Sensitive measurements using cold atoms冷却原子を用いた精密計測

Quantum Information Processing Summer School 2010Hotel Sunrise Chinen, Okinawa, Japan August 21, 2010

Takuya Hirano平野　琢也

Department of physics, Gakushuin Univerisity学習院大学理学部物理学科

Research on gaseuos BEC

1995 The first creation of gaseous BEC: Rb, Na, Li

two areas

“quantum electronics” “condensed matter physics”

“atomic condensate as a coherent gas”or “Atom lasers”

“BEC as a new quantum fluid”or “BEC as a many-body system”

Nobel Lecture, December 8, 2001By WOLFGANG KETTERLE

applications

cold molecules“ultra-cold chemistry”

atom lithography

precision measurementsgravity, angular velocity,time, magnetic field, …

nonequilibrium physics

unforeseen applications

optical latticequantum simulation

Outline

1. Introduction

2. A brief review of atomic BEC

3. Atomic magnetometer

4. Magnetometer using BEC

5. Quantum magnetometer

Making of atomic BECMagneto-Optical Trap(MOT)

I

I

Blaser

N～109

Magnetic trap

rz

Bias coil Gradient coil(radial)

Curvature coil(axial) current

atoms

Evaporative cooling

RF

10mm

1.2mm

5mm

50MHz

5MHz

2MHz

1.2MHz NBEC～106

1.2mm

1.2m

m

thermal bimodal pure

Time Of Flight measurement of atomic BEC

Critical temperature：～500nK

Atoms in a magnetic trap

87Rb

F=2

F=1

mF2

1

0

-1

-2

Magnetic sublevels

5S1/2

1

0

-1

Hyperfine states

Magnetic potential for F = 2

E 〉= 2mF

〉= 1m F

〉= 0m F

〉−= 1m F

〉−= 2m F

position

No spin degrees of freedom in a Magnetic trap

Atoms in an optical trap

Optical trap

Far-off detuned laser

BEC

Optical trap potential

2E21U ⋅−= α

∆−∝

P

α : polarizability, E :electric fieldP : laser power∆ : detuning (flaser-fresonace)

5S1/2

5P1/2

5P3/2

D1D2

D1 : 795 nmD2 : 780 nm

lens

spin degrees of freedom are liberated in an optical trap

87Rb

850 nm

Lifetime of BEC in Optical Trap - Stretched State (F=2, mF=-2) -

104

105

106

Num

ber

of

conde

nced

atom

s

Trap time (s)

magnetic trapwith rf shield

optical trap

0 2 4 6 8 10 12 14 16

s4~

s7~

trap optical

trap magnetic

τ

τ

loss rate

photon scattering rate

2×10-3 /s

(in the region of N < 1×105)

A short summary of atomic BEC

• Condensation not only in the momentum space but also in the coordinate space

• Typical number of atoms 105-107, dimension 10-100 µm, life time < several sec.

• Internal degrees of freedom are librated in an optical trap: spinor BEC

F =0 (S =0, I =0)4He*, 40Ca,174Yb, 176Yb

87Rb, 23Na, 7Li, 41K

F =1, 2

85Rb F =2, 3133Cs F =3, 452Cr F =3 (S =3, I =0)

unstable

Rb BEC with internal degrees of freedom

・Magnetic sublevels can be coherently coupled, and their populations can be controlled.

・Scattering lengths can be controlled via Feshbach Reaonance.・Rich variety of physics

Spin-exchange collision, Ground-state phase,Phase separation, Spin-squeezing, Quantized vortex, etc…

87Rb

F=1

F=2 -2 -1 0 +1 +2

+1 0 -1

mF low-field seekerhigh-field seeker

Crossed Far-Off Resonant Trap (FORT)

Trap depth: ~ 1.0 µK

r (radial)

z (axial)

g

FORT Beam (radial)

coil for magnetic trap

λ : 850 nm

beam waist radiusradial : 90 µm (21Hz)axial : 32 µm (140Hz)

5 deg.

FORT Beam(axial)

Energy level diagram of 87Rb(ground hyperfine states)

Δ=58 kHz

Initial state

mF =+2+1

0

-1

-2

B = 20 G

14.078 MHz

14.020 MHz

F = 1

6.8 GHz

Zeeman splitting at

B=20GF = 2

mF =+1

0

-1

4x105atoms

Experimental setup and spin-state manipulation

Energy level diagram of 87Rb at 20 G

Time evolution and imaging

TOF15ms for F =2

Transmission0 1

F = 1 and 2

Stern-Gerlachmethod (SG)

18ms for F =1

+2 +1 0 -1 -2-1 0 +1

Spin-state manipulation

F = 2

mF

mF

initial state

+2 +1 0 -1 -2

rf

+1 0 -1

Microwave 6.8GHz+ rf 2.0 MHz

2-photon transition(magnetic dipole transition)

F = 1

|2,-1>

|1,+1>g

z

Optical Magnetometer

review article: D. Budker and M. Romalis, Nature Phys. 3, 227 (2007).

pump light

B

probe light

"A subfemtotesla multichannel atomic magnetometer," I. K. Kominis, T. W. Kornack, J. C. Allred & M. V. Romalis, Nature, Vol. 422, pp. 596-599 (2003).

VtnTB

2

1γ

δ = )12(/ += Ig B hµγ

"A subfemtotesla multichannel atomic magnetometer," I. K. Kominis, T. W. Kornack, J. C. Allred & M. V. Romalis, Nature, Vol. 422, pp. 596-599 (2003).

１チャンネルの雑音（磁気シールドの熱雑音）

隣接チャンネルの差からもとめた固有雑音

Why magnetometer is important: Numerous and diverse applications

• detection of magnetic field from brain and heartnon-invasive studies of individual cortical modules in the brain

• detection of signals of NMR and MRI• detection of microparticles• detection of magnetic anomalies

SQUID脳磁計（横河電機： MEGvision）

Magnetic fields recorded from a brain in response to an auditory stimulation by a series of short clicks (averaged over about 600 presentations). The prominent feature at 100 ms after the stimulus is the evoked response in the auditory cortex, most clearly seen as a difference in the magnetic fields recorded by different channels. In contrast, ambient field drifts, such as those seen before the stimulus, generate similar signals in all channels. (Xia, H., Baranga, A. B., Hoff man, D. & Romalis, M. V. Magnetoencephalography with an atomic magnetometer. Appl. Phys. Lett. 89, 211104 (2006).)

Outline

1. Introduction

2. A brief review of atomic BEC

3. Atomic magnetometer

4. Magnetometer using BEC

5. Quantum magnetometer

"High-Resolution Magnetometry with a Spinor Bose-Einstein Condensate," M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kurn, Phys. Rev. Lett., Vol. 98, 200801 (2007).

Direct Nondestructive Imaging of Magnetization in a Spin-1 Bose-Einstein Gas,J. M. Higbie, L. E. Sadler, S. Inouye, A. P. Chikkatur, S.R. Leslie, K. L. Moore, V. Savalli, and D. M. Stamper-Kurn,PRL 95, 050401 (2005).

"High-Resolution Magnetometry with a Spinor Bose-Einstein Condensate," M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kurn, Phys. Rev. Lett., Vol. 98, 200801 (2007).

Quantum magnetometer

“Squeezed spin states,” Masahiro Kitagawa and Masahito Ueda, Phys. Rev. A 47, 5138–5143 (1993)

Angular momentum system

),,( zyx SSSS =r

Cyclic commutation relation

kijkji SiSS ε=],[222

41))(( kji SSS ≥∆∆

For N atoms in mF=F along the quantization axis z,FNSz =

A magnetic field along y axis causes a rotation of S in x-z plane. Polarization of light propagating along x will be rotated propotional to Sx. This measumentis limited by the projection noise of the atom,

2/2

)( 2 FNSS zx ==∆and light shot noise of polarization measurement.

"Sub-Projection-Noise Sensitivity in Broadband Atomic Magnetometry," M. Koschorreck, M. Napolitano, B. Dubost, and M. W. Mitchell, Phys. Rev. Lett., Vol. 104, 093602 (2010).

Laser cooled Rb atoms, 106, 25µK, dipole trap20 times QND measurement w/o dipole trap

“Spin Squeezing of a Cold Atomic Ensemble with the Nuclear Spin of One-Half”,T. Takano, M. Fuyama, R. Namiki, and Y. Takahashi, Phys. Rev. Lett. 102, 033601 (2009).

"Squeezed-Light Optical Magnetometry," Florian Wolfgramm, Alessandro Cerè, Federica A. Beduini, Ana Predojević, Marco Koschorreck, and Morgan W. Mitchell , Phys. Rev. Lett., Vol. 105, 053601 (2010).

Hot Rb atoms, 794.7 nm, D1 line

-3.2 dB, 3.2 x 10-8 T/√Hz

0 20 40 60 80 100

0

1

2

3

4

Num

ber

of at

om

s (×

10

5 )

Trap time (ms)

8

Decay of F=2, mF=0 BEC in OT at B = 1.5G

Time evolutionmF = -1 0 +1

mF=±1 components appeared during decay process.Atoms in BEC initially polarized in F=2, mF=0 state.

Total-spin-conserved spin-relaxation processTrap time

(ms)

0

10

20

30

80

mF=0mF=±1mF=±2total

Kuwamoto et al. Phys. Rev. A 69, 063604 (2004).

Rb BEC with internal degrees of freedom

C1

C2

Cyclic

Antiferro-magnetic

Ferro-magnetic

Ciobanu, Yip, & Ho, PRA 61, 033607 (2000).Koashi & Ueda, PRL84, 1066 (2000).

731074

74

4202

2

242

1

aaam

c

aam

c

+−=

−=

h

h

π

π

87Rb

F=1

F=2 -2 -1 0 +1 +2

+1 0 -1

mF low-field seekerhigh-field seeker

・ Ground-state phase of 87Rb　BEC

Measured coefficients

( )21 4c mπh( )22 4c mπh

( )0.99 0.06 Ba+ ±( )0.53 0.58 Ba− ±

Widera et al., New Journal of Physics 8, 152 (2006)

87Rb

New quantum phase!!

Hiroki Sato & Masahito UedaPhys.Rev.A 72, 053628 (2005)

Above configuration appears at 100mG.

Evolution of mF = -2 & mF = +2 BEC mixture

mF = -2 & +2initial configuration

If F = 2 87Rb spinorBEC is “cyclic”,

mF = -2 & 0 & +250～300 ms evolution

external magnetic field : 45mGTrap time

(ms)

50

200

mF=-2 mF=+2

300

0

100

Total remained atoms

Relative population

No other components grew ...

Miscibility of BECs

Mixture of binary BECs miscible immiscible?

BECs or BECsBECs

22112

12 aaa > 22112

12 aaa >Phase-separation conditionPhase-separation condition

time-evolution

Difference of scattering length gives rise to phase-separation.

[2] D.S. Hall et al., PRL 81, 1539 (1998).[3] K.M. Mertes et al., PRL 99, 190402 (2007).

(87Rb |F=2, mF= +1> and |1, -1>)

Scattering length in (2,-1) + (1,+1) states

[1] A. Widera et al., New J. Phys. 8, 152 (2006).95.00 Ba( *[2])22 95.68 Ba a= 11 100.40 Ba a= 21 97.66 Ba a=[1] [1] *[2]

Feshbach Resonance in mixed spin states

change in magnetic field strength

R

resonance between atomic and molecular states

T. Voltz et al., PRA 68, 012702(R) (2003).

A. Merte et al., PRL 89, 283202 (2002).

two-body loss rates scattering length

@ 1007 G(1,+1)+(1,+1)

M. Erhard et al., PRL 69, 032705 (2004).

@ 9.09 G

E.G. van Kempen et al., PRL 88, 093201 (2002).

@ 9.1 G

@ 1.9 G

• Prediction • Experiment Magnetic field dependence of two-body loss rates(2,+1)+(1,-1)

(2,-1)+(1,+1)

(2,-1)+(1,+1)

Phase-separation near Feshbach resonance

(2,-1)

(2,-1)

(1,+1)

(1,+1)

現状：磁気シールドルームでＢＥＣ装置の再構築中

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

23:2

9'1

9

01:0

9'1

9

02:4

9'1

9

04:2

9'1

9

06:0

9'1

9

07:4

9'1

9

09:2

9'1

9

時間

磁場

（Ｇ

）

外

内

山手線運休時間

今後の研究計画・F=2 Rb BECによる磁力計（バークレイはF=1）・F=1とF=2のスイッチング・フェッシュバッハ共鳴の磁力計への応用：磁場に敏感な現象・標準量子限界を超える感度：スピンスクイージング，光のスクイージング