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Collective bosonic excitations are a fascinating aspect of broken-symmetry correlated phases. A wealth of such phases emerged in tailored moir\'e heterostructures, where, in addition, new direct knobs of control exist. Our work explores how…
We study controllable exchange coupling between two singlet-triplet qubits. We start from the original second quantized Hamiltonian of a quadruple quantum dot system and obtain the effective spin-spin interaction between the two qubits…
DC-voltage-biased Josephson junctions have been recently employed in superconducting circuits for Hamiltonian engineering, demonstrating microwave amplification, single photon sources and entangled photon generation. Compared to more…
We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we…
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf…
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
Control over the coupling between multiple modes of a frequency comb is an important step toward measurement-based quantum computation with a continuous-variable system. We demonstrate the creation of square-ladder correlation graphs in a…
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We…
Four-wave parametric amplification can be extended to the TW/cm$^2$ regime using femtosecond pump pulses to amplify nearly octave spanning pulses with gain $> 20$~mm$^{-1}$, which we call Kerr instability amplification. Cross-polarized wave…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
This work aims to provide an alternative approach to modeling a two-state system (qubit) coupled to a nonlinear oscillator. Within a single algebraic scheme based upon the f-deformed oscillator description, hard and soft nonlinearities are…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…
This paper presents a detailed theoretical review of the amplification process in Josephson Parametric Amplifiers (JPAs), which are crucial for quantum-limited signal amplification in superconducting circuits. The paper begins by outlining…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim \epsilon^{-2}$ one component of the system is described in the main…
We present an experimentally realizable stabilized charge pumping scheme in a linear array of Cooper-pair boxes. The system design intrinsically protects the pumping mechanism from severe errors, especially current reversal and spontaneous…
Theoretical study is performed of a single-mode polariton system with linear coupling of spin components. When combined with an ordinary two-particle interaction, the spin coupling involves a spontaneous symmetry breaking accompanied by a…
We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave…
We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system…