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nature physics| VOL 3 | JANUARY 2007 | www.nature.com/naturephysics 13

NONLINEAR OPTICS

Shocking superfl uids

Lene Vestergaard Hauis in the Department of Physics and in the

Division of Engineering and Applied Sciences,

Harvard University, 17 Oxford Street, Cambridge,

Massachusetts 02138, USA.

e-mail: hau@physics.harvard.edu

A

BoseEinstein condensate is one o

the most intriguing states o matter.Its existence was predicted by Bose

and Einstein in the 1920s and it has beenparticularly clearly demonstrated in recentyears with laser-cooled, trapped atomicgases1. In these condensates, millionso atoms occupy the same quantumstate all atoms are in lock step witheach other and behave in many ways as asingle entity which leads to a numbero interesting properties2. For example,a condensate shows superfuidity andcan thereore fow without damping ordissipation. Similarly, BoseEinstein

condensation is responsible or thesuperfuid properties o helium below 2.17 K,and or the lossless conduction o electricalcurrents in superconductors. Yet there ismuch we do not know about BoseEinsteincondensation and superfuid behaviour.

A particularly interesting way o probingthe inner workings o BoseEinsteincondensates (BECs) is to study how shockwaves are generated and propagate withinthem. In real BECs this is challenging, andthere have been only a ew experimentalstudies36. In these experiments done incooled atom clouds, a small component o

non-condensed atoms co-exists with thecondensate and creates interactions withpropagating shock waves that are complexand o undamental importance or theunderstanding o superfuidity. o identiythese interactions, it is important to separateout the shock wave dynamics due entirelyto the condensate component. On page 46o this issue, Wan and colleagues describea system or studying superfuid-likephenomena7. By taking advantage o the actthat the interaction o laser light with certaintypes o nonlinear optical crystals is governedby similar equations to those that governthe dynamics in BECs, they demonstrate an

experimentally simple, all-optical systemor studying superfuid-like shock waves.Because laser elds are perectly coherent,the optical system mimics the behaviour o apure condensate one that is ree rom theinfuence o non-condensed components.

Shock waves have startling eects,experienced in everyday lie when sonicbooms are generated by supersonic aircra,and they have been studied in the contexto classical gases and fuids or many years.When a fuid body is subject to a localizeddisturbance in its density, such as that caused

by an object passing through it or by aninjected laser pulse, it will generate soundwaves that propagate outwards rom thedisturbance. I this disturbance is su cientlystrong, or instance when caused by a high-speed impact or by a high-energy laser pulse,the speed o sound, which increases withdensity, varies greatly across the disturbance.For a local density increase (hump), thecentral, dense part o the propagating wavewill rapidly catch up with the leading edgeo the wave. Tis in turn generates the steepront edge o a shock waves characteristic

How shock waves travel through a superfluid provides clues to understanding the deeper

nature of BoseEinstein condensation. An optical analogue that behaves as a pure superfluid

could tell us what these clues mean.

Figure 1 Exotic physics caused by shock waves in a BoseEinstein condensate.a, The density-dependent speed

of sound causes a propagating dark shock front (characterized by a drop in density relative to the surrounding

medium) to broaden at its leading edge, and sharpen at its trailing edge. b, An initial dip in the density of an

otherwise dense (black) BEC (at t= 0.0 ms) develops into a shock front that sheds dark solitons in its wake. The

solitons are observed as curved, low-density (white) fronts (at t= 3.5 ms). These nonlinear excitations maintain

their shape over large propagation distances owing to cancellation of dispersive effects by nonlinear atomatom

interactions in the fluid. The bar indicates the grey scale for atom density. (Numerical simulations: Naomi Ginsberg,

Harvard Univ., thesis in preparation.) c, A density depression in a BEC (t= 0.0 ms) develops into a shock front

that sheds dark solitons (t= 7.8 ms). Variation of atom density along the soliton front leads to a peculiar snake

instability (t= 16.2 ms). The points of high curvature along the front subsequently act as nucleation sites for

quantized vortices seen as white (low-density) cores (t= 29.0 ms). The vortices are created in pairs of opposite

circulation. (Reprinted from Europhys. News35, 3339; 2004. Copyright EPS and EDP Sciences.)

7.8 ms0.0 ms

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NEWS & VIEWS

14 nature physics| VOL 3 | JANUARY 2007 | www.nature.com/naturephysics

asymmetric shape. I a localized densitydepletion (dark hump) is induced instead,the back edge o the disturbance develops ashock ront (see Fig. 1a).

In a classical fuid, wave dynamics isdominated by dissipative eects caused byviscosity in the fuid. Tis results in well-dened, propagating shock ronts where

density and velocity change abruptly in alocalized region across the ront. But insuperfuid BECs, the dynamics o shockwaves is governed by dispersion ratherthan dissipation, and this greatly alters thebehaviour. As a consequence o the coherent(lock-step) nature o a BEC, when a densityhump is induced, the longitudinal shapeo the resulting propagating shock rontsdevelops pronounced wiggles. Tese wigglesare a result o nonlinear wave mixing andintererence eects in the coherent fuid.

In addition to the potential insightsthey provide into the physics o BECs

and related systems, superfuid shockwaves are o interest in their own right ortheir rich nonlinear excitation behaviour(Fig. 1b and c). Te creation o particle-like excitations such as dark solitonsand quantized vortices (the superfuidequivalent o classical tornadoes) representsjust some o the many peculiar phenomenathat have been seen to emerge rom thepropagation o shock waves through BECs3.But, just as in high-energy physics wherethe most interesting physics is oundwhen two particles collide, the real unbegins when multiple superfuid shock

waves interact. For example, in shock

collision experiments in sodium BECs,new, compound particles with a verycomplex structure have been discovered4.Clearly, a rich eld is emerging whereinteresting discrepancies with theory exist.In this respect, the platorm or studyingsuperfuid-like phenomena presented byWan et al. could be very useul.

Te crystal that orms the heart oWans system is one that shows a negative,Kerr-type optical nonlinearity. Te authorsilluminate the input ace o the crystal witha laser eld that consists o a gaussian peaksuperimposed on a uniorm background (ahump-on-background prole). As the eldpropagates through the crystal, the nonlinearresponse o the crystal causes the gaussianpeak to spread in a way that directly mimicsthe outward propagation o a shock wave ina two-dimensional BEC. Te light eld atthe output ace o the crystal is imaged by aCCD camera. Te strength o the shock is

controlled simply by changing the amplitudeo the gaussian peak with respect to thebackground eld. And more importantly, bysuperimposing multiple peaks on this eld,the system allows the generation and study omultiple colliding shock ronts.

Te theory with which the authorsanalyse their results is based on Maxwellsequations. Although the GrossPitaevskiiequation, with which shock behaviour inatomic condensates is usually analysed,provides a similar mean-eld description,inevitable dierences between the twoexist. Moreover, it should be noted that

the steep gradients in density and velocity

that develop at shock ronts could leadto a local breakdown o the mean-elddescription, which could exacerbate thesedierences. Recent calculations indicatethat a depletion o an atomic BEC maytake place at shock ronts originating romdark humps induced in the condensate8.Tis depletion is associated with local

excitations o atoms out o the condensateand would cause non-condensed atomsto ll the otherwise depleted cores o darksolitons and, probably, o vortices as well.

At the very least, being able to compareshock waves propagating in an atomic BECwith those in the optical system shouldallow the contribution to shock dynamicsrom the BEC component to be identiedand separated rom dynamics inducedby, or example, interactions o quantizedvortices with non-condensed atoms. Indeed,such insight could be o great value toour understanding o the breakdown o

superfuidity and superconductivity anissue that even on its own is o tremendousimportance, rom a undamental perspectiveand or practical applications.

References1. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E.

& Cornell, E. A. Science269, 198201 (1995).

2. Pitaevskii, L. & Stingari, S. BoseEinstein Condensation

(Clarendon, Oxord, 2003).

3. Dutton, Z., Budde, M., Slowe, C. & Hau, L. V. Science

293, 663668 (2001).

4. Ginsberg, N., Brand, J. & Hau L. V.Phys. Rev. Lett.

94, 040403 (2005).

5. Simula, . P.et al.Phys. Rev. Lett. 94, 080404 (2005).

6. Hoeer, M. A. et al.Phys. Rev. A74, 023623 (2006).

7. Wan, W., Jia, S. & Fleischer, J. W. Nature Phys. 3, 4651 (2007).

8. Damski, B. Phys. Rev. A73, 043601 (2006).

Quasars, along with supernovae and -raybursts, are the most energetic sources oelectromagnetic radiation in the Universe.About two billion light-years away, thenearest bright quasar, 3C 273 in the Virgoconstellation, emits a powerul radio jet.

X-ray diagnosis of a quasarASTROPARTICLE PHYSICS

Markos Georganopoulos et al. propose to useX-ray emission rom the jet to investigate itsorigin (Astrophys. J., in the press).

Although most astronomers believe thata quasar is powered by a supermassive blackhole, its not clear how that black-hole enginelights up a quasar. Inormation on the energytransport mechanism would reveal how blackholes were ormed in the early Universe.Similarly, it might explain why there are nosuch quasars in active galaxies nearby.

Tere are two main theories or theX-ray emission: inverse external Compton(EC) scattering rom relativistic electronsthat scatter cosmic microwave background(CMB) photons; and synchrotron emissionrom eV electrons the same mechanismas or radio emission rom the jet, but romanother population o electrons.

o complicate matters, synchrotronradiation would also scatter CMB photons,

so would look similar to the EC model.But as the two candidate processesinvolve electron energies diering bytwo orders o magnitude, the two energyscales should lead to dierent -raydynamics. Georganopoulos et al. havecome up with a set o diagnostics todistinguish the two models using existingand uture -ray detectors.

I no GeV or eV emission isdetected, or only low-level GeV, therewould be no additional constraint orthe synchrotron model but the ECmodel would lose support. Detectiono high-level GeV or eV emissionwould conrm the synchrotron model.Although the authors believe that thelatter is the most likely outcome, theyacknowledge that uture observationscould reute both hypotheses.

May Chiao