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the √ 2 increase in the Rabi frequency forthe collective excitation of two atoms inthe dipole blockade regime.

Rydberg atoms have been the subjectof intense investigation since the earlydays of atomic physics, with ever newtwists and surprises. Te field started

with the spectroscopical observationsof Rydberg atoms in the laboratory andin outer space during the first half ofthe twentieth century, and continuedwith the study of electron dynamics inRydberg states prepared by tunable laserfields in the second half. We are currentlywitnessing the emergence of a third era ofRydberg physics; that is, the investigationof few- and many-body effects owing tothe long-range interactions of these atoms.Investigations include exotic molecules

with extreme binding lengths, coherentmany-body energy and charge-transportphenomena, and strongly correlateddipolar gases. Te results regarding thedipole blockade between two single atoms1,2 represent a further exquisite example forthe wealth of physics offered by correlated

Rydberg atoms. Although the quantum-state and motional manipulation of singleneutral atoms has undergone tremendousprogress in the past ten years10, efficientmethods for entangling two or moreneutral atoms in a deterministic way havestill been lacking. With the advances byUrban et al.1 and Gaëtan et al.2, the dooris now wide-open for the application ofRydberg atoms for neutral-atom quantumgates and for fundamental investigations onthe nature of quantum entanglement. ❐

 Matthias Weidemüller is at the Physics

Institute, Ruprecht-Karl University Heidelberg,

Philosophenweg 12, 69120 Heidelberg, Germany.

e-mail: weidemueller@physi.uni-heidelberg.de

References1. Urban, E. et al. Nature Phys.  5, 110–114 (2009).

2. Gaëtan, A. et al. Nature Phys. 5, 115–118 (2009).3. Gallagher, . F. Rydberg Atoms (Cambridge Univ.

Press, 1994).

4. Amthor, ., Reetz-Lamou r, M., Westermann, S., Denskat, J. &

Weidemüller, M. Phys. Rev. Lett. 98, 023004 (2007).

5. ong, D. et al. Phys. Rev. Lett.  93, 063001 (2004).

6. Singer, K., Reetz-Lamour, M., Amthor, ., Marcassa, L.G. &

Weidemüller. M. Phys. Rev. Lett. 93, 163001 (2004).

7. Heidemann, R. et al. Phys. Rev. Lett.

99, 163601 (2007).

8. Jaksch, D. et al. Phys. Rev. Lett.  85, 2208–2211 (2000).

9. Lukin, M. D. et al. Phys. Rev. Lett.  87, 037901 (2001).

10. Meschede, D. & Rauschenbeutel, A. Adv. At. Mol. Opt. Phys. 

53, 75–104 (2006).

In a classical plasma, the particle numberdensity is low and the temperature high.In contrast, the electron number density

in a quantum plasma is much higher

and the temperature correspondinglylower. Reporting in Physical ReviewLetters, Gert Brodin and co-workers1 haveincreased our understanding of quantumplasmas by developing an improved modelthat includes the influence of electron spin.

Quantum plasmas are common not onlyin astrophysical environments2, such as theinteriors of superdense white dwarfs andJupiter, neutron stars and magnetars, butthey are also producible in the laboratory 3,in nanostructured materials and quantumwells. Importantly, Fermi-degenerateplasmas — plasmas at such a high density

that the Pauli exclusion principle comesinto play — may also arise when a pelletof hydrogen is compressed to many timesits solid density, which is important forinertial confinement fusion.

In a dense Fermi-degenerate plasma,electron–electron and ion–electroncollision frequencies are smaller than theclassical predictions, whereas insignificantion–ion collisions follow the classical limit.Owing to the high electron number density,the electron plasma frequency is extremelyhigh and it far exceeds the electroncollision frequency. Such properties leadto many novel effects4–6. Some of the

important ones are: a Fermi-degenerateelectron/positron equation of state thatis significantly different from that ofthe Maxwell–Boltzmann laws; quantum

electron/positron tunnelling effects dueto the finite width of the electron wavefunction; and the electron/positron-1/2-spin effect due to random orientation ofthe plasma particles in a non-uniformmagnetic field.

Brodin and colleagues1,6 haveinvestigated novel collectiveelectromagnetic wave phenomenainvolving the electron-1/2-spin effect.In thermodynamic equilibrium, some ofthe electron spins tend to align with anexternal magnetic field. Subsequently,there emerges a plasma magnetization

in the direction of this field. When the variation of the magnetic field occurs ona timescale shorter than the characteristicspin-relaxation time, the degree ofspin alignment can be approximated asconstant. Spontaneous spin changes donot occur for single electrons (owingto angular momentum conservation)and so this spin-relaxation time7 is alsolarger than the inverse electron-collisionfrequency. Te electron spin modifies theplasma current density and introduces amagnetic moment force on the electrons.Accounting for this anomalous magneticmoment, characterized by the electron-spin

 g -factor ( g  ≈ 2.002319), Brodin et al.1 havedeveloped a spin-force-modified kinetictheory for a magnetized plasma withimmobile ions. A new high-frequency

ordinary mode, which is polarized parallelto the external magnetic field direction,appears. Furthermore, the model alsoidentifies new types of wave–particleinteractions involving the electronspin state.

Tere have been several previousapproaches to treat collective interactions5,6 in dense quantum plasmas. Te quantumhydrodynamical model is one suchexample. Tis model considers a numberof forces acting on the electrons: theFermi pressure that arises because of thehigh density, the quantum force4,5 due to

collective electron tunnelling throughthe so-called Bohm potential and theelectrostatic force. Te net effect of theseforces is that the electrons oscillate aroundthe heavy ions — so-called electron plasmaoscillations. Te model of Brodin et al. extends these ideas by introducing theeffect of the anomalous electron spin,but ignores quantum mechanical andquantum tunnelling effects. Brodin et al. stress that their model is only valid inthe weak quantum regime where thecharacteristic length-scale is larger thanthe thermal de Broglie wavelength, andthe Zeeman energy density is much

PLASMA PHYSICS

A new spin on quantum plasmasA model for dense degenerate plasmas that incorporates electron spin indicates that quantum effects can be seen

even under conditions previously considered to be in the classical regime.

Padma Kant Shukla

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smaller than the electron thermal-energydensity. However, the kinetic theory can beurther generalized or the high-requencyelliptically polarized extraordinaryelectromagnetic wave, propagatingtransverse to the external magneticfield, with the spin-modified anisotropic

Fermi–Dirac distribution unction.It is worth considering the implications

o collective interactions in dense quantumplasmas that have quantum and spinorces. Collective interactions in quantumplasmas are truly interdisciplinary — theycombine quantum mechanics, plasmaphysics, fluid dynamics, condensed matterand statistical physics. Te potential or

using spin in practical applications hasalready been realized in a number odifferent fields (the award o the 2007Nobel Prize in Physics to Albert Fert andPeter Grünberg or their work on giantmagnetoresistance is just one example). Itis hoped that the field o quantum plasmas

will also find practical applications in theproduction o localized X-ray sources,quantum ree-electron lasers8,9 and plasma-assisted microelectronic components.Also, a better understanding o the roleo electron spin in quantum plasmasmay aid the development o intense-laser-beam compression or controllednuclear usion. ❐

Padma Kant Shukla is in the Faculty of Physics

and Astronomy, Ruhr University Bochum,

D-44780 Bochum, Germany.

e-mail: ps@tp4.rub.de

References1. Brodin, G., Marklund, M., Zamanian, J., Ericsson, A. &

Mana, P. L. Phys. Rev. Lett. 101, 245002 (2008).

2. Harding, A. K. & Lai, D. Rep. Prog. Phys. 69, 2631–2708 (2006).

3. Glenzer, S. H. et al. Phys. Rev. Lett. 98, 065002 (2007).

4. Gardner, C. L. & Ringhoer, C. Phys. Rev. E 

53, 157–167 (1996).

5. Manredi, G. Fields Inst. Commun. 46, 263–287 (2005).

6. Shukla, P. K. & Eliasson, B. Phys. Rev. Lett. 96, 245001 (2006).

7. Brodin, G. & Marklund, M. Phys. Rev. E 76, 055403(R) (2007).

8. Piovella, N. et al. Phys. Rev. Lett. 100, 044801 (2008).

9. Serbeto, A., Mendonça, J. ., sui, K. H. & Boniacio, R. Phys.

Plasmas 15, 013110 (2008).

Ultrashort light pulses can temporallyresolve the evolution o dynamicalsystems such as excited molecules.

Resolving aster and aster processesobviously requires shorter and shorterlight pulses. Pulses with durations in

the attosecond range (1 as = 10–18

 s)— short enough to start resolving thedynamics o electrons in matter — can begenerated and measured1 by exploitinglaser–atom or laser–molecule interactions.However, applications o these pulseshave been hindered by limits to pulseand photon energies. On page 124 o thisissue2, Yutaka Nomura and colleaguesdemonstrate experimentally a newkind o attosecond light source thatmight eventually push these limits bytaking advantage o ultrahigh-intensitylaser–plasma interactions.

For more than twenty years, lasertechnology has exploited the chirped-pulse amplification technique to produceintense light pulses that only last a ewtens o emtoseconds. Fifeen years ago,these pulses were identified theoreticallyas a promising tool or obtaining evenshorter pulses — potentially o attosecondduration3,4. Te basic idea is to make sucha pulse interact with a system at highintensity, so that its waveorm is temporallydistorted by the nonlinear response o thesystem. Because this distortion generallyhas the same periodicity as the drivinglaser, the spectrum o the resulting light

field consists o a comb o harmonics o theincident requency. For a severe distortion,these harmonics reach very high orders,thus leading to a very broad spectrum — aprerequisite or very short pulses. I thisdistortion is temporally localized withineach laser optical cycle — or, equivalently,i the harmonics making up the spectrumare approximately in phase — a train osub-laser-cycle pulses can then be obtained

simply by filtering out the undamentalrequency and selecting a group oharmonics in the spectrum.

Distortions o the laser-field waveormhave so ar been achieved by exploiting aprocess called laser-driven electron–ionrecollision1. Electron wavepackets areperiodically reed rom a target atom ormolecule by tunnel ionization. Part othese wavepackets return to their parent

ULTRAFAST SCIENCE

Attosecond plasma opticsUsing dense plasmas instead of atomic or molecular gases could enable the generation of attosecond light pulses

with higher energy, shorter durations and more energetic photons.

Fabien Quéré

ba Recolliding electron

wave-packet

Target

molecule

Polarization

vector

‘Recolliding’

electron bunch

Plasma

mirror

Polarization

vector

Fg 1 | Working in analogy. a, Laser-driven electron–ion recollision can create attosecond pulses. An

input laser (red wave) frees an electron wave-packet from a target atom or molecule. An attosecond

light pulse is generated when part of this wave-packet returns to the ion. b, Excitation lasers of much

higher intensity create a plasma. Nomura et al.2 show experimentally that this can generate attosecond

pulses in much the same way. At even higher intensities, the Doppler effect induced as the laser beam

reects on the plasma has the potential to generate attosecond pulses with a shorter duration and withhigher energy photons.

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