super-heisenberg scaling, spin squeezing & quantum

R.J.Sewell, M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, G. Colangelo, F. Martin Ciurana, M.W. Mitchell

Super-Heisenberg scaling, spin squeezing & quantum nondemolition measurement of atomic spins

QuAMP, Swansea9 September 2013

R.J.S, M. Napolitano, G. Colangelo, N. Behbood, F. Martin Ciurana & M.W. Mitchell*

M. Koschorreck(Cambridge)

www.mitchellgroup.icfo.es

http://www.mitchellgroup.icfo.es

http://www.mitchellgroup.icfo.es

11. Shen, Z.-X., Spicer, W. E., King, D. M., Dessau, D. S. & Wells, B. O. Photoemission studies of high-Tc

superconductors: The superconducting gap. Science 267, 343–350 (1995).

12. Damascelli, A., Shen, Z.-X. & Hussain, Z. Angle-resolved photoemission spectroscopy of the cuprate

superconductors. Preprint at karXiV.org/cond-mat/0208504l (2002).13. Campuzano, J. C., Norman, M. R. & Randeria, M. Photoemission in the high Tc superconductors.

Preprint at karXiV.org/cond-mat/0209476l (2002).14. Byers, J. M., Flatte, M. E. & Scalapino, D. J. Influence of gap extrema on tunneling conductance near an

impurity in an anisotropic superconductor. Phys. Rev. Lett. 71, 3363 (1993).

15. Wang, Q. & Lee, D.-H. Quasiparticle scattering interference in high temperature superconductors.

Phys. Rev. B 67, 020511 (2003).

16. Zhang, D.&Ting, C. S. Energy-dependent LDOSmodulation in cuprate superconductors.Phys. Rev. B

67, 020511 (2003)

17. Fedorov, A. V. et al. Temperature dependent photoemission studies of optimally doped

Bi2Sr2CaCu2O8þd. Phys. Rev. Lett. 82, 2179–2183 (1999).

18. Feng, D. L. et al. Signature of superfluid density in the single-particle excitation spectrum of

Bi2Sr2CaCu2O8þd. Science 289, 277–281 (2000).

19. Ding, H. et al. Coherent quasiparticle weight and its connection to high-Tc superconductivity from

angle-resolved photoemission. Phys. Rev. Lett. 87, 227001 (2001).

20. Johnson, P. D. et al. Doping and temperature dependence of the mass enhancement observed in the

cuprate Bi2Sr2CaCu2O8þd. Phys. Rev. Lett. 87, 177007 (2001).

21. Lanzara, A. et al. Evidence for ubiquitous strong electron-phonon coupling in high-temperature

superconductors. Nature 412, 510–514 (2001).

22. Valla, T. et al. Evidence for quantum critical behavior in the optimally doped cuprate


23. Hoffman, J. E. et al.A four unit cell periodic pattern of quasiparticle states surrounding vortex cores in


24. Crommie, M. F., Lutz, C. P. & Eigler, D.M. Imaging standing waves in a two-dimensional electron gas.

Nature 363, 524 (1993).

25. Howald, C., Eisaki, H., Kaneko, N. & Kapitulnik, A. Coexistence of charged stripes and

superconductivity in Bi2Sr2CaCu2O8 þ d. Preprint at karXiV.org/cond-mat/0201546l (2002).26. Polkovnikov, A., Sachdev, S. & Vojta, M. Spin collective mode and quasiparticle contributions to

STM spectra of d-wave superconductors with pinning. Preprint at karXiV.org/cond-mat/0208334l(2002).

27. Podolsky, D. et al. Translational symmetry breaking in the superconducting state of the cuprates:

Analysis of the quasiparticle density of states. Preprint at karXiV.org/cond-mat/0204011l (2002).28. Howald, C. et al. Periodic density of states modulations in superconducting Bi2Sr2CaCu2O8þd. Phys.

Rev. B 67, 014533 (2003).

29. Kivelson, S. A. et al. How to detect fluctuating order in the high-temperature superconductors.

Preprint at karXiV.org/cond-mat/0210683l (2002).30. Campuzano, J. C. et al. Direct observation of particle-hole mixing in the superconducting state by

angle-resolved photoemission. Phys. Rev. B 53, R14737–R14740 (1996).

Acknowledgements We thank J. C. Campuzano, M. E. Flatte, P. Johnson, S. A. Kivelson, B. Lake,R. B. Laughlin, J. W. Loram, M. Norman, D. J. Scalapino, Z.-X. Shen, J. Tranquada and J. Zaanenfor discussions and communications. This work was supported by an LDRD from the LawrenceBerkeley National Laboratory, the ONR, the NSF, and by Grant-in-Aid for Scientific Research onPriority Area (Japan), a COE grant from the Ministry of Education (Japan), and NEDO (Japan).J.E.H. is grateful for support from a Hertz Fellowship.

Competing interests statement The authors declare that they have no competing financialinterests.

Correspondence and requests for materials should be addressed to J.C.D.(e-mail: [email protected]).

..............................................................

A subfemtotesla multichannelatomic magnetometerI. K. Kominis*†, T. W. Kornack*, J. C. Allred‡ & M. V. Romalis*

*Department of Physics, Princeton University, Princeton, New Jersey 08544, USA‡Department of Physics, University of Washington, Seattle, Washington 98195,USA.............................................................................................................................................................................

The magnetic field is one of the most fundamental and ubiqui-tous physical observables, carrying information about all elec-tromagnetic phenomena. For the past 30 years, superconductingquantum interference devices (SQUIDs) operating at 4 Khave been unchallenged as ultrahigh-sensitivity magnetic fielddetectors1, with a sensitivity reaching down to 1 fTHz21/2

(1 fT 5 10215 T). They have enabled, for example, mapping of

the magnetic fields produced by the brain, and localization of theunderlying electrical activity (magnetoencephalography).Atomic magnetometers, based on detection of Larmor spinprecession of optically pumped atoms, have approached similarlevels of sensitivity using large measurement volumes2,3, but havemuch lower sensitivity in the more compact designs required formagnetic imaging applications4. Higher sensitivity and spatialresolution combined with non-cryogenic operation of atomicmagnetometers would enable new applications, including thepossibility of mapping non-invasively the cortical modules in thebrain. Here we describe a new spin-exchange relaxation-free(SERF) atomic magnetometer, and demonstrate magnetic fieldsensitivity of 0.54 fTHz21/2 with a measurement volume of only0.3 cm3. Theoretical analysis shows that fundamental sensitivitylimits of this device are below 0.01 fTHz21/2. We also demon-strate simple multichannel operation of the magnetometer, andlocalization of magnetic field sources with a resolution of 2mm.

Ultrasensitive magnetometers have found a wide range of appli-cations, from condensed-matter experiments5 and gravitationalwave detection6, to detection of NMR signals7,8, studies of palaeo-magnetism9, non-destructive testing10, and underwater ordinancedetection11. However, themost notable application ofmagnetic fieldsensors has been in the area of biomagnetism12,13, that is, thedetection of the weak magnetic fields produced by the humanbrain, heart and other organs. For example, measurements of themagnetic field produced by the brain are used to diagnose epilepsy,and to study neural responses to auditory and visual stimuli. Low-temperature superconducting quantum interference device(SQUID) sensors14–16, which so far have dominated all of theabove-mentioned applications, have reached sensitivity levels of0.9–1.4 fTHz21/2 with a pick-up coil area of the order of 1 cm2. Inthe low-frequency range of interest for biomagnetic studies(,100 Hz) their noise is typically somewhat higher, whereascommercial SQUID magnetometers typically17 have noise ofabout 5 fTHz21/2, partly due to magnetic noise generated byelectrically conductive radiation-shielding of the liquid-heliumdewars18.

Atomic magnetometers rely on a measurement of the Larmorprecession of spin-polarized atoms in a magnetic field19. Thefundamental, shot-noise-limited sensitivity of an atomic magne-tometer is given by

dB¼ 1

gffiffiffiffiffiffiffiffiffiffiffiffiffinT2Vt

p ð1Þ

where n is the number density of atoms, g is their gyromagneticratio, T2 is the transverse spin relaxation time,V is themeasurementvolume, and t is the measurement time20. The value of g in equation(1) depends on the details of the magnetometer operation. For acommonly usedZeeman transitionwithDm ¼ 1,g¼ gmB=!hð2Iþ 1Þ;where I is the nuclear spin of the alkali metal, mB is the Bohrmagneton, and g < 2. In our magnetometer operating at zero field,the effective g for sensitivity estimates is g¼ gmB=!h (equation (7) ofref. 21).

Most atomic magnetometers use a polarized alkali-metal vapour(K, Rb, Cs), and their transverse spin relaxation time is limited byspin-exchange collisions between alkali atoms. In one implementa-tion of such a magnetometer3,22, the shot-noise sensitivity wasestimated to be 0.3 fTHz21/2 for a 500-cm3 cell. In another state-of-the-art magnetometer2, the actual sensitivity was estimated to be1.8 fTHz21/2 with a bandwidth of about 1Hz and a measurementvolume of 1,800 cm3.

We recently demonstrated operation of a spin-exchange relaxa-tion-free (SERF) magnetometer21 where broadening due to spin-exchange collisions is completely eliminated by operating at a highalkali-metal density in a very low magnetic field. The remainingbroadening is determined by spin-relaxation collisions, whichtransfer spin angular momentum to rotational momentum of† Present address: Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.

letters to nature

NATURE | VOL 422 | 10 APRIL 2003 | www.nature.com/nature596 © 2003 Nature Publishing Group

Subpicotesla atomic magnetometry witha microfabricated vapour cell

VISHAL SHAH1,2, SVENJA KNAPPE1, PETER D. D. SCHWINDT3 AND JOHN KITCHING1*1National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA2Department of Physics, University of Colorado, Boulder, Colorado 80309, USA3Sandia National Laboratories, MS 1082, PO Box 5800, Albuquerque, New Mexico 87185, USA

*e-mail: [email protected]

Published online: 1 November 2007; doi:10.1038/nphoton.2007.201

Highly sensitive magnetometers capable of measuring magneticfields below 1 pT have an impact on areas as diverse asgeophysical surveying1, the detection of unexploded ordinance2,space science3, nuclear magnetic resonance4,5, health care6 andperimeter and remote monitoring. Recently, it has been shownthat laboratory optical magnetometers7,8, based on theprecession of the spins of alkali atoms in the vapour phase,could achieve sensitivities in the femtotesla range, comparableto9–12, or even exceeding13, those of superconducting quantuminterference devices6. We demonstrate here an atomicmagnetometer based on a millimetre-scale microfabricatedalkali vapour cell with sensitivity below 70 fT Hz21/2.Additionally, we use a simplified optical configuration thatrequires only a single low-power laser. This result suggests thatmillimetre-scale, low-power femtotesla magnetometers arefeasible, and we support this proposition with a simplesensitivity scaling analysis. Such an instrument would greatlyexpand the range of applications in which atomicmagnetometers could be used.

For decades, superconducting quantum interference device(SQUID) magnetometers have been unrivalled in their ability tomeasure low-frequency magnetic fields with extremely highprecision. Optical magnetometers now share this spotlight, withdemonstrated sensitivities below 1 fT Hz21/2 in a laboratorysetting. This level of sensitivity has helped open the door to theapplication of atomic magnetometers to imaging of heart14 andbrain tissue15 and the detection of nuclear magnetic resonance(NMR) and nuclear quadrupole resonance (NQR)4,5,16. The keyphysics that underlies several recent advances in opticalmagnetometry is the suppression of spin relaxation originatingfrom spin-exchange collisions between the alkali atoms17 and thegeneration of a large ground-state atomic polarization at lowmagnetic-field strengths. Operation of the magnetometer in thisspin-exchange-relaxation-free (SERF) regime allows for spin-relaxation times over 10 ms, even at alkali atom densities above1014 cm23, and suggests even better sensitivities may be achievedin future instruments.

Despite the exceptional progress in improving the sensitivity ofthese instruments in a laboratory setting, they remain large,complex and difficult to assemble and operate for extendedperiods. Recently, a highly miniaturized atomic magnetic sensorwas demonstrated that was fabricated using the techniques ofmicroelectromechanical systems18 (MEMS). This early device was

12 mm3 in volume and had a sensitivity of 50 pT Hz21/2. Abetter optimized chip-scale magnetometer of similar size butwith a sensitivity of 5 pT Hz21/2 was demonstrated morerecently19, as was an evanescent-wave device with a sensitivity inthe 10 pT Hz21/2 range20.

The vapour cell used in this experiment, shown in Fig. 1a,had interior dimensions of 3 mm ! 2 mm ! 1 mm and wasfabricated with a MEMS process as described previously21,22.The zero-field magnetic resonance was measured by meansof optical absorption of a single circularly polarized lightfield23 propagating in a direction perpendicular to the staticmagnetic field, B0 (Fig. 1b). The magnetic resonance, shownin Fig. 1c, has a full-width at half-maximum of 83 nT(corresponding to 580 Hz) and a transmission contrast of 40%.The linewidth obtained by extrapolating to zero light intensitywas around 15 nT (105 Hz). This linewidth is lower by a factorof 50 than the estimated spin-exchange-limited linewidth atthis alkali atom density and corresponds closely to thelinewidth limited by alkali–buffer-gas spin destruction10,24. Thisclearly indicates that the magnetometer is operating in theSERF regime.

From the resonance characteristics and noise level, a magnetic-field equivalent noise spectrum was determined and is shown bythe red trace in Fig. 1d. Throughout much of the spectrumbetween 10 Hz and 200 Hz, the noise is found to be below70 fT Hz21/2. This SERF measurement represents animprovement by a factor of almost 100 over previous results inmicrofabricated vapour cells19. Excess amplitude noise from thelaser is thought to be the main factor limiting sensitivity in thesingle-beam configuration. For comparison, the sensitivityobtained under similar conditions using an orthogonalpump–probe configuration13 is shown by the grey trace inFig. 1d. The reduced noise in the 100–200-Hz band occurs inpart because the laser-amplitude noise is suppressed by thedifferential detection in the Faraday rotation measurement.The use of a single-light-field configuration leads to aconsiderable simplification in the optical arrangement whencompared with the two-beam pump–probe configuration, butsuffers from increased susceptibility to laser-amplitude noise. Wenote, however, that laser-amplitude noise cancellation can beachieved in the single-beam configuration when the system isoperated in the gradiometer mode or when the optical power atthe entrance to the cell is monitored.

LETTERS

nature photonics | VOL 1 | NOVEMBER 2007 | www.nature.com/naturephotonics 649

MCG measurements the CSAM sensor head was mounteddirectly underneath the center of the SQUID array in which57 SQUIDs were arranged in a plane at the Dewar bottom.These SQUIDs measured the !vertical" z-component of thecardiomagnetic field. The modulation field of the CSAM dis-torted the signal of the central sensors in the bottom plane ofthe SQUID array but the 45 sensors located several centime-ters from the CSAM operated normally.

The CSAM was positioned directly above the left chestof a recumbent male human subject and the z-component ofthe magnetic field, perpendicular to the subject’s torso, wasmeasured. The intrinsic bandwidth of the CSAM wasroughly 1 kHz, limited by the width of the resonance line,and the lock-in integration time constant was set to 1 ms. TheCSAM control box was placed outside the shielded room,yet within the rf shield, and the optical fibers connecting thecontrol box to the sensor head were routed through smallholes to the interior !Fig. 1".

The CSAM output signal was calibrated independentlywith two coils in the vicinity of the sensor. The output of theCSAM and 45 SQUID magnetometers oriented in the z di-rection were simultaneously recorded at 1000 samples/s, andan antialiasing filter was set below 500 Hz. A digital phase-adapted sine-wave filter was used to suppress power lineinterference at 50 and 100 Hz in the CSAM signal. Thisinterference was most likely caused by the heater power sup-ply. Several runs were performed on two subjects at differentpositions over the chest, each recording lasting for 5 min.

Continuous raw data are shown in Figs. 2!a" and 2!b" forone of the off-center SQUIDs and the CSAM. The QRS-complex is clearly visible in both data sets, as well as theT-wave. It can be seen that the optical sensor exhibits morenoise than the SQUID sensor. The higher noise is partly off-set by larger signal amplitudes due to the proximity of theoptical sensor to the chest of the subject, with a distance ofonly 5 mm between sensor and skin. The CSAM R-peak isroughly three times stronger than the corresponding SQUIDsignal. This is in agreement with an inverse cubic field at-tenuation with distance and estimated distances betweenCSAM and heart of 5.0 cm and SQUID and heart of 7.5 cm.In order to average the data, a threshold was placed on thevalue of the R-peak in the signal of one of the SQUID sen-sors. The time that the signal crossed this threshold was usedas a trigger to synchronize the signals for averaging. An av-

erage over 200 beats is shown in Figs. 2!c" and 2!d". Nowdetailed features of the QRS-complex and the T-wave areclearly visible. The P-wave exhibits a morphology clearlydifferent from the SQUID-MCG, probably due to the differ-ence in location between SQUID and CSAM. Besides theSQUID-MCG shown here 45 other channels were measuredencircling the CSAM, which was placed centrally below theSQUID array. The P-wave shows a gradual change across theSQUID array signals and the morphology of the CSAMP-wave is consistent with this. These measurements demon-strate the similar capabilities of the two types of sensors andvalidate the signal recorded with the CSAM.

MRX refers to measurements of the magnetization decayof magnetic nanoparticles after removal of a magnetizingfield that initially aligns their magnetic moments.3 The relax-ation signals are specific to the magnetic nanoparticles with-out any interference from surrounding tissue backgroundsand their amplitudes are proportional to the iron content inthe nanoparticle sample. Two different thermally induced re-laxation processes can be distinguished: The Brownian relax-ation process in which rotation of the nanoparticles results ina decay of the magnetization of the sample with a relaxationtime !B that is proportional to the particle volume V. In thesecond relaxation process, the Néel relaxation, the magneticmoment changes its orientation within the particle overcom-ing the energy barrier constituted by the particles !crystal andshape" anisotropy resulting in an exponential relaxation time!N#exp!V". Furthermore, real nanoparticle ensembles al-ways contain a range of particle sizes, thereby leading to asuperposition of exponential decays having different timeconstants.3 MRX has been proven useful for localization,quantification, and imaging of magnetic nanoparticles in-serted into biological tissue in medical applications such asmagnetic drug targeting14 or hyperthermia.15 Iron oxide-based nanoparticles, usually suspended in an aqueous me-dium and encapsulated by an organic shell to enhance stabil-ity and biocompatibility, are most commonly used in suchapplications. We prepared a series of nanoparticle samples16

with decreasing total iron content 400, 40, and 4 "g!140 "l total volume, stock suspension diluted 1:10, 1:100,and 1:1000 in distilled water and freeze-dried to suppressBrownian relaxation". Each sample was positioned 10 mmbelow the CSAM and magnetized for 3 s in a homogenousmagnetic field of 1 mT. After the field had been turned off,the decaying residual magnetic field from the magnetic nano-particles was recorded by the CSAM over 10 s with an inte-

FIG. 1. !Color online" Photograph of the measurement setup from the side.The CSAM is attached to the bottom of the Dewar containing the SQUIDsensors. The optical fibers are fed to a control unit outside the shieldedroom. The Dewar can be positioned freely above the chest of the subject.!Top left inset" Schematic of the CSAM arrangement. Modulation coilsaround the sensor head allow the measurement of the z-component of themagnetic field.

B/

pT

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CSAMCSAM

SQUID SQUID

0

0

20

40

60

50

100

150

T waveP waveQ

R

S

FIG. 2. Raw MCG signal of a subject detected simultaneously with !a" theCSAM and !b" a SQUID. Averaged MCG signal !200 beats" of the sameperson measured simultaneously with !c" the CSAM and !d" a SQUID.

133703-2 Knappe et al. Appl. Phys. Lett. 97, 133703 !2010"

Downloaded 15 Mar 2012 to 147.83.123.131. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Cross-validation of microfabricated atomic magnetometerswith superconducting quantum interference devices forbiomagnetic applications

Svenja Knappe,1,a! Tilmann H. Sander,2 Olaf Kosch,2 Frank Wiekhorst,2 John Kitching,1

and Lutz Trahms21NIST, Time and Frequency Division, 325 Broadway, Boulder, Colorado 80305, USA2Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, 10587 Berlin, Germany

!Received 8 June 2010; accepted 27 August 2010; published online 28 September 2010"

We compare the performance of a chip-scale atomic magnetometer !CSAM" with that of asuperconducting quantum interference device !SQUID" sensor in two biomedical applications.Magnetocardiograms !MCGs" of healthy human subjects were measured simultaneously by aCSAM and a multichannel SQUID sensor in a magnetically shielded room. The typical features ofMCGs are resolved by the CSAM, matching the SQUID results. Magnetorelaxometry !MRX"signals of iron nanoparticles were also obtained with the CSAM and compared to similarmeasurements with a SQUID. © 2010 American Institute of Physics. #doi:10.1063/1.3491548$

The field of biomagnetic measurements is largely domi-nated by magnetic sensors based on superconducting quan-tum interference devices !SQUIDs". The high sensitivity ofthese devices in the frequency band from 1 Hz to 1 kHzenables measurements of many biologically relevant mag-netic sources inside the human body,1 as well as low fieldmagnetic resonance imaging.2 In addition, SQUIDs are usedin magnetorelaxometry !MRX",3 which provides a quantita-tive and spatially resolved imaging through the detection ofmagnetic nanoparticles.

Because SQUIDs require cryogenic cooling, which im-plies significant cost and operational complexity, it is desir-able to investigate the use of alternative sensors for some ofthese measurements. Recently, magnetometers based on theprecession of atomic spins have demonstrated sensitivities!noise equivalent magnetic field" of 0.2 fT /Hz1/2 in labora-tory settings over a limited frequency range.4 With theseatomic or optical magnetometers, measurements of the mag-netic fields produced by the human brain5 and heart6 havebeen carried out. These instruments are based on glass-blownvapor cells with volumes of several thousand cubic millime-ters; a complete measurement apparatus typically occupiesseveral tens of liters.

Chip-scale atomic magnetometers !CSAMs" !Ref. 7" arebased on microfabricated, millimeter-scale alkali vapor cellsintegrated with small optical components such as diode la-sers and fiber optics. These devices have reached sensitivitiesbelow 5 fT /Hz1/2 at 100 Hz in tabletop setups8 and the fun-damental sensitivity limits are better than this by more thanan order of magnitude.9 Advantages of these sensors overlarger conventional optical magnetometers include lower-power operation, the possibility of low-cost manufacturingof large arrays, the arrangement in flexible or conformal ge-ometries around the magnetic field source to be measured,a higher intrinsic bandwidth and enhanced proximity tosources.

In this paper we investigate the use of an optical fiber-coupled CSAM in two typical biomagnetic measurements,

magnetocardiogram !MCG" and MRX. Simultaneous mea-surements of biomagnetic signals from humans with theCSAM and a SQUID allow a clear comparison of these twosensors in a typical biomagnetic measurement setting. Thecontinuous raw signals obtained by the CSAM show manyfeatures present in the SQUID measurements and confirmthat CSAMs are a promising technology for biomagnetic ap-plications.

The CSAM consisted of a microfabricated silicon/glasssensor head of volume 0.75 cm3, coupled to a portable con-trol box by optical fibers of length 5 m. At the heart of thesensor head was cell of volume 8 mm3 containing 87Rb at-oms along with roughly 1 amagat of nitrogen. The distancebetween the center of the vapor cell and the outside of thesensor head housing was 2.5 mm, defining the minimumdistance of the sensitive volume from a magnetic source.Thermal isolation enabled the outside surface of the sensor toremain at room temperature, while the cell was heated to150 °C. Details of the fabrication and design of the sensorcan be found elsewhere.10

The laser light transmitted through the fibers opticallypumped the atoms into an oriented state and simultaneouslyprobed the effects of the magnetic field.9 The CSAMachieved sensitivities of several hundred fT / %Hz at frequen-cies between 10 and 100 Hz when operated at low magneticfields and high alkali densities, where spin-exchange colli-sions between the Rb atoms can be suppressed.11

In order to reduce 1/f noise in the optical sensor, analternating transverse magnetic field at 2.2 kHz was appliedto the sensor head by use of a pair of small coils outside ofthe sensor.10 A dispersive resonance signal was detected withphase-sensitive detection at 2.2 kHz. A bias field cancelledany residual static background field and tuned the magneto-meter to the zero crossing of this resonance. The lock-inoutput was then proportional, over a range of roughly 100nT, to the time-varying component of the local magnetic fieldthat was parallel to the modulation field.

Biomagnetic fields were measured with the CSAM andsimultaneously with a multichannel low-temperature SQUIDmagnetometer system.12 The experiment was performed in-side the magnetically shielded room BMSR-2.13 For thea"Also with University of Colorado, Boulder 80309, USA.

APPLIED PHYSICS LETTERS 97, 133703 !2010"

0003-6951/2010/97"13!/133703/3/$30.00 © 2010 American Institute of Physics97, 133703-1

Downloaded 15 Mar 2012 to 147.83.123.131. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Kominis, Nature 422, 596 (2003)

Shah, Nat. Phot. 1, 649 (2007)

Knappe, APL 97, 133703 (2010)

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4 Sewell, et al. PRL 109, 253605 (2012)

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Bi ,m1 HmTL

B i,m

2HmTL

mm1= 0.91mTsm1= 40nT

0.8 0.9 1.0Bx ,m1HmTL

mm2= 0.89mTsm2= 41nT

mm2 1=-14nTsm2 1=9nT

-0.1 0 0.1Bx ,m2 m1 HmTL

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• background subtraction to 9 nT RMS• entirely limited by environmental noise

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pump Jx

probe 87Rb atoms

L2

PD3

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polarimeterPD1

PD2PBS

WPSy

z

x Sx

B

87Rb D2 line

f=1

f’

�

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52P3/2

collective spin

Jx

Jy

Jz

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probe

H = 1

Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

Jx

Jy

Jz

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Sx

�

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H = 1

Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

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probe

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Jx

Jy

Jz

Sx

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Jx

Jy

Jz

Jx

Jy

Jz

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Jz

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(Sx

Jx

+ Sy

Jy

)

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QND with spin-1/2 atoms

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Sx

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H = 1

Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

tensorial light shift

QND with large spin atoms

� / Fz

Sx

Koschorreck, et al. PRL 105, 093602(2010)Jx

Jy

Jz

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Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

Jx

Jy

Jz

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/2

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Sx



Jy

Jz

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Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

� / K

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Jy

Jz

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Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

+

Jx

Jy

Jz

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Jy

Jz

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probe

H = 1

Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)

Jx

Jy

Jz

K

+ =

Jx

Jy

Jz

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-Sx



Jy

Jz

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� ⌘ cov(�1,�2)

var(�1)

HaL

-1 0 1

-1

0

1

f1 H103 spinsL

f 2H103

spinsL HbL

-1 0 1f1 H103 spinsL

HcL

-1 0 1f1 H103 spinsL

conditional variance

R.J.S. et al. PRL 109, 253695 (2012)

Jx

Jy

Jz

Jx

Jy

JzK

Jx

Jy

JzKQND1 QND2

var(K|�1) ⌘ var(�1 � ��2)

R.J.S. et al. PRL 109, 253695 (2012)

Squeezing & entanglement

Jx

K

3dB

projection noise

spin squeezing

89%

QND measurement?

Grangier et al. Nature 396, 527 (1998)

Jy

Jz

QND?

Jy

Jz

Qua

ntum

Sta

te P

rep

(QSP

)

Information-Damage Tradeoff (IDT)

Jx

Jy

Jz

Jx

Jy

JzK

Jx

Jy

JzKQND1 QND2

Jx

Jy

JzKQND3

Mitchell et al. NJP 14, 085021 (2012)

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f1 H103 spinsL

f 2H103

spinsL

-1 0 1

f1 H103 spinsL

f 3H103

spinsL

Repeated measurements

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Classical

QSP

IDT

QND

d0=1 25

1020

50100h=0.05

0.10.15

0.20.25

@7,9D@8D@10D

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0.5

1.0

1.5

2.0

Transfer coefficients: Tm+Ts

Conditionalvariance:DX s

m

[7] Appel, Proc. Natl. Acad. Sci. USA 106, 10960 (2009) [8] Schleier-Smith PRL 104, 073604 (2010)[9] Chen PRL 106, 133601 (2011)[10] Sewell PRL 109, 253605 (2012)

R.J.S. et al. Nat. Phot. 7, 517 (2013)

QND measurement of atomic spins

�

Sx

probe

Quantum-enhanced magnetometry

Jx

Jy

Jz

B Jy / Bz

�

R.J.S. et al. PRL 109, 253695 (2012)

�

Sx

probe

Jx

Jy

Jz

B

/ Sx

K = sin ✓Jy

✓ ⌘ 2Sx

/2

Jy / Bz

�

R.J.S. et al. PRL 109, 253695 (2012)


Jx

15%

R.J.S. et al. PRL 109, 253695 (2012)


Sx

probe

Sz

Sy

Sx

Jx

Jy

Jz

B

/ Sx

K = sin ✓Jy

✓ ⌘ 2Sx

/2

Jy / Bz

Sy

=12

2S2x

Jy

�� / Jy

R.J.S. et al. PRL 109, 253695 (2012)


Sx

probe

Sz

Sy

Sx

Jx

Jy

Jz

B

/ Sx

K = sin ✓Jy

✓ ⌘ 2Sx

/2

Jy / Bz

Sy

=12

2S2x

Jy

�� / Jy

R.J.S. et al. PRL 109, 253695 (2012)

Nonlinear quantum metrology

nonlinear Faraday rotation

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Jx H105 spinsL

J yH103

spinsL

J x=2.8¥105

Jx=1.8¥

105

Jx=1.2¥10

5

Jx=0.5¥105

0 25 50 75 1000

25

50

75

100

125

SxHinL H106 photonsL

S yHoutL H10

3photonsL

Bz = 109± 2 nT

Sy

=12

2S2x

Jy

Jy / Bz

Nonlinear read-out

�Jy =1

12N�3/2

L

Super-Heisenberg scaling

R.J.S. et al. submitted (2013)

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projection noise0 50 100 150 2000

1

2

DFH103

spinsL

AOC measurement

nonlinear Faraday rotationLTE measurement NL H106 photonsL

106 107 108103

105

107

NL HphotonsL

DJ yHspi

nsL

DF zHspi

nsL

Sx

probe

Sz

Sy

SxJx

Jy

Jz

B Jy / Bz

�� / Jy

Sz = 2

Sx

Jy

Linear read-out

H = 1

Sz

Jz

+ 2

(Sx

Jx

+ Sy

Jy

)


Sx

probe

Sz

Sy

Sx

Jx

Jy

Jz

B

/ Sx

K = sin ✓Jy

✓ ⌘ 2Sx

/2

Jy / Bz

�� / Jy

Sz = 2

Sx

Jy

Linear read-out


�Jy =1

12N�3/2

L

Super-Heisenberg scaling


Ê

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projection noise0 50 100 150 2000

1

2

DFH103

spinsL

AOC measurement

nonlinear Faraday rotationLTE measurement NL H106 photonsL

106 107 108103

105

107

NL HphotonsL

DJ yHspi

nsL

DF zHspi

nsL

Nonlinear beats linear readout


hgNL=0.

1h gNL=0.5

LTE

AOC

AOC

LTE

-0.2 0 0.2 0.4104

106

108

1010

Detuning HGHzL

NLHpho

tonsL

squeezing

-0.2 0 0.20.4

0.6

0.8

1.0

Detuning HGHzLx m2(a) (b)

R.J.S, M. Napolitano, G. Colangelo, N. Behbood, F. Martin Ciurana & M.W. Mitchell*

M. Koschorreck(Cambridge)

super-heisenberg scaling, spin squeezing & quantum

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