Exact quantum field mappings between different experiments on quantum gases

TL;DR

This paper introduces an exact spacetime mapping between different quantum gas experiments, enabling the simulation of complex many-body dynamics through more accessible experiments, applicable to various gases and initial states.

Contribution

It presents a general identity relating quantum field operators that allows mapping between different experiments involving quantum gases with scaling interactions.

Findings

Enables perfect simulation of complex experiments using simpler ones.

Applies to arbitrary measurements on Bose and Fermi gases.

Works for any initial states with scaling interactions.

Abstract

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact solutions. Here we present an exact result which holds even when no exact solutions can be found: a class of spacetime mappings of different experiments onto each other, as long as the gas particles interact via two-body potentials which possess a scaling property that most real interactions do possess. Since our result is an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics, it is otherwise general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. Practical applications of this mapping include perfect simulation of non-trivial experiments with other experiments which may be easier to perform.