Keywords: nonequilibrium quantum dynamics, theory of open quantum systems, quantum response theory, quantum fluctuation theorems, quantum thermodynamics, quantum control theory, quantum technologies.
Progress in quantum technologies relies on understanding how quantum phenomena govern the dynamics of quantum systems far from equilibrium and on identifying the available quantum resources. This knowledge then allows us to manipulate the systems in order to obtain a desired outcome. Our group seeks to:
- Develop dynamical descriptions that capture effects of quantum phenomena on the single-atom/molecule level and for systems far-from-equilibrium.
- Identify quantum resources and utilize them in controlling quantum transport processes and quantum state preparation.
- Thoroughly define the relationship between quantum effects and concepts from nonequilibrium thermodynamics.
For over a century, thermodynamics has been considered one of the pillars of physics. The theory deals with energetic and entropic processes in the macroscopic scale under a set of constraints. It was initially formed as a phenomenological theory in which the fundamental laws were developed without a microscopic theory in hand. Quantum theory, on the other hand, is concerned with dynamics and properties of microscopic systems at the atomic length scale. The field of quantum thermodynamics aims to bridge the two fields. The fundamental questions in the field are: To what extent do the paradigms and the laws of thermodynamics apply in the quantum domain? What role do quantum effects, such as quantum correlations and coherences, play in energy and entropy flows in the quantum realm? In other words, can we use quantum phenomena as resources to drive thermodynamic processes? Our group develops various mathematical and physical frameworks to answer these questions and provide new theoretical predictions that can be tasted in the lab. The study of thermodynamics in the quantum regime branches into many other fields, including quantum foundations, solid state physics, and atomic, molecular, and optical physics.
Quantum fluctuation theorems:
Fluctuation theorems (FTs) have the important role of generalizing basic concepts from thermodynamics to microscopic finite-size systems and are also relevant to systems driven strongly far from equilibrium. Broadly speaking, FTs relate the probability distributions of the forward and reversed nonequilibrium processes of some fluctuating quantity. They are most evident in the microscopic realm where fluctuations carry more weight. Classically, these theorems are relevant to biomolecules, molecular motors, colloidal particles, etc. In the quantum regime, they are applicable to, and experimentally observed in, a wide variety of quantum devices such as trapped ions, superconducting qubits, quantum dots, and NMR setups.
However, the standard approach to deriving fluctuation theorems fails to capture important quantum effects such as quantum correlations and coherence in the initial state of the system. We seek to develop new approaches to account for these genuinely quantum phenomena, and reveal quantum-thermodynamic signatures – that is, thermodynamic measurable quantities which witness non-classicality.
Quantum control theory:
Control theories are at the heart of the effort to turn scientific knowledge into technology. The scope of control theory is to find a control law for accomplishing a certain task, e.g. driving a system from some initial state to a final target state under a set of constraints, or optimizing the performance of some quantum device. Typically, external electromagnetic fields are applied in order to execute the control law. The two main goals of quantum control theory are: (i) to determine whether, and under what conditions, a quantum system is controllable, i.e. if a target state or a process outcome can be reached; and (ii) to develop systematic and robust methods for manipulating quantum systems and processes at the atomic and molecular level.
While quantum control theories are elementary to quantum state preparation and to achieving desired quantum protocols, the methods are still limited to closed systems that follow a unitary evolution. Because all quantum systems are subject to noise that may arise from parasitic couplings to the environment or from sensitivities in the control fields, we are interested in developing systematic methods that minimize these effects or even utilize them to obtain a control law.