Dynamical Phases in Open Quantum Many-Body Systems

Quantum physics research is entering a fascinating era in which the design and control of synthetic quantum matter is becoming a reality. Pertinent experimental platforms span a wide variety of systems which include cold atomic gases, crystals of ions, and solid-state structures. Synthetic quantum matter has the potential to not only reveal new facets of quantum many-body physics in controlled laboratory settings, but also to advance technological applications in the field of quantum information science. The experimental realization of such artificially engineered quantum matter relies among other things on the ability to isolate complex quantum systems from their environment and in this way protect fragile quantum properties. Reversely, it is also possible to couple quantum systems in a controlled way to different types of environments. In this project, we will study the dynamics of such open quantum systems. Interestingly, coupling a quantum many-body system to an environment can lead to completely new physical properties. In particular, different types of environments can induce dynamical phase transitions. Such phase transitions separate distinct dynamical phases, which are characterized by qualitatively different dynamics of an open quantum system. For example, in one dynamical phase, atoms in a gas can be immobile, while they can be free to move around in space in another dynamical phase when the gas is allowed to interact strongly with its environment. Also the measurement of different properties of a physical system can be interpreted as the interaction of the system with an environment which corresponds to the measurement apparatus. A distinguishing feature of physical systems which obey the laws of quantum mechanics is that they are affected by measurements in a rather drastic and counterintuitive manner. Consequently, also the measurement of quantum many-body systems can induce dynamical phase transitions. Central goals of this project are to identify novel types of dynamical quantum phase transitions in open quantum many-body systems, to develop theoretical models to describe these transitions, and to suggest experimental realizations in the framework of synthetic quantum matter.

In recent years, there has been spectacular progress in the abilities of experimental physicists to study matter that obeys the laws of quantum mechanics. Such quantum matter as realized in today's laboratories is open in the sense that it is not perfectly isolated from its environment. But how does openness affect fundamental properties of quantum matter? Are there be phases of matter that can only be realized in open systems? What are signatures of such phases? We have provided answers to these questions, focusing on specific examples, and, in particular, on the dynamics of open quantum systems. In the first part of the project, we have investigated signatures of topology in the dynamics of open quantum matter. Topology is a mechanism that underlies a suprising degree of robustness of physical properties against various perturbations. Topological properties of closed quantum systems have been studied extensively, but topology of open systems is largely unexplored. We have identified robust signatures of topology in open quantum matter, and we have found phenomena that cannot occur in closed quantum systems. The second part of the project has been concerned with the question, how symmetries of the mathematical equations that describe the dynamics of open quantum matter are reflected in the dynamics. In particular, we have studied the effects of the symmetry under a reflection of both space and the direction of time, which is called parity-time symmetry. We have shown that due to parity-time symmetry, many properties of the dynamics that are commonly believed to be unique to closed systems can also occur in open systems. These properties are thus protected by parity-time symmetry against disturbances caused by the environment of an open system. Our findings have potential applications in the protection of calculations performed on quantum computers against errors. Another sense in which quantum matter can be open is through interactions with an external observer who is taking measurements. Recent research work has shown that repeated measurements can qualitatively alter the properties of quantum matter by inducing phase transitions. In conventional phase transitions, the behavior of the system under investigation strongly depends on conservation laws such as the conservation of energy or the number of particles. In the third part of the project, we have given a comprehensive characterization of measurement-induced phase transitions for systems with and without particle number conservation. We have shown that while the dynamics of these systems are completely different, quite surprisingly, most static properties are almost identical. Our work represents a first step toward a comprehensive theory for the of conservation laws for measurement-induced phase transitions.