Non-local exciton-Non-local exciton-polariton spin polariton spin

switchesswitchesLaboratoire Kastler Brossel,

Paris (experimental part) :

C. Adrados

R. Hivet

J. Lefrère

A. Amo

E. Giacobino and A. Bramati

University of Southampton :

A.V. Kavokin (theoretical part)

EPFL, Lausanne :

T.C.H. Liew (theoretical part)

R. Houdré (fabrication of the sample)

PLMCN 10, Cuernavaca, Mexique, avril 2010

Semiconductor Microcavities in strong coupling regime : POLARITONS, mixture of excitons and

photons.

Excitons :

High non-linearities at low thresholds due to the Coulomb interaction

Photons :

Propagate fast (~ 1% speed of light)

Short lifetime (a few ps)

All optical control :

… power of the incident beam : density of polaritons

… transverse direction of the incident beam : polaritons velocity

… polarization of the incident beam : polaritons spin state

+ reduced size of the system : integrability

Why the use of SC microcavities for all-optical spin switches ?

High repetition rateExciton switch with electrical

control : G. Grosso et al. Nature Photonics 3, 577–580 (2009)

Non linear transmission (theory) :

kp (μm-1)

A

A

off

All-optical switch

Excitation power P1< Pthreshold

Power dependence of the pump

Pthreshold

B

kp (μm-1)

B

on

Renormalization of the dispersion Renormalization of the dispersion curvecurve

Power dependence of the pump

All-optical switch

Excitation power P2> Pthreshold

Non linear transmission (theory) :

Pthreshold

Polariton switch configuration : the amount of power P2-P1 necessary to switch is added thanks to a small probe.

Cw pump (red) : big spot 60 μm (diameter)

Cw probe (blue) : small spot 6 μm (diameter)

Experimental set up

(d)

X

Y

Near field CCD

k

kz

k║

Microcavity sample

Pump + probe superposed, with same k

with incident in plane angle = 3.8°

Laser wavelength = 836.95 nm, blue detuned by 0.16 meV from blue detuned by 0.16 meV from the LPBthe LPB

Sub threshold cw pump laser, large

Very localized cw probe laser

Pump + probe : switch (renormalizationrenormalization) of the whole pump spot, induced by the

probe.

Pump (σ+) Probe (σ+) Pump+Probe

Detectionσ+

20 µm

Non local switch

Polariton flow

Polariton flow

Transmitted power : 9 mW

Transmitted power : 54 mW

Transmitted power : 3 mW

A off

B on

A

off

B

onPolariton density of the σ+pump vs excitation

power

PROBE

xE

nerg

y

PUMP

ELPB

ELaser

A

Bt=0 t=60 ps

Blueshift propagation

Non local switch

Non-local action :

The small probe switches on the pump polaritons of the arrival probe area.

vpolariton = hk///mpolariton= 0.94 μm/ps : propagation all over the pump beam.

Model :

x

Po

larit

on

s E

ne

rgy

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Non local switch

Polariton flow (pump and probe)

Propagation : we move the area of incidence of the probe, same k// for pump and probe, from left to right.

Exciton-Polariton Spin

Strong EXCHANGE INTERACTION (exchange of holes and electrons) between 2 excitons (Sz=±1) dressed with light

Ref : P.Renucci et al, PRB 72, 075317 (2005); C.Ciuti et al, PRB 58 p7926-7933 (1998); M.Wouters, PRB 76, 045319 (2007); M.Vladimirova et al, PRB 79, 115325 (2009); M.Combescot, PRB 74, 125316 (2006).

|g↑↑| >> |g↑↓|

With Interaction constant between polaritons with parallel spins g↑↑

Interaction constant between polaritons with antiparallel spins g↑↓

25 μm

pump σ + (no probe) probe σ + (no pump)

pump σ ++ probe σ + pump σ ++ probe σ -

FLOW

1

0

EX

PE

RIM

EN

T

pump σ ++ probe σ + pump σ ++ probe σ -T

HE

OR

Y1

0

A

B

g g

on

off

Spin selectivity

Pump σ+

Polariton density of the σ+pump vs excitation

power

>>

Solution of the Gross-Pitaevskii equation

Pump σ+

On

ly o

n t

he p

um

p

(zon

e w

ith

ou

t p

rob

e)

0 25 50 75 100 0 25 50 75 100

Em

itted

inte

nsity

(arb

. uni

ts)

X (m)

X (m)

4 4

0 2

TE TE

pump+probe

pump

probe

probe

detection

0

2

4

6-1

0

1

Em

itte

d in

ten

sity

(arb

. u

nits

)

+ emission - emission

c (

pro

be

)

(rad; ellipticity of the probe)

(a)

(b)

(c) (d)

0 25 50 75 100 0 25 50 75 100

Em

itted

inte

nsity

(arb

. uni

ts)

X (m)

X (m)

4 4

0 2

TE TE

pump+probe

pump

probe

probe

detection

0

2

4

6-1

0

1

Em

itte

d in

ten

sity

(arb

. u

nits

)

+ emission - emission

c (

pro

be

)

(rad; ellipticity of the probe)

(a)

(b)

(c) (d)

Ellipticity of the probe

σ+ σ-

σ+

Pump σ+ and probe

σ+ * Gain x6

* Propagation and spin dependence

Spin selectivitypump σ ++ probe σ + pump σ ++ probe σ - 1

0

Threshold in the ellipticity of the probe : minimum amount of σ+ required to switch on

the σ+ pump.

Polarization control

Linearly polarized pump

Spin dependent interaction

Final polarization: that of the probe A

B

on

off

g g

pump TE + probe σ +

25 μmFLOW

pump TE + probe σ +

det det det det

σ++σ -

1

0

EXPERIMENT

THEORY

σ+

>>

Polarization control

Linearly polarized pump

Spin dependent interaction

Final polarization: that of the probe A

B

on

off

g g

25 μmFLOW

det det det det

σ++σ -

1

0

EXPERIMENT

THEORY

σ -

pump TE + probe σ - pump TE + probe σ -

>>

TE TM

pump+probe

4 4

0 2

probe

pump TE

0.1 1 10 100

0

1

2

3

Em

itted

inte

nsity

(arb

. un

its)

Probe power (mW)

(rad; ellipticity of the emission)

probe

(a)

(b)

(c)

pump TE

pump+probe

emission

probe

0

1

2

0

1

2

Inte

grat

ed in

tens

ity (

arb.

uni

ts)

x4

x4

emission

TE TM

pump+probe

4 4

0 2

probe

pump TE

0.1 1 10 100

0

1

2

3

Em

itted

inte

nsity

(arb

. un

its)

Probe power (mW)

(rad; ellipticity of the emission)

probe

probe

(a)

(b)

(c)

pump TE

pump+probe

emission

probe

0

1

2

0

1

2

Inte

grat

ed in

tens

ity (

arb.

uni

ts)

x4

x4

emission

Pump TE (linear)

Polarization control

Detected Ellipticity

● Interaction between parallel spins >> interaction between opposed spins

Pump purely circular + probe : EXCLUSIVE SWITCH

Pump linearly polarized + probe : polarization CONTROL

● Non local action

● Low threshold : strong non-linearities and 5 ps polariton lifetime

we need low energy densities to induce the switch : 1-2 fJ/μm2 ,

2 orders of magnitude less than the state-of-the-art all optical spin switch.

● High potential repetition rate (for a 60 μm spot and a 3.8° incident angle) :

about 10 GHz

CONCLUSION spin switch at k≠0

Amo et al., Nature Photonics (DOI : 10.1038/NPHOTON.2010.79 )

Bistability at k// = 0

At normal incidence, we can observe a hysteresis cycle

(ref : A.Baas, PRB 70, 161307(R), 2004)

Transmission vs excitation power, pump only, circularly polarized

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

0 10 20 30 40 50 60 70

Excitation power mW

Tra

ns

mit

ted

inte

ns

ity

, arb

itra

ry u

nit

Transmission vs excitation power, pump only, circularly polarized

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

0 10 20 30 40 50 60 70

Excitation power mW

Tra

ns

mit

ted

inte

ns

ity

, arb

itra

ry u

nit

++

Switch off the probe

COPOLARIZED probepum

p

pump + probe : ON

Pump only : ON

Spin switch at k// = 0 with bistability

736 10800

● Exclusive switch : when the pump and the probe are crosspolarized, no switch.

● Propagation mecanism : diffusion of the polaritons (probe and pump) thanks to their Δk (around k=0).

To check in real time.

Spin switch at k// = 0 with bistability

Transmission vs excitation power, pump only, circularly polarized

0,00E+00

1,00E+07

2,00E+07

3,00E+07

4,00E+07

5,00E+07

6,00E+07

7,00E+07

0 10 20 30 40 50 60 70

Excitation power mW

Tra

nsm

itte

d in

ten

sity

, arb

itra

ry u

nit

Constructive interferencesDestructive

interferences

Excitation power

● How to switch off the pump thanks to the probe only ? By dephasing the probe with respect to the pump. Probe and Pump must have the SAME SIZE.

Spin switch at k// = 0 with bistability

Pump OFF state

Pump + probe : ON

Pump only : ON state

Switch off the probe

Add a probe (same size as pump) in phase with pump

Pump + probe out of phase

Ref : I.A.Shelykh et al, PRL 100, 116401 (2008)

CONCLUSION spin switch at k=0

● We have one bit : we can go from 1 state to the other by tuning an external probe (perturbation), and the bit keeps the memory of the perturbation.

● Also here, we have a high speed of switch : when pump and probe with the same size, it is given by the polariton lifetime (ps range), repetition rate of about 1 THz.

● Very low thresholds (strong non-linearities thanks to the excitonic part of the polaritons)