on the capacitor arises from the electrochemical potential difference between the two plates.
• Figure 2: Schematic of transmission line quantization, each infinitesimal section is modeled as an LC oscillator with distributed inductance and capacitance.
• Figure 3: Schematic representation of an open quantum system. The total system, described by the density matrix $\rho_T$, consists of a subsystem of interest (system, $\rho_S$) interacting with its surrounding environment (environment, $\rho_E$). The system environment coupling leads to an exchange of energy and information, giving rise to open-system dynamics.
• Figure 4: (a) Energy level diagram of a two-level atom with ground state $|g\rangle$ and excited state $|e\rangle$, separated by the transition frequency $\omega_{eg}$. The atom interacts with a monochromatic EM of frequency $\omega$ with Rabi frequency $G$. The detuning is defined as $\Delta = \omega - \omega_{eg}$. (b) Real part $\chi'(\omega)$ and imaginary part $\chi"(\omega)$ of the complex electric susceptibility $\chi$ as a function of detuning $\Delta$. The imaginary part represents absorption and exhibits a Lorentzian profile centered at $\Delta = 0$, while the real part represents dispersion and shows a dispersive line shape. The parameters used in the plots are: $\lambda = 780\,\text{nm}$, $\gamma = 3.81 \times 10^{7}\,\text{s}^{-1}$, $N = 10^{18}\,\text{m}^{-3}$, and $G = 0.5\,\gamma$..
• Figure 5: Circuit diagrams. (a) A single Josephson junction with Josephson energy $E_J$ and junction capacitance $C_J$. (b) A Cooper pair box consisting of a Josephson junction ($E_J, C_J$) in parallel with a shunt capacitance $C_S$.