Universal scaling laws for correlated decay of many-body quantum systems

Increasing the density of quantum devices opens avenues to explore novel regimes of many-body quantum dynamics and enhance the performance of various quantum applications such as precise sensing. At the same time, this effort poses new challenges as densely packed systems exhibit correlated dissipation, significantly impacting the decay rate of correlated quantum states. It is thus natural to ask: What is the maximum decay rate of a system with correlated dissipation? Addressing this question for large numbers of particles is however complicated by the exponential scaling of the Hilbert space dimension. We reformulate the problem of maximal decay rate into finding the ground state energy of a 2-local Hamiltonian. While finding the ground state is widely believed to be hard, it is possible to find upper and lower bounds efficiently. In particular, using ideas from quantum approximation theory and semidefinite programming relaxations, we provide analytical bounds for the maximal decay rate of generic many-body quantum systems. Our bounds are universal in that they only depend on global properties of the decoherence matrix (which describes dissipative couplings between atoms) and agnostic of the specific microscopic interactions. For many classes of physically-relevant systems, the bounds are tight, resulting in scaling laws with system size. As a particular application, I will discuss Superfluorescence in extended system — a well-known open problem in quantum optics. I will demonstrate how our general method allows us to derive rigorous scalings for the radiation burst, illustrating its broader applicability in understanding complex quantum phenomena. In particular, I will show how these theoretical scaling arise from the optical depth of the system. I will then discuss how the derived scaling of the maximum decay rate determine the properties of collective resonance fluorescence in free space atomic arrays and in the superradiant emission propertier of incoherently pump atoms.