Ite A. Yu

Experimental Demonstration of

Spinor Slow Light

Department of Physics

Frontier Research Center on Fundamental & Applied

Sciences of Matters

National Tsing Hua University

Taiwan

Motivation

Photons: ultimate speed, inert to the environment, no

collision with each other Ideal carriers for quantum

information.

Quantum information wave function.

One qubit = single photon, so qubit-qubit operation or

photon-photon interaction: nonlinear optical process.

Nonlinear efficiency = (transition rate) (interaction time),

but transition rate light intensity and is usually very low

at single-photon level (10 W 1020 photons/second).

Slowing or stopping light can greatly enhance the

interaction time A sufficient nonlinear efficiency can be

achieved even at single-photon level.

Experimental setup

Electromagnetically induced transparency,

slow light & stopped light

Quantum memory & low-light-level nonlinear

optics

Outline

Double tripod (DT) scheme & two-component or spinor

slow light (SSL)

Oscillation between the two components & the SSL

interferometer

SSL qubits and DT scheme as quantum memory/rotator

Conclusion

Experimental System of Cold Atoms

We produce 109 atoms with a temperature of 300 K with a magneto-

optical trap (MOT).

Coherence time (coh) ~ 100 s & optical density (OD) ~ 200, where OD

is defined by Iout = Iin e-OD.

F' = 3

F = 2

Trapping

1 0

1

|5P3/2

|5S1/2

2

Coupling

Probe Repumping

Coupling

Laser

Probe

Laser

PD T

T

T

T

T

T

y

x

Quadrupole

Magnet

Quadrupole

Magnet

T: trapping laser beams

z

PD

87Rb

NTHU Optical Jungle

8 diode lasers; MOPA; UHV system; > 300 optical components

simple physics system; complicate experimental setup

Magneto-Optical Trap

1mm

0

1 1mm

0

1

Dimension: 9.21.81.8 mm3

The Phenomenon of

Electromagnetically Induced Transparency (EIT)

probe laser

probe laser coupling laser

atoms

atoms

|1

|3

Probe

Coupling

|1 |2

|3

Probe

Large Optical Density (OD)

Transmission

= e-200 10-87!!!

Transmission

1

OD = 7

<<

Near the resonance, OD = 7 and probe transmission is e-7 (less than 0.1%).

Transmission is nearly 100% at the resonance and the transparency window

is much narrower than the natural linewidth, .

Narrow & high-contrast absorption profile. => large dispersion => slow

group velocity.

Y. F. Chen, Y. C. Liu, Z. H. Tsai, S. H. Wang, & IAY, PRA 72, 033812 (2005).

Probe

|1 |2

|3

Coupling

Narrow and High-Contrast EIT Spectrum

OD = 7

<<

Near the resonance, OD = 7 and probe transmission is e-7 (less than 0.1%).

Transmission is nearly 100% at the resonance and the transparency window

is much narrower than the natural linewidth, .

Narrow & high-contrast absorption profile. => large dispersion => slow

group velocity.

Y. F. Chen, Y. C. Liu, Z. H. Tsai, S. H. Wang, & IAY, PRA 72, 033812 (2005).

Transmission10%

@ detuning=5

C. C. Lin, M. C. Wu, B. W. Shiau, Y. H.

Chen, IAY, Y. F. Chen, & Y. C. Chen,

PRA 86, 063836 (2012).

e-228 10-99

Probe

|1 |2

|3

Coupling

Narrow and High-Contrast EIT Spectrum

Slow Light and Stopped Light

In the constant presence of the coupling, speed of the light pulse c/105.

The 1 km-long probe pulse is compressed to 1 cm inside the atoms.

The gap of ~ 4 s in the probe signal demonstrates the light storage.

Delay Time ~ 3.5 s

Storage Time ~ 4 s

0.0

0.5

1.0

0 2 4 6 8 10 12 14

0.0

0.5

1.0

OD = 147

c = 1.15

= 5.5*10-4

QE = 69%

Pro

be

Tra

nsm

issi

on

Time (s)

Input

Pulse

Output Pulse

Coupling Field

in = 1.24s

Input

Probe

|1 |2

|3

Writing

Coupling

|1 |2

Output

Probe

|1 |2

|3

Reading

Coupling

two-photon

Raman transition

atomic wave function: ground-state

(Raman) coherence or spin excitation

The EIT storage is a coherent process and provides a method for exchange

of wave functions between photons and atoms.

Coherent Storage for Photons

reversed two-photon

Raman transition

(a)

High Storage Efficiency and Large Delay-Bandwidth Product Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, & IAY,

PRL 110, 083601 (2013).

(b) DBP = 74

Optimal pulse shape & backward retrieval to enhance SE.

We report a EIT memory with storage efficiency of 78%, delay-bandwidth

product of 74 at SE = 50%, and fidelity 0.9.

DBP tstorage

tpulse

Fidelity 𝜓out 𝜓in

2

𝜓in 𝜓in 𝜓out 𝜓out

SE 𝐸out

𝐸in

100 ns

Reference Write-in

Read-out

(c)

Time (s)

Beat-Note Interferometer Data

|4

|3

|2

|1

Ground-State Coherence

Probe Writing

c p

Storage

Signal

Phase Modulation

Probe

c p

Retrieval

Reading

Low-Light-Level Nonlinear Optics Cross-Phase Modulation (XPM) based on Stored Light

Y. F. Chen, C. Y. Wang, S. H. Wang, & IAY, PRL 96, 043603 (2006).

The stored ground-state coherence is equivalent to the probe pulse.

Single-photon XPM or AOS: quantum phase gates, entangled photon pairs,

quantum nondemolition measurements.

XPM: a phase shift of 44 is obtained at 18 photons per atomic absorption

cross section. How to further improve?

|4

|3

|2

|1

Ground-State Coherence

Probe Writing

c p

Storage

Signal

Phase Modulation

Probe

c p

Retrieval

Reading

Low-Light-Level Nonlinear Optics Cross-Phase Modulation (XPM) based on Stored Light

Y. F. Chen, C. Y. Wang, S. H. Wang, & IAY, PRL 96, 043603 (2006).

The stored ground-state coherence is equivalent to the probe pulse.

Single-photon XPM or AOS: quantum phase gates, entangled photon pairs,

quantum nondemolition measurements.

XPM: a phase shift of 44 is obtained at 18 photons per atomic absorption

cross section. How to further improve?

|4

|3

|2

|1

Ground-State Coherence

Signal

Amplitude Modulation

Probe

c p Reading

Retrieval

All-Optical Switching (AOS) = 0

30 50 70 90 110 1300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

(a)

D2

SLP (

s)

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5

Rem

aini

ng E

nerg

y

(arb

. uni

ts)

SLP Duration (s)

40 60 80 100 1200.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0(b)

D2OD

two stopped pulses

All-Optical Switching with Stopped Light Pulses

Y. H. Chen, M.J . Lee, W. Hung, Y. C. Chen, Y. F. Chen, & IAY, PRL 108, 173603 (2012).

Switching Ratio = exp[(N/A)]

The interaction time can be, in principle, as long as possible.

With stopped light pulses, 1.8 or the switch was achieved at 0.56

photons per atomic absorption cross section 4-fold improvement.

Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W. Cho, P. C. Kuan, & IAY, PRL 102, 213601 (2009).

0 20 40 60 80 1000.0

0.1

0.2

0.3

0.4

0.5 (b)

D1

/ (c)

20.0 0.5 1.0 1.5 2.0

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0(a)

R

(N/A)a

two moving pulses

OD

Frozen “light switch” “Frozen light” switch

Nature Physics, April 2012, p. 252.

Stopping light

pulses and making

them interact in a

medium is a way to

get more for less.

Summary of EIT, Slow Light and Stopped Light

However, previous experiments all dealt with single-component slow

light.

Acknowledgments for collaborators:

Prof. Yong-Fan Chen (PHYS, NCKU)

Dr. Ying-Cheng Chen (IAMS, AS)

The EIT/slow light effect enhances the

light-matter interaction and achieves

significant nonlinear optical efficiency

even at single-photon level.

EIT-based storage of light transfers

quantum states between photons and

atoms, making quantum memory

feasible.

30 50 70 90 110 1300.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

(a)

D2

SLP (

s)

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5

Rem

aini

ng E

nerg

y

(arb

. uni

ts)

SLP Duration (s)

40 60 80 100 1200.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0(b)

D2OD

Neil

HWC

Acknowledgments

Collaboration Projects:

Taiwan-Latvia-Lithuania

&

EU FP7 COLIMA

Theory: Vilnius U.

Gediminas Juzeliūnas

Julius Ruseckas

Viačeslav Kudriašov

Experiment: Nat’l

Tsing Hua U.

Dr. Meng-Jung Lee

Neil Lee

Kao-Fang Chang

Dr. Hung-Wen Cho

MJL GJ KFC

$$$ MOST $$$ $$$ NTHU Top-Notch $$$

Double Tripod System

Spinor (Two-Component)

Slow Light

|1 |2

|A

A2

|0

A1

|B

A

B

B2 B1

𝜀𝐴,𝑜𝑢𝑡

𝜀𝐵,𝑜𝑢𝑡 = 𝑒−(2𝜙2/OD) cos 𝜙 − sin 𝜙

sin 𝜙 cos 𝜙

𝜀𝐴,𝑖𝑛

𝜀𝐵,𝑖𝑛, 𝜙 =

OD Γ2Ω2

A1 = A2 = B1 = B2 ,

10

|1 |2

A2

|0

|A

A1

|B

A

B2 B1

B

Three atomic ground states coupled to two excited states by 4 coupling

fields A1, A2, B1 & B2 and 2 probe fields A & B.

δ

|A

A

|1 |0

|2

|B

|0

B 𝟐 𝟐

DT Two Coupled EITs

Transition Scheme

|2 |5S1/2,F=1,m=0

|1 |5S1/2,F=2,m=0

|0 |5S1/2,F=2,m=2

|B |5P3/2,F= 2,m=1

δ

δ

A B

A2 A1

B2 B1

780nm

795nm

6.8

GHz

|A |5P1/2,F= 2,m=1

Optically pump all population to a single Zeeman state A simple

5-level DT system.

of the probe field A and the coupling fields A1 & A2 is ~ 795 nm.

of the probe field B and the coupling fields B1 & B2 is ~ 780 nm.

Experimental Scheme

Adjust the position of a prism to make four coupling fields in phase.

Overlap all coupling fields as they interact with the atoms.

= 0

/(2) = -160 kHz

Output probe A (red) & probe B (blue)

as functions of detuning:

-600 -400 -200 0 200 400 600

0.0

0.2

0.4

0.6

0.8

Ene

rgy

Tra

nsm

issi

on

(kHz)/(2) (kHz)

𝜀𝐴,𝑜𝑢𝑡

𝜀𝐵,𝑜𝑢𝑡 = 𝑒−(2𝜙2/OD) cos 𝜙 − sin 𝜙

sin 𝜙 cos 𝜙10

,

Oscillation between the Two Components

|𝜀𝐴,𝑜𝑢𝑡|2

𝜀𝐵,𝑜𝑢𝑡2 = 𝑒−(4𝜙2/OD) cos2 𝜙

sin2 𝜙,

where 𝜙 = OD Γ2Ω2 .

Stored Spinor Slow Light

where 𝜙 = OD Γ2Ω2 .

𝜀𝐴,𝑜𝑢𝑡

𝜀𝐵,𝑜𝑢𝑡 = 𝑒−(2𝜙2/OD) cos 𝜙 − sin 𝜙

sin 𝜙 cos 𝜙10

,

OD Γ/(22) is the delay time of slow light propagation, i.e. 𝜙 = 𝑑.

Can 𝒅 be replaced by 𝒔 (storage time)?

Large phase

change

& little decay

Phase-sensitive

detector

or interferometer

s = 15 s

/(2) (kHz)

Interferometer based on Stored Spinor Slow Light

𝝓 = 𝒔: fix and vary s (the storage time).

Set 2 /(2) = 20.0 kHz Set 1/(2) = 10.0 kHz

Measured 2 - 1 = 9.7 kHz

|1 |2

A2

|0

|A

A1

|B

B2 B1

|1 |2

A2

|0

|A

A1

|B

A

B2 B1

|1 |2 |0

|A

|B

|1 |2

A2

|0

|A

A1

|B

B2 B1

B

|1 |2

A2

|0

|A

A1

|B

B2 B1 A

|1 |2

A2

|0

|A

A1

|B

B2 B1

B

A

A storage time ~ O(100s) results

in a precision ~ O(100Hz).

The SSL interferometer can be

used to detect two-photon

detuning, Zeeman shift, AC Stark

shift, etc.

SSL as a Two-Color Qubit

/(2) (kHz)

Frequency-Domain Measurement

Ramsey Fringe

Single-photon SSL is a qubit with the superposition state of two frequency

modes. ( ,) = (cos, sin) and where 𝜙 = 𝑠.

In long-distance quantum communication, photons of two-color quantum

states are inert to the birefringent material, i.e. optical fibers.

| = |1A, 0B

+ | 0A, 1B

Time-Domain Measurement

s (s)

Rabi Oscillation

Quantum Memory for SSL or Two-Color Qubits

| = |1A, 0B

+ | 0A, 1B

= 0

|1 |2 |0

|A

A

|B

B

B

A

|0

|/|2 = 0.5 |/|2 = 1 |/|2 = 2

The shapes of the two retrieved pulses and their energy ratio after the storage

time of 3 s are very close to those after the storage time of 33 s.

3 s 33 s

Quantum Rotator for SSL Qubits

| = |1A, 0B

+ | 0A, 1B

|1 |2

A2

|0

|A

A1

|B = 0

B2 B1

B

|1 |2 |0

|A

|B

0

|1 |2

A2

|0

|A

A1

|B = 0

B2 B1 A

(,) = (1,0)

(0,1)

or

(cos,sin) where 𝜙 = 𝑠

s = 15 s

One can utilize a two-photon detuning (induced by the Zeeman or AC Stark

shift) applied during the storage to change the -to- ratio.

Nonlinear Frequency Conversion

𝜀𝐴,𝑜𝑢𝑡

𝜀𝐵,𝑜𝑢𝑡 = 𝑒−(2𝜙2/OD)

cos 𝜙 − sin 𝜙sin 𝜙 cos 𝜙

10

|𝜀𝐵,𝑜𝑢𝑡|2

|𝜀𝐴,𝑖𝑛|2 = 𝑒−(4𝜙2/OD) sin2 𝜙

Widely-Used Double- Scheme

At = /2,

|𝜀𝐵,𝑜𝑢𝑡|2

|𝜀𝐴,𝑖𝑛|2

= 𝑒−(2/OD)

|B,out|2 / |A,in|2

OD

0.9

OD = 190

|1

|0

|A

A

|B

A

B B

opt

0.9 = 𝑒−(2/OD) OD = 94

𝜀𝐴 − Ω𝐴 + Ω𝐵 𝜀𝐵

Double-Tripod Scheme

𝜀𝐴 − Ω𝐴1 + Ω𝐵1 𝜀𝐵 𝜀𝐴 − Ω𝐴2 + Ω𝐵2 𝜀𝐵

Better!

Conclusion

We report the first experimental demonstration of two-

component or spinor slow light (SSL).

In a proof-of-principle measurement, our data show that the

stored SSL behaves like an interferometer for precise

frequency determination.

The double tripod scheme can lead to quantum memory for

the two-color qubit, i.e. the superposition state of two

frequency modes.

In the nonlinear frequency conversion, the SSL is a better

method than the widely-used double- scheme.

1. M. J. Lee, J. Ruseckas, C. Y. Lee, V. Kudriasov, K. F. Chang, H. W. Cho, G.

Juzeliunas, & IAY, Nature Commun. 5, 5542 (2014).

2. 吳京，「唱反調的一對光」，泛科網 http://pansci.tw/archives/73825。

Thank you for your attention.

http://atomcool.phys.nthu.edu.tw/

contact: yu@phys.nthu.edu.tw

Postdoc Position Available

in the Rydberg EIT Experiment