Condensation of Excitons in a Trap

Alex High, Jason Leonard, Mikas Remeika, & Leonid Butov

University of California at San Diego

Micah Hanson & Art Gossard University of California at Santa Barbara

50 m

K

4 K

30 m

T=7 K

I (arb. units) 10

Emission of Excitons in the Trap

0 7 140.0

0.3

0.6

Inte

rfer

ence

vis

ibili

tyShift x ( m)

50 mK 2 K 4 K 8 K

Coherence of Excitons in the Trap

• Traps are critical for studies of atomic condensates

→ atomic BEC

• Traps for excitons can be created through customized external potentials

goal → exciton condensation in a trap

MH Anderson, JR Ensher, MR Matthews, CE Wieman, EA Cornell, Science 269, 198 (1995)

CC Bradley, CA Sackett, JJ Tollett, RG Hulet, PRL 75, 1687 (1995)

KB Davis, MO Mewes, MR Andrews, NJ van Druten, DS Durfee, DM Kurn, W. Ketterle, PRL 75, 3969 (1995)

Traps in Low Temperature Physics

• An indirect exciton is composed of an electron and hole in separate quantum wells

An Introduction to Indirect Excitons

Characteristics of indirect excitons•bosons•long lifetime

Model system for studies of physics of ultracold bosons in CM materials

•electronically controllable

QM1G.7: Yuliya KuznetsovaTransport of Indirect Excitons in a

Potential Energy GradientMonday, 9:45 AM

QM2G.7: Mikas RemeikaElectrostatic Lattices for Indirect

Excitons in Coupled Quantum WellsMonday, 12:15 PM

QTh4E.4: Alex HighSpontaneous Coherence in

a Cold Exciton GasThursday, 5:15 PM

﹚• “Quantum gas” when thermal de Broglie wavelength

comparable to separation between excitons

• Excitons in GaAs CQW: n = 1010 cm-2, mexciton = 0.2 m0

Onset of Quantum Degeneracy

TdB ~ 3 KTX

Time (ns)

• Excitons can cool to 100mK within lifetime

L.V. Butov, A.L. Ivanov, A. Imamoglu, P.B. Littlewood, A.A. Shashkin, V.T. Dolgopolov, K.L. Campman, and A.C. Gossard, PRL 86, 5608 (2001)

λdB = n-1/2 TdB = mkB2πħ2 n

λdB = mkBT2πħ2﹙ 1/2

+–

+–

+–

Vg

zx

y

Electronic Control of Excitons

Customized electrode design creates desired potential landscape

Electrode Voltage Vg

Exci

ton

Ener

gy (e

V)

δE=eFzd

Indirect excitons are dipoles with energy controlled by electrode potential

-5 01.52

1.56

-2.5

more info: physics.ucsd.edu/~lvbutov

lattices

rampstraps

transistors

conveyers

circuits

The Diamond Trap

Parabolic-like potential along both x- and y-axis

A. A. High, A. K. Thomas, G. Grosso, M. Remeika, A. T. Hammack, A. D. Meyertholen, M. M. Fogler, L. V. Butov, M. Hanson, and A. C. Gossard, PRL 103, 087403 (2009).

-10 0 10 y (µm)

a b

x (µm)

h

0

E (

meV

)

5

e

z

Ex

10 m

y

-5 0 5

-10 0 10-10

0

E (m

eV)

x (µµµµm)10

e

h

xz

zE

xy

xy

e

c

electrode geometry

simulated potential-10 0 10

-10

0

E (m

eV)

x (µµµµm)10

e

h

xz

zE

xy

xy

e

c

xz

xy

Vg

Diamond Trap Characterization

• In situ control• Parabolic-like potential• Collection to trap center

simulated potential

-20 0 20

-10

0

0

1

-2 -3-10

-5

0

Tra

p D

epth

(meV

)

T r ap V oltage (V )

5 ! m

0

1

a

h1550

1545

1540

0

-10

r

-20 0 20 -20 0 20

-10

-100

-20 0 20

-10

0

0

1

-2 -3-10

-5

0

Tra

p D

epth

(meV

)

T r ap V oltage (V )

5 ! m

0

1

a

h1550

1545

1540

0

-10r

-20 0 20 -20 0 20

-10

-100

-20 0 20

-10

0

0

1

-2 -3-10

-5

0

Tra

p D

epth

(meV

)

T r ap V oltage (V )

5 ! m

0

1

a

h1550

1545

1540

0

-10r

-20 0 20 -20 0 20

-10

-100

x-y emission

x-Energy emission

Trap OFF Trap ON

10

0

10

-10

0

-20 200x (μm)

-20 200

y (μm

)

x (μm)

1540

1545

1550

ener

gy (m

eV)

ener

gy (m

eV)

Remote Excitation Schematic

• Excitons are created 6μm from trap center

-10 0 10 y (µm)

a b

c

x (µm)

h

0

E (m

eV)

5

e

zE

Laser excitation

x

10 µm

y

-5 0 5

d

-15 0 15

d

c 5

E (m

eV)

x (µm)

laser excitation

0

zE

sample inside dilution refridgerator

movable stage

CCDspectrometer Beam

Splitter

Mirror 1

Mirror 2

BeamSplitter

Arm 1

Arm 2

HeNeLaser

IF

sample inside dilution refridgerator

movable stage

CCDspectrometer Beam

Splitter

Mirror 1

Mirror 2

BeamSplitter

Arm 1

Arm 2

HeNeLaser

IF

b 10 µm

xy

-404-15 0 15

e I1 (arb. units)

x (µm)

y (µ

m)

-15 0 15

h

I12

(arb. units)f

x (µm)

ae

1

0

emission

• Remote excitation reduces laser heating at the trap center

-10 0 10 y (µm)

a b

c

x (µm)

h

0 E

(meV

)

5

e

zE

Laser excitation

x

10 µm

y

-5 0 5

d

50 m

K

4 K

30 m

T=7 K

I (arb. units)

10

Emission of Excitons in the Trap

0 7 140.0

0.3

0.6

Inte

rfer

ence

vis

ibili

ty

Shift x ( m)

50 mK 2 K 4 K 8 K

Coherence of Excitons in the TrapEmission of Excitons in the Trap

Sharp peak at trap center emerges with decreasing temperature

Coherence Measurements with M-Z interferometer

Shift interferometry measures the first-order spatial coherence function

40

-4

S ampleDetector y

(µm

)

x = 4µm

I2

40

-4-10 0 10

I1

x (µm)

y (µ

m)

I12

-10 0 10

I inte

rf

x (µm)

+0.4

-0.4

1

Em

issi

on(a

rb. u

nits

)

0

Iinterf vs. δx → g1(x)

Coherence Measurements: Temperature Dependence

• Excitons condense at the trap bottom• Exciton spontaneous coherence emerges with lowering temperature

0 2 4 6 8

0.07

0.15

0.22

0.29

0.36

0.44

1

2

3

4

5

6

-10 0 100

1

-4 0 40

1-4 40

1

Inte

rfere

nce

visi

bilit

yat

shi

ft !x

= 4"m

HW

HM

of e

xcito

n cl

oud

(µm

)

T (K)-10 0 10

x (µm)-10 0 10

0

0

0

0

0

0

0

y

1K

7K

x (µm)

6K

5K

4K

3K

2K

10 µ

m

Tbath= 50mK

0

f

ca

Em

issi

on (a

rb. u

nits

)

x (µm)

Tbath

= 50mK 3K 7K

bI1 (arb. units)10

I12 (arb. units)1.30

e

y (µm)

d

-10 0 10 y (µm)

a b

c

x (µm)

h

0

E (m

eV)

5

e

zE

Laser excitation

x

10 µm

y

-5 0 5

d

Coherence Measurements: Density Dependence

• Asymmetry in coherence due to laser heating

• Peak in coherence corresponds to minimum exciton cloud width

laser excitation(weak coherence)

cold excitons(strong coherence)

0.1

0.2

0.3

0.4

1 10 100

2

4

6

-6 -3 0 3 6 9 120.0

0.2

0.4

0.6

Tbath= 50mK 4.5K

Inte

rfere

nce

visi

bilit

yat

shi

ft !x

= 4"m

Tbath= 50 mK 4.5K

HW

HM

of e

xcito

n cl

oud

(µm

)

Pex (µW)

c

b

Inte

rfere

nce

visi

bilit

yshift !x (µm)

Pex = 0.31 µW 2.2 µW 88 µW

a

0.1

0.2

0.3

0.4

1 10 100

2

4

6

-6 -3 0 3 6 9 120.0

0.2

0.4

0.6

50 mK 4.5 K

Inte

rfere

nce

visi

bilit

yat

shi

ft !x

= 4"m

HW

HM

of e

xcito

ncl

oud

(µm

)

Pex (µW)

c

b

Inte

rfere

nce

visi

bilit

y

Shift !x (µm)

0.31 µW 2.2 µW 88 µW

a

• Non-monotonic dependence on density at 50mK

Coherence Measurements: g1(x) vs. T

0 2 4 6 8 10 12 140.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 4 82

4

6In

terfe

renc

e vi

sibi

lity

shift !x (µm)

Tbath= 50mK 2K 4K 8K

a b

!"(µm)

T (K)

Coherence extends over entire cloud at Tbath=50mK

0 7 140.0

0.3

0.6

0 4 82

4

6

-2 0 2

-0.2

0.0

0.2

Inte

rfer

ence

vis

ibili

ty

Shift !x (µm)

50 mK 2 K 4 K 8 K

a

c

!"(µ

m)

T (K)

8K

b

I inte

rf at #

x=7µ

m

y (µm)

50mK

0

1

2

3

4

5

6

0 2 4 6 8

ξ (µ

m)

Temperature (K)

0

1

2

3

4

5

6

0 2 4 6 8

ξ (µ

m)

Temperature (K)

F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)

Tc≈2K

M. Remeika, J.C. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 102, 186803 (2009)

Estimate of transition temperature

ΔE = 1.3meV → N = 3000

ξexperimental ξclassical

(λdB / π1/2)

ξexperimental vs. T corrected for optical spatial resolution

Coherence Length vs. T

ωx ~ 4 × 109 s-1 ωy ~ 3 × 1010 s-1Trap Frequency:Number of Excitons:

Tc = ﹙﹚gN 1/2π61/2 ħω2D ω2D = (ωx ωy)1/2BEC temperature in a 2-D harmonic trap:

Conclusions

Observed condensation of excitons in a trap

• Excitons condense at the trap bottom• Exciton spontaneous coherence emerges with

lowering temperature

• Below a temperature of about 1 K coherence extends over the entire trapped cloud

A. A. High, J. R. Leonard, M. Remeika, L. V. Butov, M. Hanson, A. C. Gossard, Condensation of Excitons in a Trap, arXiv:1110.1337, Nano Lett. DOI: 10.1021/nl300983n (17 April 2012)