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arXiv:1207.6772 · Physical Review A

Squeezing of collective excitations in spin ensembles

Christian Kraglund Andersen, Klaus Mølmer

Published Oct 22, 2012• 8 citations
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Abstract

We analyze the possibility of creating two-mode spin squeezed states of two separate spin ensembles by inverting the spins in one ensemble and allowing spin exchange between the ensembles via a near resonant cavity field. We investigate the dynamics of the system using a combination of numerical and analytic calculations, and we obtain squeezing for a wide range of parameters. We also investigate the transfer of the squeezing properties to the cavity field and to an output mode from the cavity. Finally, we investigate how the squeezing is affected by effects of inhomogeneities which would be present in solid-state implementations of the spin ensembles.

DOI
10.1103/physreva.86.043831

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We analyze the possibility of creating two-mode spin squeezed states of two separate spin ensembles by inverting the spins in one ensemble and allowing spin exchange between the ensembles via a near resonant cavity field. We investigate the dynamics of the system using a combination of numerical and analytic calculations, and we obtain squeezing for a wide range of parameters. We also investigate the transfer of the squeezing properties to the cavity field and to an output mode from the cavity. Finally, we investigate how the squeezing is affected by effects of inhomogeneities which would be present in solid-state implementations of the spin ensembles.
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It has been shown elsewhere that two spatially separated atoms can jointly absorb one photon, whose frequency is equal to the sum of the transition frequencies of the two atoms. We describe this process in the presence of an ensemble of many two-level atoms and show that it can be used to generate spin squeezing and entanglement. This resonant collective process allows us to create a sizable squeezing already at the single-photon limit. It represents a way to generate many-body spin-spin interactions, yielding a two-axis twisting-like interaction among the spins, which is very efficient for the generation of spin squeezing. We perform explicit calculations for ensembles of magnetic molecules coupled to a superconducting coplanar cavities. This system represents an attractive on-chip architecture for the realization of improved sensing.
We propose a potentially practical scheme for realization of two-mode squeezed state with respect to two distant nitrogen-vacancy center ensembles coupled to two interconnected mechanical modes of diamond nanoresonators. By making use of the tunable phonon-spin interaction and the engineered phonon-phonon tunneling, both the desired excitation transfer process and the optimal two-mode squeezing between spin ensembles can be realized. We investigate the dynamics of the total system under infulences from the mechanical decay using both analytical and numerical methods, where the realistic conditions that leads to optimized squeezing between spin ensembles are analyzed.
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We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. Leroux, M. H. Schleier-Smith, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.
An advantageous architecture for producing deterministic spin squeezing is cavity QED. We show that the recently discovered one photon - two atom excitation process can be used to generate optimal squeezing (scaling as 1/N1/N1/N) of an ensemble of NNN spins coupled to a single-mode cavity. This method has some remarkable features. It is a resonant phenomenon mediated by real photons, which provides the advantage of tunability. This allows to create a sizeable squeezing already at the single-photon limit. Finally, in the strong cavity-driving regime the effective theory is similar to a two-axis Hamiltonian. We calculate that reaching −30-30−30dB is possible already with the known reported spin-cavity and decoherence rates in magnetic molecules coupled to superconducting circuit resonators. This system represents an attractive on-chip architecture for the realization of technological solutions in sensing.