Abstract
We propose an approach to analytically solve the quantum dynamics of bosonic systems. The method is based on reconstructing the quantum state of the system from the moments of its annihilation operators, dynamics of which is solved in the Heisenberg picture. The proposed method is general in the sense that it does not assume anything on the initial conditions of the system such as separability, or the structure of the system such as linearity. It is an alternative to the standard master equation approaches, which are analytically demanding especially for large multipartite quantum systems. To demonstrate the proposed technique, we apply it to a system consisting of two coupled damped quantum harmonic oscillators.
Highlights
One of the most intriguing problems in modern physics is understanding the dynamics of open quantum systems [1]
The method is based on reconstructing the quantum state of the system from the moments of its annihilation operators, dynamics of which is solved in the Heisenberg picture
The essence of the method is in reconstructing the quantum state of the system under interest using the normally ordered moments of its annihilation operators, the dynamics of which is solved in the Heisenberg picture
Summary
One of the most intriguing problems in modern physics is understanding the dynamics of open quantum systems [1]. Several approaches to solve master equations analytically have been presented, including algebraic methods [18,19,20,21], exact diagonalization [22,23], series expansions [24], and effective Hamiltonian approaches [25,26] These techniques are technically demanding, especially for multipartite quantum systems [20]. To demonstrate the utilization of the dynamical reconstruction method, we consider a system of two bilinearly coupled damped quantum harmonic oscillators This system can be realized, for example, as capacitively coupled coplanar waveguide resonators [30].
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