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Entangled anddisentangled evolution forasingle atomina driven cavity

Perry R. Rice, Julio R. Gea-Banacloche, Luis A. Orozco

Published Jan 1, 2005• 0 citations

Abstract

Foranatominadriven cavity wefind states that arehighly entangled, andthat spontaneous emission cantransiently increase entanglement. Wepropose a correlation function measurement anddiscuss timeevolution ofentanglement. C2003Optical Society ofAmerica OCIScodes:270.5580 Quantum Electrodynamics, 270.5290 Photon Statistics Inarecent, beautiful experiment, Auffeves andcoworkers (1) haveverfied theprediction (2)that, fora two-level atominteracting with asingle modeoftheelectromagnetic field, inacoherent state with a moderately large number ofphotons, thenatural evolution ofthesystem leads toasuperposition state inwhich twodifferent states oftheatomarecorrelated with twodistinguishable states ofthefield, in whatisoften referred toasaSchrodinger cat.Suchsuperpositions ofcorrelated states, ifpure, are naturally entangled states. Interestingly, thepossibility ofpreparing suchentangled superpositions in theabove system (which isdescribed bytheso-called Jaynes-Cummings model, orJCM)arises from theexistence, inthis model, ofspecial trajectories along whichthejoint evolution offield andatomis toagoodapproximation unentangled, i.e., factorizable. Itisthecoherent superposition ofsuch trajectories that results inanentangled state.

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Publisher's Note: Entangled and Disentangled Evolution for a Single Atom in a Driven Cavity [Phys. Rev. Lett.94, 053603 (2005)]

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Received 14 February 2005DOI:https://doi.org/10.1103/PhysRevLett.94.069905©2005 American Physical Society

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Foranatominadriven cavity wefind states that arehighly entangled, andthat spontaneous emission cantransiently increase entanglement. Wepropose a correlation function measurement anddiscuss timeevolution ofentanglement. C2003Optical Society ofAmerica OCIScodes:270.5580 Quantum Electrodynamics, 270.5290 Photon Statistics Inarecent, beautiful experiment, Auffeves andcoworkers (1) haveverfied theprediction (2)that, fora two-level atominteracting with asingle modeoftheelectromagnetic field, inacoherent state with a moderately large number ofphotons, thenatural evolution ofthesystem leads toasuperposition state inwhich twodifferent states oftheatomarecorrelated with twodistinguishable states ofthefield, in whatisoften referred toasaSchrodinger cat.Suchsuperpositions ofcorrelated states, ifpure, are naturally entangled states. Interestingly, thepossibility ofpreparing suchentangled superpositions in theabove system (which isdescribed bytheso-called Jaynes-Cummings model, orJCM)arises from theexistence, inthis model, ofspecial trajectories along whichthejoint evolution offield andatomis toagoodapproximation unentangled, i.e., factorizable. Itisthecoherent superposition ofsuch trajectories that results inanentangled state.

For an atom in an externally driven cavity, we show that special initial states lead to near-disentangled atom-field evolution, and superpositions of these can lead to near maximally entangled states. Somewhat counterintutively, we find that (moderate) spontaneous emission in this system actually leads to a transient increase in entanglement beyond the steady-state value. We also show that a particular field correlation function could be used, in an experimental setting, to track the time evolution of this entanglement.

We explore the entanglement between a single atom and a single, resonant field mode of a driven optical cavity, focusing on the strong driving regime. We show that, in the absence of spontaneous emission, there are special initial conditions that lead to approximately disentangled trajectories, whereas spontaneous emission results in coherent superpositions of such trajectories that may lead to (transient) near-maximally entangled atom-field states. We also discuss the possibility of using a special "asymmetric" field correlation function to track the time evolution of this entanglement.

Wereport thecomplete measurement ofthespectral properties ofphoton pairs generated viaspontaneous parametric down-conversion. Themeasurements, which include notonlysingle-photon spectra, butalso two-photon joint spectra, wereperformed forbothcwandultrafast pumping configura- tions. Inagreement withtheoretical predictions, thespectra fortheultrafast pumpedcasereveal asym- metries notpresent with cwpumping. © 2005Optical Society ofAmerica OCIScodes: (270.0270) Quantum optics; (270.5290) Photon statistics Entanglement between photons hasplayed animportant role instudies ofthefoundations ofquantum physics, andis relevant today indisciplines suchasquantum information processing, quantum communication, quantum-enhanced imaging andmetrology, etc. Themostcommonmethod forthegeneration ofentangled photons isspontaneous para- metric down-conversion (SPDC). Type-II SPDCisofparticular interest, notonlybecause oftherelatively narrow bandwidths ofthephotons, butalso because itispossible togenerate polarization-ent angled