Staircase in magnetization and entanglement entropy of spin squeezed condensates

TL;DR

This paper demonstrates that spin-1 atomic condensates exhibit staircase patterns in magnetization and entanglement entropy when subjected to certain Hamiltonians, revealing discrete responses to continuous parameter tuning.

Contribution

It introduces the concept of magnetization staircase in spin-squeezed condensates and connects it to experimentally realizable Hamiltonians, expanding understanding of quantum response phenomena.

Findings

Magnetization exhibits staircase behavior under specific Hamiltonians.

Entanglement entropy also shows staircase patterns.

Results are applicable to real atomic condensate experiments.

Abstract

Staircases in response functions are associated with physically observable quantities that respond discretely to continuous tuning of a control parameter. A well-known example is the quantization of the Hall conductivity in two dimensional electron gases at high magnetic fields. Here, we show that such a staircase response also appears in the magnetization of spin-1 atomic ensembles evolving under several spin-squeezing Hamiltonians.We discuss three examples, two mesoscopic and one macroscopic, where the system's magnetization vector responds discretely to continuous tuning of the applied magnetic field or the atom density, thus producing a magnetization staircase. The examples that we consider are directly related to Hamiltonians that have been implemented experimentally in the context of spin and spin-nematic squeezing. Thus, our results can be readily put to experimental test in spin-1 ferromagnetic $^{87}$Rb and anti-ferromagnetic $^{23}$Na condensates.