Related papers: Analysis and synthesis of attractive quantum Marko…
We study the Markovian dynamics of a collection of n quantum systems coupled to an irreversible environmental channel consisting of a stream of n entangled qubits. Within the framework of repeated quantum interactions, we derive the master…
We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with…
Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for…
Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to…
The squeezing dynamics of a damped harmonic oscillator are studied for different types of environment without making the Markovian approximation. The squeezing dynamics of a coherent state depend on the reservoir spectrum in a unique way…
The quantum master equation (QME), used to describe the Markov process of interaction between atoms and field, has a number of significant drawbacks. It is extremely memory intensive, and also inapplicable to the case of long-term memory in…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases,…
We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an…
A Markovian open quantum system which relaxes to a unique steady state $\rho_{ss}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by Karasik and Wiseman [Phys. Rev.…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
An important challenge in non-Markovian open quantum systems is to understand what information we gain from continuous measurement of an output field. For example, atoms in multimode cavity QED systems provide an exciting platform to study…
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
Ultracold atomic physics offers myriad possibilities to study strongly correlated many-body systems in lower dimensions. Typically, only ground state phases are accessible. Using a tunable quantum gas of bosonic cesium atoms, we realize and…
Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit, or the…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…