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The concept of weak invariant is introduced. Then, the weak invariants associated with time-dependent quantum dissipative systems are discussed in the context of master equations of the Lindblad type. In particular, with the help of the…
We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been…
In periodically-driven quantum systems, resonances can induce exotic nonequilibrium behavior and new phases of matter without static analog. We report on the emergence of fractional and integer resonances in a broad class of many-body…
Multi-component quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum…
Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
Hybrid quantum systems combine the unique advantages of different physical platforms with the goal of realizing more powerful and practical quantum information processing devices. Mechanical systems, such as bulk acoustic wave resonators,…
We prove the existence of a Lie algebra of first integrals for time dependent Hamiltonian systems of Lie type. Moreover, applying the Floquet theory for periodic Euler systems on Lie algebras, we show the existence of an abelian Lie algebra…
Being able to reliably transfer the quantum state from one system to another is crucial to developing quantum networks. A standard way to accomplish this transfer of information is by making use of an intermediate information carrier (e.g.,…
Stimulated by the recent progress in engineering topological band structures in cold atomic gases, we study the dynamic topological phenomena for atoms loaded in a periodically driven optical lattice. When the frequency of the periodic…
We develop a theory to derive effective Floquet Hamiltonians in the weak drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially-periodic and weak potential, such as occurs in some…
In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case…
The properties of SU(1,1) SU(2),SU(2,1) and SU(3) have often been used in quantum optics. In this paper we demonstrate the use of these symmetries. The group properties of SU(1,1) SU(2), and SU(2,1) are used to find the transition…
Nonreciprocal conversion is essential for protecting sources and enabling unidirectional signal routing in photonic, phononic, electronics, and quantum systems, yet conventional implementations rely on magnetic bias that could be…
The periodically modulated Bose-Hubbard dimer model offers an experimentally realizable and highly tunable platform for observing the scrambling of quantum information and the apparent thermalisation of isolated, interacting quantum…
We investigate the energy distribution and quantum thermodynamics in periodically driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional…
In recent years there has been an increasing interest on the theoretical and experimental investigation of space-time dual quantum circuits. They exhibit unique properties and have applications to diverse fields. Periodic space-time dual…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…