Open quantum systems

A large variety of phenomena is inherent to open systems; among them : relaxations and decoherences. Relaxations are due to the exchange of energy between the open system and its environment. Decoherences are due to the quantum nature of the open system. They dramatically affect quantum computing and remain the main obstacle for these machines to work. Understanding and controlling decoherences is an essential step towards our capability to use quantum properties of matter for tomorrow's technologies. On the promising future of quantum matter as technological tools, see for instance the interesting viewpoint of Octave Klaba (founder and president of OVHcloud): "Too few companies in Europe are interested in quantum" (Figaro article).

A quantum computing platform is a typical example of open system because it interacts with particles inside the atmosphere. More generally, open systems are systems in interaction with an environment. As a consequence of these interactions, the open system exchanges energy with its environment. In contrast, closed systems are isolated, and as a consequence, their energy is conserved. In theory, an open system and an environment can always be considered together as a closed system.

Because open systems are "made", why don't we always consider a closed system ?

The interactions and the motions involved between the open system and its environment are in general extremely complex. They are so complex, that we cannot solve the full system, or even not describe it microscopically. Effective descriptions for these interactions are required. Developing, analyzing and predicting the effective dynamics, decoherence and relaxations inside of an open system is the objective of the domain of physics: open (or disspative) quantum systems.

References

Figure: Illustration of closed versus open systems. An open system can exchange energy with an environment (yellow arrows). 

Research projects

Decoherence-free subspaces for quantum many-body systems

Decoherences are the main obstacle to coherent oscillations in a many-body system, used for quantum computing and quantum information. However, there can be subspaces in which decoherence does not occur. These subspaces are referred to as decoherence-free subspaces (DFS). How to engineer DFS efficiently for a given open system? How could we engineer technological devices with DFS? These are ongoing questions with the long-term goal of understanding and controlling decoherence phenomena in many-body quantum systems.

In my project, I have used symmetries of the open system in order to build its DFS. If a system and its environment share at least one symmetry, then DFS can be efficiently engineered using ghost operators. These operators do not act on the coherent oscillations associated with the symmetries of the open system. As a consequence, coherences are preserved. 

Figure: Dynamics of a quantum spin model projected on the Bloch sphere with initial condition (a). (b) and (c) do not have DFS, the distribution diffuses along the equator (b) or to the north pole. (d) and (e) have DFS, the distribution remains a blob, and oscillations persist.

Publication

Semi-classical limit of the Lindblad master equation for spin dynamics

Open systems are generally very difficult to solve, and also a few pieces of information on the dynamics can be extracted from the full solution of the quantum evolution equation. This information is however crucial for controlling and predicting efficiently the underlying phenomena observed in open systems.

One characteristic of open quantum systems is that they manifest strong classical behaviors due to the decoherences. Therefore, the classical limit of the quantum models is often used and analyzed in order to deduce information on its dynamics and underlying mechanisms. These classical limits can be derived in many different ways, but most of them result in equations that do not fulfill the fluctuation-dissipation theorem, and they do not allow the analysis of correlations between different particles.

In this work, using the algebra of the quantum model and its semi-classical limit, we have been able to provide a semi-classical evolution equation that fulfills the fluctuation-dissipation theorem, and which fully takes into account correlations between particles. The resulting equation allow to describe the dynamics in terms of an ensemble stochastic trajectories (and not deterministic). This can also be used to study diffusion effects in the phenomena in open systems, such as spins in a cavity.

Figure: Spin of atoms inside a cavity with two laser modes. The lower panel is the asymptotic distribution of the spin on the Bloch sphere. The white curves are stochastic trajectories.

Publication