Superfluidity from a Classical-Field Perspective

K.H. Bennemann, John B. Ketterson

Boris V. Svistunov, Egor S. Babaev, Nikolay V. Prokof'ev

Superfluidity is the phenomenon of matter flow-referred to as a superflowwithout any resistance from the walls or other obstacles. It is common to refer to superfluidity as a macroscopic quantum phenomenon. The word “quantum” here is only conditionally correct. Furthermore, it is somewhat confusing since it creates an impression that superfluidity cannot exist within the domain of classical physics. It is unquestionably true that the system of classical particles cannot support a superflow, and it is from that classical-particle perspective that superfluidity is associated with the quantum world. However, it turns out that for certain complex-valued classical fields, the superfluid phenomenon is absolutely natural. Hence, superfluidity looks quantum only from either the classical-particle or quantum-field point of view, while being classical from the complementary perspective. In general, this is reflective of the dual nature of quantum fields, which under certain conditions can mimic the behavior of purely classical particles, while under other conditions can also behave as classical fields.

Nikolay N. Bogolubov

Boris V. Svistunov, Egor S. Babaev, Nikolay V. Prokof'ev

Up to this point in our discussion of the superfluidity phenomenon, we have deliberately not mentioned quantum mechanics: this is in contrast with the conventional approach that usually starts with the notion of the condensate wavefunction. In previous chapters, we have shown that classical systems, whether they are dynamical or purely statistical, can be in the superfluid state. Thus, an important connection to follow in the quantum case is the development of the classical-field component that then undergoes the superfluid transition. This can be achieved naturally within the coherent states approach advocated by Langer [1]. As we will see shortly, this connection is rather straightforward and, surprisingly, brings about the counterintuitive (from the classical-particle perspective) question: “Do we ever have an insulating quantum solid state in bosonic systems?” In Chapter 9, we answer this question positively.

Xiang-Can Cheng, Zong-Yao Wang, Jinyi Zhang +2 more

The study of the gauge field is an everlasting topic in modern physics. Spin-orbit coupling is a powerful tool in ultracold atomic systems, resulting in an artificial gauge field that can be easily manipulated and observed in a tabletop environment. Combining optical Raman lattices and atom-atom interactions, the artificial gauge field can be made density dependent. In this work we propose a straightforward way to engineer a one-dimensional density-dependent gauge field in a Bose-Hubbard model in spin-orbit-coupled Raman lattices. We study the model from two perspectives: few-body quantum-walk dynamics and the many-body ground state. From the first perspective, we show that large spin-flipped tunneling can lead to a deep two-body bound state. From the second perspective, mean-field and density-matrix renormalization-group calculations consistently reveal three different phases, i.e., the Mott insulator phase, the superfluid phase, and the magnetic superfluid phase. Finally, we discuss the experimental protocol with Raman lattices based on existing experimental platforms.

Eduardo C. Marino