Entangled-State Cycles of Atomic Collective-Spin States

TL;DR

This paper explores how collective atomic spin states evolve into entangled-state cycles driven by laser and cavity fields, revealing probabilistic state switching and methods to prepare specific Dicke states with potential for multipartite entanglement.

Contribution

It introduces the concept of entangled-state cycles in atomic collective-spin states and demonstrates probabilistic preparation of Dicke states using quantum trajectories.

Findings

Entangled-state cycles occur probabilistically at equal Raman transition rates.

States switch between superpositions of Dicke states with each photon emission.

Steady-state preparation of Dicke state |N/2,0> is possible for even N.

Abstract

We study quantum trajectories of collective atomic spin states of $N$ effective two-level atoms driven with laser and cavity fields. We show that interesting ``entangled-state cycles'' arise probabilistically when the (Raman) transition rates between the two atomic levels are set equal. For odd (even) $N$, there are $(N+1)/2$ ($N/2$) possible cycles. During each cycle the $N$-qubit state switches, with each cavity photon emission, between the states $(|N/2,m>\pm |N/2,-m>)/\sqrt{2}$, where $|N/2,m>$ is a Dicke state in a rotated collective basis. The quantum number $m$ ($>0$), which distinguishes the particular cycle, is determined by the photon counting record and varies randomly from one trajectory to the next. For even $N$ it is also possible, under the same conditions, to prepare probabilistically (but in steady state) the Dicke state $|N/2,0>$, i.e., an $N$-qubit state with $N/2$ excitations, which is of particular interest in the context of multipartite entanglement.