An informationally complete Wigner function for the Tavis\u2013Cummings model

Russell P Rundle,Mark J Everitt

doi:10.1007/s10825-021-01777-6

Russell P Rundle, Mark J Everitt

Open Access

https://doi.org/10.1007/s10825-021-01777-6

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Abstract

Here we consider an informationally complete Wigner function approach to look at multiple atoms (qubits) coupled to a field mode. We consider the Tavis–Cummings interaction between a single field mode with two qubits and then with five.

Highlights

The Jaynes–Cummings model describes a simplified model of an atom coupled to an electromagnetic field in the rotating wave approximation [1,2,3,4]
What we describe in this paper is the complete representation in phase space for systems such as those described by the Tavis–Cummings model
Understanding how efficiently information can be swapped between one system to another will provide a way into understanding how efficient such technologies are, as the efficacy of quantum memory can only be as good as the information received from the state

Summary

Introduction

The Jaynes–Cummings model describes a simplified model of an atom coupled to an electromagnetic field in the rotating wave approximation [1,2,3,4]. We can label each coherent state as i⟩f , where i is a complex number that describes the position of the coherent state in phase space, and relates to the avera√ge number of photons in a given coherent state, where n = α When coupling this initial coherent states to a single atom using the Jaynes–Cummings model, one can specify the atom field coupling strength of g; this coupling strength is typically present as a coefficient in Eq (1); we have set it equal to one in this analysis. If we plot the Wigner function in such a way that any correlation between the phase space of one subsystem can be seen to be correlated with another we may see the entanglement correlations and get deeper insight into the nature of these correlations over the phase space This will allow for general study beyond the Tavis–Cummings model and should provide a framework for verification and validation of important quantum states for information processing and sensing applications

Composite systems in phase space

Two‐atom Tavis–Cummings interaction

Five‐atom Tavis–Cummings interaction

Conclusions