Dissipative processes
In many-body physics a lot of attention is given to properties of matter in thermal equilibrium with some external reservoir. However, while this is a vast and interesting field in itself, it is far from covering all possible topics. Firstly, even though we can access information about dynamical properties of the system in this way, it is possible only within the limit of linear response. If the system is driven strongly by some external force its response can go beyond this regime. Indeed, it is often difficult to even estimate when the linear response approximation will fail. Secondly, in experiments one usually works with imperfect systems, where dissipation and relaxation processes occur and affect its behaviour. The only way to account for them is to consider a system out of equilibrium which requires a somewhat different theoretical approach. A very common approach is to use the Lindblad master equation for describing the time evolution of the density matrix. The simplest example of such an equation is the following
There are many interesting questions in this field, and answering them poses a significant challenge. Does a closed system approach thermodynamic equilibrium and if so, how? What are the differences between the behaviour of closed and open systems? How does the nature of phase transitions change if we are not in equilibrium, but in some kind of steady state?
In our research we are interested in dissipative processes and steady states in optical lattices. The fact that a system is subject to dissipation can be used to our advantage there, e.g., as a measurement tool. Using controlled dissipation focused on a single site in an optical lattice allows for a measurement with single atom resolution [1]. In such processes interesting physical phenomena emerge, such as the quantum Zeno effect: counter-intuitively, stronger bare loss rates at a single site can lead to a suppression of the number of particles leaking from the system [2]. This is depicted in Fig. 1, where the loss rate decreases with growing dissipation strength after exceeding certain threshold. The dashed green line has been obtained by using following expression
where nl(t) is the occupation of the lossy site and N is the total occupation of the system. As the dissipative term grows the average occupation of this site is strongly reduced and hence the decay rate of the entire system is suppressed.
Fig. 1. Particle number decay rate as a function of dissipation strength for a homogeneous superfluid. Figure taken from Ref. [2].
Another interesting problem is the relaxation of Rydberg atoms in optical lattices to their hyperfine ground states. Dressing atoms with Rydberg states results in additional long-range interactions. Using this technique in optical lattices, where the system parameters are highly tunable, would allow for a thorough study of the resulting many-body states and long-range order. However, Rydberg states are short lived due to spontaneous emission and black-body radiation processes [3]. Therefore, Rydberg-dressed atoms in an optical lattice should be treated as an open system. This complicates the theoretical description of the problem considerably.
[1] W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, Nature 462, 74 (2009).
[2] I. Vidanovi?, D. Cocks, and W. Hofstetter, Phys. Rev. A 89, 053614 (2014).
[3] T. F. Gallagher, Rydberg Atoms, Cambridge University Press, New York (1994).
